Sofistik help.pdf

SOFiMSHC

Geometric Modelling

Version 12.01

This manual is protected by copyright laws. No part of it may be translated, copied or reproduced, in any form or by any means, without written permission from SOFiSTiK AG. SOFiSTiK reserves the right to modify or to release new editions of this manual.

The manual and the program have been thoroughly checked for errors. However, SOFiSTiK does not claim that either one is completely error free. Errors and omissions are corrected as soon as they are detected.

The user of the program is solely responsible for the applications. We strongly encourage the user to test the correctness of all calculations at least by random sampling.

1 General. . . . . 1−1 2 Theoretical background . . . . 2−1

2.1. Coordinate systems . . . 2−1 2.2. Curves and alignment axes . . . 2−2 2.2.1. Alignment axes . . . 2−3 2.2.2. Freeform curves . . . 2−4 2.3. Regions and geometric surfaces . . . 2−5 2.3.1. Rotational and sweep surfaces . . . 2−6 2.4. Structural elements . . . 2−6 2.5. Mesh generation. . . 2−7 2.6. Literature . . . 2−7 2.7. Limitations . . . 2−8

3 General program control . . . . 3−1

3.1. Input language . . . 3−1 3.2. Units . . . 3−1 3.3. Remarks for the conversion from SOFiMSHB . . . 3−1 3.4. Input records . . . 3−2 3.5. SYST − Global system definition . . . 3−4 3.6. CTRL − Control of analysis. . . 3−7 3.6.1. Analysis and generation of structural model. . . 3−8 3.6.2. Geometry healing . . . 3−10 3.6.3. Meshing control . . . 3−11 3.6.4. Element generation and boundary conditions . . . 3−12 3.6.5. Mesh decomposition and band−width optimization . . . 3−13 3.6.6. Warnings and error messages . . . 3−14 3.7. GRP − Group control . . . 3−15 3.7.1. Primary group number . . . 3−15 3.7.2. Secondary groups. . . 3−16 3.8. IMPO − Import of data . . . 3−18 3.9. EXPO − ANSI export of data . . . 3−19 3.10. ECHO − Control of output . . . 3−20 3.11. COOR − User defined coordinate system . . . 3−21 3.12. XSUB − Extraction of subsystems . . . 3−24

4 Definition of geometric elements. . . . . 4−1

4.1. Input records . . . 4−1 4.2. GAX − Geometric curve or axis . . . 4−2 4.3. GAXA − Axis plan view . . . 4−4

4.4. GAXH − Axis heights . . . 4−7 4.5. GAXB − Straights and circular arcs in 3D . . . 4−8 4.6. GAXC − 3D curve point data . . . 4−10 4.7. GAXN − Knot value of a NURBS−curve . . . 4−12 4.8. GAXP − Axis placements . . . 4−13 4.9. GAXS − Secondary axis . . . 4−16 4.10. GAXV − Variables along axis . . . 4−17 4.11. GAR − Geometric surface. . . 4−19 4.12. GARA − Plane, rotational and sweep surfaces . . . 4−20 4.13. GARC − Coons surface . . . 4−22 4.14. GARS − Area by points . . . 4−23

5 Definition of structural elements. . . . . 5−1

5.1. Input Records . . . 5−1 5.2. SPT − Structural point . . . 5−3 5.3. SPTP − Structural point properties . . . 5−7 5.4. SPTS − Spring element at point . . . 5−14 5.5. SPTH − Halfspace pile at point . . . 5−18 5.6. SLN − Structural line . . . 5−19 5.7. SLNB − Straights and circular arcs . . . 5−24 5.8. SLNP − 3D curve point data . . . 5−25 5.9. SLNN − Knot value of a NURBS−curve . . . 5−27 5.10. SLNS − Supports and kinematic couplings on a SLN . . . 5−28 5.10.1. Supports and coupling conditions . . . 5−29 5.10.2. Elastic beddings and spring elements . . . 5−30 5.10.3. Interface−elements. . . 5−32 5.11. SAR − Structural area . . . 5−33 5.12. SARB − Structural area boundaries and constraints . . . 5−38 5.13. SARR − Rotational and sweep surfaces . . . 5−40 5.14. SARP − 3D Surface data point . . . 5−42 5.15. SARN − Knot value of a NURBS surface . . . 5−44 5.16. SARC − Coons−Patch surfaces . . . 5−45 5.17. SVO − Structural volume . . . 5−46 5.18. SVOS − Structrual volume faces . . . 5−47 5.19. GUID − Globally Unique Identifier . . . 5−49 5.20. BBOX − Bounding box . . . 5−50

1

General

.

SOFiMSHC is a tool for creating and processing geometric models and finite ele-ment structures. SOFiMSHC can be used as stand−alone program within Teddy and is integrated as geometry processing module in the SOFiSTiK programs SOFiPLUS, Extensions for Revit and Rhinoceros Interface.

Basis and starting point of SOFiMSHC is an abstract structural model similar to a CAD model which includes all relevant geometric and structural information ne-cessary for describing a calculation model. After this model is read from database or entered by the user via CADINP, SOFiMSHC analyzes and processes it and creates as result a finite element mesh consisting of beam, area and/or volume elements. In addition to classical building structures, SOFiMSHC also provides a rich set of input facilities for the definition of alignment axes and bridge systems. SOFiMSHC basically differentiates between geometric entities carrying geo-metry related data and structural elements containing all further information needed for definining a calculation model. As for the geometric entities following types are supported:

Geometric axes:

− straight lines

− circles and circular arcs in space

− alignment axes for road design defined separately in plan view and elevation

− polygonal lines

− cubically interpolating splines

− Hermite interpolation with defined tangents

− arbitrary NURBS curves (Non Uniform Rational B−Splines)

Geometric surfaces:

− flat surfaces

− surfaces of revolution − sweep surfaces

− bicubically interpolating surfaces − arbitrary NURBS surfaces

The basic geometric elements are usually defined independently from the overall structural model and should be used in as comprehensive units as possible. A bridge with multiple spans, for example, can be defined with one single axis along its whole length. The individual spans and all additional superstructures,

however, are modeled with structural elements which inherit their geometry from the underlying axis definition. Once the geometry is changed the structural sys-tem will be automatically readjusted.

The static system itself with all mutual topological relationships comprises the fol-lowing set of basic structural elements:

Structural Points are defined at a specific position in space and may have

Column Heads, Punching periphery and haunches assigned as structural properties.

Structural Lines connect two structural points and may have a geometric

curve assigned. Structural data includes supports and section definitions, for example.

Structural Regions are defined by a closed set of inner and outer

bound-ary curves and may also have a geometric surface description assigned. Structural properties contain thickness, element formulation etc.

Structural Volumes are defined by a set of enclosing structural regions

and can be meshed either unstructured with tetrahedral elements or struc-tured by extrusion or rotation with hexahedral elements.

A number of possibilities are provided within the SOFiSTiK program environment, to access and define the input of SOFiMSHC:

• Definition using CADINP−ASCII−Files (Teddy + SOFiMSHC) • Input of structural systems using SOFiPLUS (AutoCAD)

• Transfer of models from Autodesk Revit Structural (SOFiSTiK Extensions for Revit)

• Modeling in McNeel Rhinoceros (SOFiSTiK Rhinoceros Interface)

• Interface to the CDBASE for third party developers and for the import of building information models (e.g. IFC).

SOFiMSHC is both used as stand−alone batch program and as backend module in the above mentioned CAD−programs. It contains interfaces to mesh−generat-ors from the University of Munich (DOMESH) and the University of Linz (NET-GEN) and to mesh−partitioning software (METIS).

2

Theoretical background

2.1.

Coordinate systems

Global as well as local coordinate systems are described in SOFiMSHC as carte-sian right−handed system X−Y−Z. Rotations are applied in a mathematical posi-tive sense. Within record SYST a global gravity direction can be specified at parameter GDIR. This global gravity or ’downward’ direction affects the default orientation of loads, supports and other geometric attributes of structural items within the model if not specified differently at the respective location.

Z

Y

X

Phi

If the observer is looking from the birds eye view he will believe to see a right or left handed 2D coordinate system depending on the orientation of the vertical axis . We use the designation of the “first” and the “second” horizontal axis in the counter clock wise orientation.

Each geometric or structural object in SOFiMSHC possesses a local orientation or a local coordinate system, which affects the direction of loads, cross−sections or support conditions:

• Points, for example, have a local coordinate system which defines primar-ily the local direction of supports and kinematic couplings. If no coordinate system is given explicitly the local z−direction defaults to the globally de-fined gravity direction or, if the point lies within a region or on a structural line, to the local coordinate system defined there.

• For structural lines, up to three different local coordinate systems can be identified. A first coordinate system is related to the underlying geometric curve and is primarily used to define the orientation of circular arcs or alignment axes. On the structural line, an independant coordinate system can be defined which sets the orientation of cross−sections and beam elements. A third coordinate system may be specified in order to set the local direction of supports, springs or kinematic couplings connected to a

line. If one of the three mentioned directions is not explicitly set by the user, it defaults to the previously defined system. If no coordinate system is de-fined at all, the global gravity direction is used.

The local coordinate system of a structural line is normally specified by the user by setting the direction of the local z−axis. As the local x−axis always points into the direction of the curve tangent, the local y−axis is defined automatically.

• Geometric surfaces and structural regions have a local coordinate system assigned which normally varies within the surface for curved shapes. The z−axis of the coordinate system always remains perpendicular on the surface. The coordinate system of a structural region defines, for example, the clock−order of outer boundary edges and the local orientation of the quadrilateral finite elements created on the surface.

• For volumes there might be a direction of orthotopic material properties, but there is no local coordinate system. However all surfaces describing the volume will have a unique interior and exterior side. Thus a separating surface between two volumes will have a different orientation for the two cases.

2.2.

Curves and alignment axes

Curves in SOFiMSHC are defined as parameter curves in three dimensional space. Parameter curves are basically defined by a local parameter s which runs along the curve from its start to its endpoint. A ’curve function’ c(s) maps this local parameter s to global xyz−coordinates and therefore describes the curve in space when s is changed from smin to smax:

s Ê c

³

(s) +

ȧȧ

ȱ

Ȳ

x(s)

y(s)

z(s)

ȧȧ

ȳ

ȴ

s + [s

min

,s

max

]

, (1)

Apart from its shape other parameters might also be specified along a given curve as a function of s, like for example the orientation, the size or the shape of varying cross−sections. SOFiMSHC also allows to define so−called secondary lines, which are connected to a basis curve and whose distance is defined as a function of s.

2.2.1.

Alignment axes

As a special type of curve SOFiMSHC allows to define alignment axes as primarily used in road and railway design. These curves typically consist of a se-quence of straights and circular arcs with transition elements in between. In order to avoid sudden changes in curvature transition curves (or easement curves) are placed between sections with different radii providing a gradual change of ture from one section to another. Depending on the characteristics of the curva-ture gradient different types of transition elements can be identified:

• Clothoid: Curvature varies linearly with distance s along the track

Ë(s) + 1

r(s)

+ s

R·L

+ s

_A

2 (2)

• Bloss−Curve: Curvature varies cubically with distance s

Ë(s) + 1

r(s)

+ 3·s

2

R·L

2

* 2·s

3

R·L

2 (3)

• Sinusoidal transition curve:

Ë(s) + 1

r(s)

+

2ps * sin(2ps

L

)

2pLR

(4)

• Cosinusoidal transition curve:

Ë(s) + 1

r(s)

+

1 * cos(ps

L

)

2R

(5)

Above formulas apply for a transition curve of length L which starts from curvature=0 (straight axis) to a circular arc with radius R (curvature = 1/R). For transitions between sections with different radii (e.g. reversing clothoid, egg− shaped clothoid), they have to be modified accordingly. SOFiMSHC supports all variants.

The definition of alignment axes in SOFiMSHC is carried out separately in plan view and elevation. In plan view, sections consisting of straights, circular arcs and transition curves are combined into a sequence defining a two−dimensional curve in x,y−coordinates. The elevation of the curve can be defined independently from the plan view by setting height values and elevation radii. Curvatures in the elev-ation are applied as parabolas.

The following two pictures show an alignment axis in ground view and elevation. The axis consists in the ground view of a circular arc segment and a reversing clothoid with a start radius of RA = −100m and an end radius RE = +50m. In the elevation view the curve is rounded off parabolically with a radius of 100m.

2.2.2.

Freeform curves

For defining freeform curves SOFiMSHC provides an implementaton of NURBS based on the openNURBS library. NURBS (Non−Uniform Rational B−Splines) comprise a special class of curves widely used in computer aided design or com-puter graphics for modelling curves and surfaces of arbitrary shapes. Mathemat-ically, they consist of piecewise rational polynomials of a given order which are connected together under consideration of certain continuity conditions (e.g. tan-gentially continuous, curvature continuous). Due to their construction using ra-tional polynomials, NURBS are also capable of representing circles, ellipses or hyperbolas mathematically exact. A definition of NURBS−curves basically involves the following set of properties and elements:

• Degree

The degree decribes the highest polynomial exponent of the NURBS basis functions. Degree 1 is called linear, degree 2 quadratic, 3 cubic etc. A cubic degree is generally sufficient, but curves with degrees up to 32 may be de-fined and used.

• Control points

Control points are the basic construction points of a NURBS curve or surface. With exception of the first and the last point they are not necessarily located directly on the curve but will stay close to it. Since NURBS curves are constructed using piecewise polynomials, the position of a single control point only changes the shape of its adjacent basis polynoms. This so−called ’local property’ of Nurbs − in contrast to pure polynomial curves − allows to modify a curve locally without affecting the whole shape of the curve. In addition to its xyz−coordinates a control points may also have a weight assigned. By changing the control−point weights to values <> 1.0 the basis functions convert to rational polynoms which offers the possibility to model also circular arcs, hyperbolas or ellipses with NURBS.

• Knots

Basically, a single knot−value defines the location on a curve where two Nurbs basis functions are connected. For a given NURBS curve with N control points they are usually stored internally as monotone list of size (de-gree+N−1). The knot−vector may be defined by the user in order to set the local curve parametrisation explicitly. In general cases however there is no need to define the knots by the user as SOFiMSHC creates an appropriate distribution automatically. Knots can also be defined repeatedly at the same location. This knot multiplicity changes the default transition condition at the interface between two basis functions such that also kinks and even jumps could be modeled within one single curve.

2.3.

Regions and geometric surfaces

SOFiMSHC supports different types of geometric surfaces which can be refer-enced in order to describe the shape of a structural region which is to be meshed. If no geometry is defined explicitly, SOFiMSHC tries to create the shape of a surface from its boundary description. This works, of course, for all plane surfaces and normally also for curved shapes with a less complex boundary description (e.g. four boundary edges in a rectangular like pattern). For complex shapes

however, it is more reasonable to specify the geometric shape of a region explicitly.

2.3.1.

Rotational and sweep surfaces

The general idea of these type of surfaces is that a surface is defined by moving an arbitrary curve in space. In case of a surface of revolution a curve c(v) is rotated around a straight axis. The parametric description of the surface s(u,v) is given by

s(u, v) + M(v)·c(u)

(6) where the matrix M(v) defines rotation around an arbitrary axis in space. The parameter v denotes the rotation angle in radians.

A sweep surface is defined by moving a curve c(u) along a traction curve t(v). The general form of a sweep surface s(u,v) is given by

s(u, v) + t(v) ) M(v)·c(u).

(7) The curve c(u) may also be rotated by M(v) within the local coordinate system of the traction curve after moving it along t. In most cases however, c(v) is only trans-lated along t(v) without rotation. The rotation matrix M defaults to the unity−matrix then.

2.4.

Structural elements

As previously mentioned SOFiMSHC basically distinguishes between geometric entities and structural objects. Geometric elements primarily define the shape and the position of objects in space. Structural objects are referencing the shape of the geometry elements and furthermore contain all relevant structural information together with necessary mutual topological relationships. The structural model within SOFiMSHC corresponds to a classical B−Rep (boundary representation) data model which can be found in a similar form in other common CAD−systems. B−rep models describe objects in space by describing the boundary of the objects. Structural lines, for example, are bounded by their endpoints and structural regions are bounded by a closed sequence of structural edges. Structural regions may also have internal boundaries forming openings inside the region.

2.5.

Mesh generation

The 2D−mesh generation is based on the work by Rank et al. for unstructured mesh generation for pure quadrilateral meshes. [1]. The first step is to generate a triangular mesh which is then divided into a quadrilateral mesh. This is the rea-son why along all edges the number of sections will be even.

However there are specific macros for supports like columns modifying the basic generated mesh in a post processing step.

The 3D−mesh generation is either done as a structured mapped mesh generation based on the surfaces generated before, or a unstructured mesh generation for pure Tetrahedron meshes. This is adopted from a mesh generator developed at the University of Linz [2]. As the quality of Tetrahedron is significantly less than that of Hexahedron we have to generate a more dense element mesh. Both methods may be mixed within one system.

2.6.

Literature

[1] E. Rank, M. Rücker, M. Schweingruber (1994)

Automatische Generierung von Finite−Element−Netzen Bauingenieur Heft 10, 1994

[2] Joachim Schöberl (1997)

NETGEN − An advancing front 2D/3D−mesh generator based on ab-stract rules. Comput.Visual.Sci, 1:41−52, 1997.

Software available under the Lesser−Gnu−Public−Licence (LGPL) [3] Karypis,G. , Kumar,V. (1997)

A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs. http://www.cs.umn.edu/~karypis

[4] Farin, G. (1996)

Curves and Surfaces for Computer−Aided Geometric Design Academic Press, San Diego

[5] Rank, E., Halfmann, A., Rücker, M., Katz, C., Gebhard, S. (2000) Integrierte Modellierungs− und Berechnungssoftware für den

konstruktiven Ingenieurbau: Systemarchitektur und Netzgenerierung Bauingenieur 75, pp 60−66, Springer Verlag Berlin

[6] Piegl,L., Tiller,W. (1997)

The NURBS Book, Monographs in Visual Communication Springer, Berlin

2.7.

Limitations

The following limits can not be exceeded in principle: Number of nodes : 9 999 999 Largest node number : 9 999 999 Largest element number: 9 999 999 Structural points SPT 99 999 Structural lines SLN 99 999 Structural regions SAR 99 999 Structural volumes SVO 99 999

Basically, the numbers of structural elements should not be selected with a unreasonably high value. The program needs to allocate unnecessary amounts of memory, which might increase the overall running time of the program.

Attention should be paid to the fact that only numbers below 1 Mio can be entered and accessed within CADINP. This means that even though element numbers above 1 Mio can be created in SOFiMSHC, these elements cannot be accessed from CADINP in order to set additional properties or apply loads etc. Thus, the group divisor setting the base number of the elements created within a group should be set to a reasonably small value.

3

General program control

3.1.

Input language

The input in SOFiMSHC is generally carried out in CADINP language. More in-formation on this can be found in the general SOFiSTiK manual ’FEA / STRUCTURAL Installation and Basics’.

3.2.

Units

SOFiSTiK programs offer the possibility to carry out all input and output of data in engineering units. A number of unit sets are provided for this purpose, which are preset according to the design code used in the given project. This default can additionally be changed for each program run separately using the keyword PAGE. More information about unit sets can be found in the general SOFiSTiK manual, section ’Units’.

The description of the input values in this manual will always contain the unit, in which a given record is expected to be given. It shows also, if the input record fol-lows a predefined unit set.

Three categories of units are distinguished:

m Fixed unit. Input is always required in the specified unit.

[mm] Explicit unit. Input defaults to the specified unit. Alternatively, an

explicit assignment of a related unit is possible (eg. 2.5[m] ). [mm]1011 Implicit unit. Implicit units are categorised semantically and

denoted by a corresponding identity number (shown in green). Valid categories referring to the unit ’length’ are, for example, geodetic elevation, section length and thickness. The default unit for each category is defined by the currently active (design code specific) unit set. This input default can be overridden as described above. The specified unit in square brackets

corresponds to the default for unit set 5 (Eurocodes, NORM UNIT 5).

3.3.

Remarks for the conversion from SOFiMSHB

As of version 2012, the previous mesh generator SOFiMSHB will be entirely re-placed by SOFiMSHC. Following remarks may help to convert old data sets:

• Compared to SOFiMSHB, SOFiMSHC provides considerable more ca-pabilities for modeling structural systems. Especially due to the fact, that structural elements will be intersected and joined automatically in SOFiMSHC, there is no need to model adjacencies between elements explicitly any more. Structural elements can be defined in independent units, which simplifies modification and extension of given data sets considerably. In general it is therefor recommended to revise old data sets and to adapt them to the new concept of SOFiMSHC.

• The syntax of the input records for structural elements in SOFiMSHC is similar to those of SOFiMSHB. In order to convert a given input to a SOFiMSHC data set, it is therefore often sufficient to replace the record na-mes in the text file as follows:

GPT −> SPT GLN −> SLN

GAR −> SAR (analogue GARB −> SARB) GVO −> SVO (analogue GVOS −> SVOS)

In the case that couplings and elastic beddings have been defined they must be revised manually however, since their definition has been changed and enhanced within SOFiMSHC.

• The finite element model created with SOFiMSHB can basically also be ex-ported into a SOFiMSHA data set, which can be read in with the most cur-rent version in any case. In the case that none of the above approaches has been successful, at least this might be a way to reuse already existing databases.

3.4.

Input records

Record Items SYST GRP CTRL

TYPE GDIV GDIR FIX XREF YREF ZREF T11 T12 T13 T21 T22 T23 T31 T32 T33

NO REF BASE TITL

OPT VAL V2 V3 V4

IMPO EXPO ECHO

OPT FROM PASS

OPT VAL TO PASS OPT VAL

Record Items

COOR TYPE ID IDP S X Y Z T11 T12

T13 T21 T22 T23

XSUB TYP FIXA FIXL FIXM CD

Records HEAD, END and PAGE are described in the general manual SOFiSTiK: ’Basics’.

See also: SPT SPTPSLN SLNPSLNS SAR SARB SVO SVOS

3.5.

SYST − Global system definition

ÄÄÄÄÄÄÄÄÄ ÄÄÄÄÄÄÄÄÄ ÄÄÄÄÄÄÄÄÄ

SYST

Item Description Unit Default

TYPE SPAC 3D spatial structures

SOFiSTiK YX−plane accord. DIN 1080: FRAM Plane frame

PAIN Plane strain planar system PESS Plane stress planar system AXIA Axial symmetric system

(X is rotation axis)

GIRD Plane girder or plate bending PGIR Prestressed plate system International XY−plane

WFRA Plane frame

WPAI Plane strain planar system WPES Plane stress planar system WAXI Axial symmetric system

(X is rotation axis)

SLAB Plane girder or plate bending PSLA Prestressed plate system INIT Keep existing system type REST Keep structural system

Item Description Unit Default

GDIV GDIR FIX

Group divisior

Direction of gravity load

XX, YY, ZZ, NEGX, NEGY or NEGZ Global default constraints

− LIT LIT 0 * − XREF YREF ZREF T11 T21 T31 ... T33

Origin of coordinate system in WCS

Transformation matrix WCS −> UCS Default: T11 T12 T13 1.0 0.0 0.0 T21 T22 T23 = 0.0 1.0 0.0 T31 T32 T33 0.0 0.0 1.0 m m m − 0.0 0.0 0.0 1.0 0.0 0.0 1.0 This record defines the type of the analytical model used for the given system. With the exception of TYPE REST, all structural elements will be deleted and the system will be reinitialized. An input of SYST REST keeps the system type along with all structural elements of a previous SOFiMSHC−run. Existing finite elements will be deleted in any case.

The user coordinate system (UCS) in SOFiSTiK is always defined as a right− handed coordinate system, which can be linked to a global project coordinate sys-tem using a reference point and a transformation matrix. Since SOFiSTiK works in the mks−system, the transformation matrix can be employed for connecting a mm− based CAD−systems, for example.

For planar systems there are different conventions about the orientation of the global X,Y and Z axis. German Design Codes (e.g. DIN 1080) usually request that the global Z axis has to be aligned downwards into gravity direction (i.e. GDIR POSZ). On the other hand, in an international setting often classical coordinate systems are used with the Z axis pointing upwards (i.e. GDIR NEGZ). You may select your convention freely. Similar applies for planar 2D systems. Systems of type FRAM, PAIN, PESS, AXIA, GRID or PGIR are systems where the global Z−axis is directed into viewing direction whereas for WFRA, WPAI, WPES, WAXI, SLAB or PSLA the z−axis will be aligned towards the observer.

In the case of planar systems like FRAM/GIRD only half of the global unknowns are activated during analysis such that either out−of−plane or in−plane−deforma-tions and stress−resultants will be suppressed. Therefore, beams with principal

axes different to the axes of the global coordinate system can be analyzed only in three dimensions.

The group divisor GDIV sets the mode how element numbers are assigned to groups. Further information can be found in the description of record GRP. The default of 0 deactivates all group selection possibilities.

The global gravity direction sets the default direction of, for example, loads, boundary conditions or sections. It will be also used to set the default viewing di-rection of graphical programs.

See also: SPT SPTP SLN SLNP SLNS SAR SARB SARS SVO SVOS

3.6.

CTRL − Control of analysis

ÄÄÄÄÄÄÄÄ ÄÄÄÄÄÄÄÄ ÄÄÄÄÄÄÄÄ

CTRL

Item Description Unit Default

OPT A literal from the following list:

TOPO Topological decomposition ON OFF DEL GAXP SARB XFLG

TOLG Intersection tolerance

NODE Start index of automatically assigned numbers

DELN Deletion of unused elements

LIT LIT/− − − − − − [m]₁₀₀₁/− − − ! ON 0 − +3 +8 +1 −0.01 1000 1 HEAL Geometry healing

JOIN DELO LIT [m]1001 [m2]₁₀₀₂ ! 1.0 1.0 MESH Start of mesh generation

HMIN Mesh size

FINE Refinement at nodes

EFAC Refinement at short edges PROG Progression factor

− [m]1001 [m]1001/− − − 0 1.0 HMIN 1.4 1.5 LOCA Local coordinate systems

TOLN geom. tolerance detection of identical FE−nodes

PSUP Point support modelling LSUP Line support modelling

− − − − 1 1.e−6 0 1 OPTI Renumbering optimisation

SUB No of subdomains

PART Controls mesh−partitioning

− − − 49 − −

Item Description Unit Default

WARN Suppress warning message − − VAL

V2 V3 V4

Value of control

Second value if needed Third value if needed Fourth value if needed

− − − − − − − − This record is used to set global program control options. They can be classified as follows:

3.6.1.

Analysis and generation of structural model

In a first processing step, SOFiMSHC reads in the model entered by the user or given by CAD and intersects all elements with each other in order to obtain a me-chanically consistent structural system. The general behaviour during this pro-cess can be controlled using the following options.

TOPO ON V2

Stores the input model entered by the user at the reference key given at parameter V2 and activates the analysis and intersection of the structural system.

TOPO OFF

Deactivates the import and analysis of the structural system entirely, even if meshing of the structure has been activated (CTRL MESH ac-tivates CTRL TOPO ON automatically). This setting is usually only needed for debugging purposes. The model must have been already imported and analyzed in a previous run.

TOPO DEL V2

Deletes the structural elements stored at the given reference key. Un-der normal circumstances, the database will be properly initialized and structural elements deleted, when setting the system type in-ternally (see SYST). Hence this option is usually only necessary in order to analyze failed program runs.

TOPO GAXP V2

Controls the automatic generation of structural elements between placements on a geometric axis. Following options are possible (bit− mask):

+1: Generate structural points at placements +2: Generate structural lines beween placements

TOPO SARB V2

Controls the definition and processing of boundary edges of structural regions. Following options available (bit−mask):

+1: Boundary edges are always given in sorted order. Usually the case when importing from CAD and can be set to avoid unnecessary and extensive tests

In some cases, especially when importing data from external CAD systems, the type of the boundary edges is not clearly specified. Fol-lowing bitmask allows to control edges, which are internal to a region and which has not been explicitly defined as opening (SARB IN) or constraining edges (SARB CONS):

+4: edges will be classified as boundary of an opening

+8: edges will be classified as edges of a separate internal region +12: edges will be classified as constraining edges

TOPO XFLG V2

This parameter controls the structural element intersection process on a global level. Following options (bit−mask) are available:

+1: Structural points, which have been defined explicitly by the user (i.e. both have been assigned a number) will not be merged, even if they are located at the same position in space In addition to that, the intersection of elements can also be controlled for each structural element individually. See parameter XFLG in re-cords SPT, SLN and SAR, respectively.

TOLG This parameter sets the tolerance used during intersection of structu-ral elements. Elements (structustructu-ral points, lines and areas) with a distance below the given tolerance will be merged. The tolerance can be given in absolute or relative lengths:

TOLG>0: absolute length in m

TOLG<0: relative factor which will be scaled by characteristic lengths of the model. Default setting is TOLG = −0.01

NODE This parameter sets the start index for the numbers of automatically created structural elements and FE−nodes. During analysis of the in-put model, new structural elements can be created, which will be assi-gned a number automatically. Especially when working with multiple SOFiMSHC input blocks within one project, it is recommended to set this parameter to a higher value in order to separate automatically as-signed from explicitly defined numbers.

DELN Deletion of unused structural points and lines.

Basically, SOFiMSHC deletes structural points and lines which are not connected with the model and which have no stiffness properties: 0: Unused structural points and lines will not be deleted

1: Unused structural points and lines will be deleted (default)

3.6.2.

Geometry healing

Models from external CAD−systems or files often exhibit geometric inconsisten-cies resulting in failed meshing runs or poor element quality. SOFiMSHC provides a number of options for correction of geometry:

HEAL JOIN V2[m] V3[deg]

In some cases basically connected curve or line sequences will be exported from external systems fragmented into multiple short struc-tural lines. A large number of such short strucstruc-tural lines might incre-ase the number of elements in the resulting finite element mesh unne-cessarily. This options allows to join adjacent structural lines of similar type to single edges.

Two neighboring lines will be connected, if the following requirements are met:

− The length of the adjacent lines lies below the given parameter V2 − The angle between the two lines is lower than V3

− There is no other edge connected (no Y−joint)

− Boundary and cross−section properties do not change.

HEAL DELO V2

This options deletes openings with a surface area below the given va-lue V2.

3.6.3.

Meshing control

MESH This parameter activates the mesh generation for the defined model. Following options exist:

0 deactivate meshing

1 meshing of beam structures

2 meshing of beam and shell structures 3 meshing of beam, shell and/or volumes In addition to the basic options 1−3 one may add the following values:

+ 16 keep explicit old elements + 32 triangular elements only + 64 quadrilateral elements only + 96 mixed element shapes allowed

+ 128 disable dupl. run with background mesh + 256 post−processing only (partitioning, optim.) A CTRL MESH automatically activates the topological analysis and intersection of structural elements (STEU TOPO 0)

HMIN Parameter HMIN controls globally the element size of the resulting finite element mesh. It defines the maximum allowed length of a beam and/or the edge of a shell or volume element. Please note, that the mesh density defines only an upper bound for the element size. Local geometric features or other constraints might require a smaller element size.

In addition to the global setting, the mesh size can be overwritten indi-vidually for single structural objects (structural points, lines, regions).

EFAC This parameter controls the mesh density in the vicinity of short struc-tural edges. In the neighborhood of short strucstruc-tural edges, whose length are below the global element size HMIN, the mesh density is reduced locally in order to avoid distorted quad elements with highly different edge lengths. The parameter describes the factor

“Local mesh size” / “Length of short edge”

Default setting is a factor of EFAC=1.40. For models containing many small edges, however, this setting might result in meshes with many local refinements, which increase the total number of elements considerably. In order to avoid the local refinements, this factor

should be increased with the disadvantage, that the element quality might be reduced. On the other hand, if a model contains relatively long and small structural areas, whose width lies below the global mesh density, it is recommended to deactivate this parameter entirely (EFAC = 0). This avoids the reduction of the mesh density to the ends of the areas which results in a more regular mesh.

PROG This parameter defines the rate, how the mesh density is increased

from a local refinement to the global part. It describes basically the maximum allowed ratio of the edge size between two adjacent quad elements. Standard setting is a progression factor of PROG = 1.5.

3.6.4.

Element generation and boundary conditions

LOCA Controls the definition of the local coordinate−system of beam ele-ments.

0 = local z−axis points into gravity direction resp. the local y−axis into the first global horizontal axis if the former is not possible (i.e. beam axis parallel to gravity). User defined orientations are applied to the local y−axis.

1 = local z−axis points into gravity direction resp. into the first global horizontal axis if the former is not possible (i.e. beam axis parallel to gravity). User defined orientations are applied to the local z−axis. 2 = local z−axis points into global Z resp. into global X if the former is not possible (i.e. beam axis parallel to global Z). User defined ori-entations are applied to the local z−axis. (Default in Industry Founda-tion Classes, IFC)

3 = local z−axis points into global Z resp. into global Y if the former is not possible. User defined orientations are applied to the local y−axis (GENF).

TOLN This parameter controls the detection of double finite element nodes. FE−nodes whose distance lies below the given tolerance are in-tersected and replaced. The parameter is given as relative factor which will be scaled internally by model dimensions.

PSUP controls the mesh generation for Point−Support (Bitpattern) −1= no special action

0 = generate 4 rectangular quad elements (default) 1 = increase thickness of elements at support 2 = cinematic constraints of mid points

4 = cinematic constraints of corner points 8 = additional centre node for constraints

16 = deactivate the correction of minimum mesh size

LSUP controls the generation of boundary elements (= supporting lines) on structural lines:

0 = create boundary elements if the line has an elastic support or contains only a group nr > 0 without a section nr.

1 = create boundary elements also for structural lines with rigid support in gravity direction (default setting)

2 = create boundary elements if any type of support is given. 3 = create boundary elements for all edges.

4−15: reserved for internal tests.

+16 = create elastic springs instead of boundary elements.

3.6.5.

Mesh decomposition and band−width optimization

OPTI SOFiMSHC optimizes the internal numbering of the created FE− nodes in order to allow a efficient storage and solution of the resulting finite element equation system. This can be controled using the fol-lowing options (bit−mask):

0 = no reordering

1 = fast global reordering 2 = best global reordering

3 = best local and global reordering

+16 use Metis−random Matching (RM) +32 use Heavy−Edge Matching (HEM) +48 use Sorted HEM

+49 use for Sparse−Solver (default)

The type of optimisation should be adapted to the equation solver to be used. An improper setting may have adverse effects.

CTRL SOLV 1 options 1 to 3 CTRL SOLV 2 option 1

CTRL SOLV 3 options >16 (recomm. 49) CTRL SOLV 4 options >16 (recomm. 49)

Option 2 should not be used for systems which decompose into sev-eral independant subsystems.

SUB By setting the parameter SUB the mesh partitioning tool metis is re-quested to decompose the finite element mesh into the given number subdomains.

PART Bitpattern to control partitioning

0 = use PMETIS or KMETIS (SUB>8) 1 = use KMETIS for mesh partioning 2 = use PMETIS for mesh partioning

+16 = use Random Matching (RM)

+32 = use Heavy−Edge Matching (HEM) +48 = use Sorted HEM (Default)

256 = use reordered nodal−Bisection 257 = use group definitions

3.6.6.

Warnings and error messages

See also: SYST

3.7.

GRP − Group control

ÄÄÄÄÄÄÄÄ ÄÄÄÄÄÄÄÄ ÄÄÄÄÄÄÄÄ

GRP

Item Description Unit Default

NO BASE TITL

Group number

Base number for this group Title of the group

−/LIT − Lit32 ! * − Element groups are an important aid for the definition of construction stages or the assignment of loads, for example. Structural lines, areas and volumes defined in SOFiMSC can be assigned to different groups. Thereby it must be distinguis-hed between primary and secondary groups:

3.7.1.

Primary group number

The primary group number is uniquely defined for each element. Each group is associated with a range of element numbers which easily allows to reconstruct the group id from the element id. SOFiMSHC provides different methods for the assigment of element numbers to a group. The kind of assignment is specified by the group divisor GDIV in the main system record SYST.

• GDIV > 0

The group number of a single element is defined by the integer division of the element number by the group divisor.

Example: Group number Group divisor Element numbers

0 1000 0 − 999

1 1000 1000 − 1999

2 1000 2000 − 2999

• GDIV=0

All groups must be assigned an individual base number in increasing order. An element number within one of the intervals defines the membership to the respective group.

Example: Group Base Element number

0 1 1−99999 1 100000 100000−199999 2 200000 200000−249999 3 250000 250000−259999 4 260000 from 260000 • GDIV<0

The base values of all groups will be defined automatically after all ele-ments have been generated. It is thus not any longer necessary to define base values individually. The value at GDIV<0 defines the lowest common multiple from which the element numbers of the next higher group will be assigned to. The current limit for elements within a group is set to 1 Million. For all cases, the maximum group number is 999. The base number and designa-tion is identical for all elements within a group. Large element numbers will be splitted into its group and element part in print outputs in order to support better readability. It is therefor also recommended to use base numbers which are a mul-tiple of 100, 1000 or 10 000.

3.7.2.

Secondary groups

In addition to their primary group number, elements can be assigned to any num-ber of so called secondary groups. Secondary groups are labeled using a text string of maximum four characters (e.g. ’GR1’). The assignment of elements to secondary groups is done separately after definition of the structural system. Subsequently to the definition of the secondary group using this record any num-ber of selection records can be given. Following type of selections are possible:

SLN NO selection of a structural line SAR NO selection of a structural area

GUID ID selection using the Globally Unique Identifier of a structural element (usually defined in a CAD−system)

Example:

GRP NO ’GR1’ SLN NO 1,2,3 SAR NO 5

defines a secondary group labeled ’GR1’, which contains all beam and area elements created on the structural lines 1, 2 and 3 and structural area 5.

Apart from this selection mechanism, elements can also be assigned to a secon-dary group using attribute regions. For more information please see at the de-scription of attribute regions at record SAR.

3.8.

IMPO − Import of data

ÖÖÖÖÖÖÖÖÖ ÖÖÖÖÖÖÖÖÖ ÖÖÖÖÖÖÖÖÖ ÖÖÖÖÖÖÖÖÖ

IMPO

Item Description Unit Default

OPT Special options

0 no special options

1 convert xyz to yzx system 2 convert xyz to zxy system 4 Set origin pointer to elementno 8 Set origin pointer to elementno

without group number

16 do not extrude support conditions 256 Use Group instead of geometry

numbers for selections

− 0 FROM PASS Name of a database Password of database Lit96 Lit16 * − With the record IMPO you may select for the 3D−extrusions the meshes to be used for the extrusion from a different database. This record may be defined only once and is then valid for all extrusions.

3.9.

EXPO − ANSI export of data

ÖÖÖÖÖÖÖÖ ÖÖÖÖÖÖÖÖ ÖÖÖÖÖÖÖÖ ÖÖÖÖÖÖÖÖ

EXPO

Item Description Unit Default

OPT

VAL

Data to be exported

GAX Geometric axis GAR Geometric surface RAW Basic structural model ID of axis, surface (optional)

LIT Lit4 RAW − TO PASS

Name of a file to write to Password of database

Lit96 Lit16

* − Using record EXPO geometric or structural elements within the database can be exported into an input file for SOFiMSHC. This can be useful when analyzing the data after an error occured or to make further use of the data in different settings. If an Identifier is given additionally at GAX or GAR, only the selected geometric axis or surface is exported to the file, otherwise all elements of the given type are exported. When using option RAW, an additional literal ’FULL’ may be added which allows to extend the export also to internally used datatypes. In this case for example, globally uniqe identifier (GUID) of the structural elements, which will be used for idenfication of structural objects in different CAD−systems, will be exported to the input file.

If no file name is specified the data will be exported to a file named

project_MEX.dat.

The units of the values will be set to the current setting of UNIE from record PAGE. The language of the new file will be the same as the current CADINP input file.

See also:

3.10.

ECHO − Control of output

ÄÄÄÄÄÄÄÄÄ ÄÄÄÄÄÄÄÄÄ ÄÄÄÄÄÄÄÄÄ

ECHO

Item Description Unit Default

OPT A literal from the following list: MAT Material data SECT Section for beams GEOM Geometric items NODE Generated nodes

QUAD Generated quadrilaterals BRIC Generated volume elements BEAM Generated beam elements BOUN Generated elastic supports SYST System summary

STAT Analysis statistics FULL all the above options

LIT FULL

VAL Value of output option NO no output YES regular output FULL extensive output EXTR extreme output

LIT FULL

The name (ECHO) of this record must be repeated every time the command is being used, otherwise it may be confused with other records with the same name.

See also: GAXPSPTSLN SAR

3.11.

COOR − User defined coordinate

system

ÄÄÄÄÄÄÄÄ ÄÄÄÄÄÄÄÄ ÄÄÄÄÄÄÄÄ

COOR

Item Description Unit Default

TYPE

ID IDP

Type / reference of coordinate system WRLD: world coordinate system SPT: reference to structural point AXIS: reference to axis

GAXP: reference to placement

CYLI: cylindrical coordinate system SPHE: spherical coordinate system Number / ID of reference item

ID of placement (Type GAXP)

LIT −/Lit8 Lit4 WRLD − − S X Y Z T1X T1Y T1Z T2X T2Y T2Z

Parameter on axis (Typ AXIS, GAXP) Coordinate of origin

(Type WRLD, CYLI, SPHE)

Direction first axis

Direction second axis

− [m]1001 [m]1001 [m]₁₀₀₁ − − − − − − − 0.0 0.0 0.0 1.0 0.0 0.0 0.0 1.0 0.0 This record sets a new reference coordinate system for position and direction in-put in SOFiMSHC. After setting the coordinate system, all succeding inin-put of a position or a direction in any structural or geometrical record will be interpreted according to the given coordinate system. The coordinate system can be changed within a data record as often as desired. Setting COOR WRLD resets the coordinate system to the default, an euclidian coordinate system with origin at (0,0,0).

• WRLD: world coordinate system

This type defines an euclidian (orthogonal) coordinate system with origin given at X,Y,Z. The orientation of the coordinate system can be set using the paramters T11 to T23. They define the first local direction T1 (T11,T12,T13) and the second local direction T2 (T21,T22,T23) . The third direction is derived from the cross product of the first and second axis. In the case that the second direction is not orthogonal to the first, it will be or-thogonalized.

• SPT: Reference to structural point

By setting a structural point number at ID, the coordinate system will be moved to the local coordinate system of an already defined structural point. • AXIS: Reference to structural line/axis at station S

The coordinate system will be moved to the respective station S of an axis or a structural line and rotated according to the local coordinate system of the axis. The axis or structural line resp. is given at ID. It is also possible to reference secondary axes (e.g. ID ’A1.B’).

• GAXP: Reference to placement

The coordinate system is moved to the location of a placement, which has been defined using GAXP at an axis. The second and third direction of the coordinate system (local y and local z) will be aligned according to the cut− plane of the placement (local z usually points into gravity direction). The axis is given at parameter ID. The placement can be identified by its pa-rameter position at S or its identifier given at IDP.

• CYLI: Cylindrical coordinate system

By indicating an origin at X,Y,Z and two direction vectors at T1 (T11,T12,T13) and T2 (T21,T22,T23), a cylindrical coordinate system can be defined.

All succeding input of a position (X,Y,Z) or a direction (DX,DY,DZ) will be interpreted according to the following scheme:

X: Radius (distance) from rotational axis Y: Azimut angle in rotational plane

Z: Height along rotational axis • SHPE: Spherical coordinate system

By indicating an origing at X,Y,Z and two direction vectors at T1 (T11,T12,T13) and T2 (T21,T22,T23), a spherical coordinate system can be defined.

All succeding input of a position (X,Y,Z) or a direction (DX,DY,DZ) will be interpreted according to the following scheme:

X: Radius (distance) from origin

Y: Azimut angle ’phi’ in equatorial plane Z: Inclination from equatorial plane

See also: GUID BBOX

3.12.

XSUB − Extraction of subsystems

ÄÄÄÄÄÄÄÄÄ ÄÄÄÄÄÄÄÄÄ ÄÄÄÄÄÄÄÄÄ

XSUB

Item Description Unit Default

TYPE FIXA FIXL FIXM CDB Systemtype of Submodel SPAC spatial system

SLAB 2D plate/girder system Type or factor of axial stiffnes Type or factor of lateral stiffness Type or factor of rotational stiffness Name of File to be created

Lit4 −/Lit −/Lit −/Lit LIT SPAC FIX 1.0 1.0

This records allows to extract a partial system from a general structural model for a detailed analysis. The extracted model will be stored in a new database as planar slab or again as new spacial system, which can be then meshed and calcu-lated in a separate independent project.

In the case, that the partial model will be extracted as plate system (TYPE SLAB) all selected structural elements will be projected onto the xy−plane at coordinate z=0.0.

All structural elements connected to the partial model which will be cut during the extraction, like adjacent columns or walls, will be replaced by linear elastic spring elements or fixed supports approximating the stiffness at the connection. The generation of these boundary conditions can be controlled using the parameters FIXA to FIXM. The three parameters can be distinguished between axial, lateral and rotational stiffness components.

• FIXV: Control of axial stiffness

The bedding component in axial direction of connected elements will be calculated as follows:

Connected Structural line c_a = E*A/l Structural area: c_a = E*T/h

’A’ denotes the cross section area and ’l’ the length of the connected struc-tural line (e.g. column). For adjacent strucstruc-tural areas the linear elastic line

bedding replacing the area will be calculated from the plate thickness and the average height.

• FIXH: Control of lateral stiffness

The stiffness in transversal direction will be calculated under the assump-tion, that the connected building element has hinged support at the bottom:

Structural line: c_l = 3 * E I_y / l3 (bzw. 3 * E I_z / l3) Structural area: c_l = 3 * E I_y / h3

For an adjacent structural line two spring elements will be created for the stiffness in the direction of the local y− and z−axis of the cross section. For a connected structural region, the supported line will be fixed in longitudinal direction.

• FIXM: Control of rotational stiffness

For the computation of the rotational stiffness, it is again assumed, that the connected building element has hinged support at the bottom:

Structural line: c_r = 3 * E I_y / l2 (bzw. 3 * E I_z / l2) Structural area: c_r = 3 * E I_y / h2

In all three cases, a numerical value > 0.0 or one of the two literals FIX or FREE can be given at FIXA to FIXM. In the case, that a numerical value is given, it will be interpreted as factor multiplying the default stiffness values calculated as given above. The literal ’FIX’ creates a fixed support and the literal ’FREE’ releases the respective degrees of freedom entirely.

The elements of the partial system are selected by entering subsequent records directly after XSUB:

• SLN: Selection of a structural line with number NO • SAR: Selection of a structural region with number NO • GUID: Selection using a Globally Unique Identifier (GUID)

A GUID uniquely identifies a structural element and will be usually set when exporting the model from a CAD system (e.g. SOFiPLUS, Exten-sions for Revit).

• BBOX: Selection using a rectangular bounding box

This option is especially suitable for selecting all structural elements on a specified floor level (e.g. BBOX z1 9.5 z2 10.5).

4

Definition of geometric elements

.

This chapter describes the definition of general geometrical elements like geome-tric axes or surfaces.

4.1.

Input records

Record Items GAX GAXA GAXH GAXB GAXC GAXN GAXP GAXS GAXV

NO TYPE ID2 ID3 ID4 ID5 REF SUR1 SUR2 TYPC DEG TITL

S X Y SX SY L R RA RE LA LE TYPS S H R R XM YM ZM NX NY NZ X1 Y1 Z1 X2 Y2 Z2 X3 Y3 Z3 X Y Z W NX NY NZ ALFX ALFY ALFZ S MUL DIV ID IDS S TYPE GPT GRP NCS Y Z

ALF ALFX ALFY ALFZ INCR INCL

ID IDS GPT GRP Y Z TITL ID NAME S V DV TYPE GAR GARA GARC GARS

NO TYPE DEGU DEGV M N TITL

NO TYPE GIDI GID2 X Y Z NX NY

NZ SMIN SMAX TMIN TMAX M N TITL

NU0 NU1 NV0 NV1 XUV1 YUV1 ZUV1 XUV4 YUV4 ZUV4

See also: GAXA GAXH GAXB GAXC GAXN GAXP GAXS GAXV

4.2.

GAX − Geometric curve or axis

ÄÄÄÄÄÄÄÄÄ ÄÄÄÄÄÄÄÄÄ ÄÄÄÄÄÄÄÄÄ

GAX

Item Description Unit Default

ID TYPE

Axis identifier Type of axis

DEL delete this entry NONE no specific type

AXIS system axis (e.g. A−A) BEAM axis of beam sequence LANE traffic lane

TEND tendon axis

Lit4 LIT ! LANE ID2 ID3 ID4 ID5

Reserved for export of additional data Reserved for export of additional data Reserved for export of additional data Reserved for export of additional data

− − − − − − − 1 REF SUR1 SUR2 TYPC DEGR

Reference to a master axis Number of a geometric surface

Number of a second geometric surface Type of curve to be generated

Degree of spline curve (see GAXC)

Lit4 Lit4 Lit4 LIT − − − − * *

TITL Designation of axis Lit32 −

This record defines alignment axes for road design or arbitrary geometric curves which are generally idependent from structural elements. In SOFiMSHC, geometry axes represent mainly general data structures allowing to define fully parametrc input data sets. One important application area, for example, is bridge design, where all elements of a bridge can be defined relatively to this central axis. Once the geometry of the axis is changed, all dependent structures will be adapted automatically. In addtition, arbitrary variable distributions can be defined for a geometry axis, which can be used, for example, to describe varying sections, additional load lines or secondary girders.

As axis identifier at ID only literals consisting of maximum four characters are allo-wed, for example GAX ID ’AX1’.

For defining the geometry SOFiMSHC provides a number of possibilities (parameter TYPC). The geometry of an axis is defined by subsequent records of following types:

• AXIS (GAXA / GAXH) Alignment axes in plan view and elevation

• ARC (GAXB) Straight lines and circular arcs in 3D • POLY (GAXC) Polygonal line

• SPLI (GAXC) Cubic B−Spline Interpolation • HINT (GAXC) Hermite−Interpolation

• NURB (GAXC / GAXN) Arbitrary Freeform Curves (B−splines, NURBS)

In addition to its geometric shape the following records allow to define additional dependant parameters and properties:

• GAXS Secondary axes

• GAXP Placements: special positions along an axis

• GAXV Definition of variables along an axis Freeform curves of type GAXC can also be defined relatively to an other axis.If a previously defined curve is given at record REF, all following coordinates are interpreted relatively to the curve. This allows to define offset curves or to create an identical copy of an axis.

It is also possible to project curves onto a surface or to create a curve by intersecting two arbitrary surfaces:

• If a single surface is given at SUR1, the curve will be projected onto the given surface.

• In the case that two surfaces are defined at SUR1 and SUR2, the generated curve is the intersection of the two given surfaces.

See also: GAX GAXH GAXP GAXS GAXV

4.3.

GAXA − Axis plan view

ÄÄÄÄÄÄÄÄÄ ÄÄÄÄÄÄÄÄÄ ÄÄÄÄÄÄÄÄÄ

GAXA

Item Description Unit Default

S X Y SX SY L R RA RE LA LE TYPS Station value

Coordinates of startpoint / tangential intersection

Direction of tangent Length of section Radius

Radius of the axis at start Radius of the axis at end

Length of first transition element or <0 for Clothoidal parameter (R*L=A2) Length of second transition element or <0 for Clothoidal parameter (R*L=A2) Type of transition curve

− m m − − m m m m m m LIT * * * * * * * R R * LA CLOT Record GAXA defines sections of a setting out line in plan view for a preceeding axis GAX. SOFiMSHC provides two different possibilities of definition:

Length based definition:

Using this mode, an axis always starts with a startpoint (station + coordinate) and a tangential direction, e.g.

GAXA S 250.0 X 0 0 0 SX 1 0 0.

Subsequently, single segments are defined with their length and possible start and end radius:

GAXA L 50.0 RA 0.0 RE 200.0 GAXA L 50.0 R 200.0

GAXA L 50.0 RA 200.0 RE 0.0 GAXA L 50.0

For segments with different radius between start and end, a transition curve is in-serted. A radius with positive value cause a curvature to the right−hand side, whilst a negative value a curvature to the left−hand side. Using the input above, for example, a sequence consisting of a transition element, a circular arc, a transi-tion element and a straight segment at the end will be created.

Tangentially based definition

Pi−1 Pi PC R RA RE R

In this kind of input, the user defines the intersections of the curve tangents to-gether with a curvature radius and different length parameters, for example:

GAXA X 0.0 Y 0.0

GAXA X 30.0 Y 10.0 R 40.0 LA 10.0 LE 10.0. GAXA X 60.0 Y 0.0

Using this parameters SOFiMSHC inserts a curve sequence such, that its end points fits tangentially to the predefined polygon. For the parameter following pos-sibilities exist:

• The minimum radius at R and the total length of the curve sequence is gi-ven at L. In this case, a curve sequence is inserted under consideration of the symmetry condition A1=A2. This is called a “symmetric standard se-quence”.

• The minimum Radius R and the length of the two transition segments LA and LE are given. This case defines a so called “asymmetric standard se-quence”. The length of the circular segment is calculated automatically. The user may also define a start radius RA and an end radius RE. In this

case, the curve sequence does not any longer fit curvature continuously to the tangents.

• If no radius is given at all, a polygonal axis with kinks is created.

In the case that the parameters of the transition elements define a shorter length than needed, a straight segment will be inserted before the standard curve se-quence and the position of the tangent points will be adjusted accordingly. Instead of a Clothoid, also a cubic parabola (TYPS CUBI) (not recommended) or a Bloss Curve (TYPS BLOS) may be used as transition element. And finally, SOFiMSHC also allows to use sinusoidal (TYPS SIN) and cosinusoidal (TYPS COS) transition elements.

See also: GAX GAXA GAXP GAXS GAXV

4.4.

GAXH − Axis heights

ÄÄÄÄÄÄÄÄ ÄÄÄÄÄÄÄÄ ÄÄÄÄÄÄÄÄ

GAXH

Item Description Unit Default

S H R Station value Height Radius of elevation − m m * * * GAXH defines the elevation of an alignment axis defined previously at GAX. Ac-cording to the convention used in road design positive height values will be placed in a direction opposite to the globally defined gravity direction (POSZ, NEGZ). Curvature radii will be applied as quadratic parabolas.

R

P2

P1

P3

See also: GAX GAXA GAXH GAXP GAXS GAXV

4.5.

GAXB − Straights and circular arcs

in 3D

ÄÄÄÄÄÄÄÄÄ ÄÄÄÄÄÄÄÄÄ ÄÄÄÄÄÄÄÄÄ

GAXB

Item Description Unit Default

R XM YM ZM NX NY NZ Radius Coordinates of center

Direction of normal to circle plane

[m]1001 [m]₁₀₀₁ [m]₁₀₀₁ [m]1001 − − − − − − − − − − X1 Y1 Z1 X2 Y2 Z2 X3 Y3 Z3

Startpoint of circular arc / straight

Endpoint of circular arc / straight

Third point on circular arc

[m]₁₀₀₁ [m]1001 [m]1001 [m]1001 [m]1001 [m]₁₀₀₁ [m]1001 [m]₁₀₀₁ [m]1001 − − − − − − − − − S1 S2

Parameter at start (optional) Parameter at end (optional)

− −

0.0 − Records of type GAXB can be used to define straight lines, circles and cicular arcs in space. Records of this type always refer to the most recently defined curve at GAX. Multiple segments are allowed to be entered in order to define polycurves. For the definition of a single segment following possibilities exist:

• A straight line is defined by its start− and endpoint at (x₁,y₁,z₁) and (x₂,y₂,z₂).

• A full circle can be defined by its center (x_m,y_m,z_m), the radius and the nor-mal on the circular plane (n_x,n_y,n_z).

• A circular arc can be defined by its start− and endpoint at (x₁,y₁,z₁) und (x₂,y₂,z₂), a radius and the normal or by entering the start−, the endpoint and the center.

• In addition, circular arcs can also be defined by entering three points on the arc. (x₁,y₁,z₁) und (x₂,y₂,z₂) describe the start− and the endpoint, (x₃,y₃,z₃) a third point on the arc.

When multiple segments are defined, the transition between two segments should be modeled with continuous tangents. Kinks are possible but should be avoided as they can lead to incorrect or erroneous meshes. In order to define kinks it is better to define two curves with a structural point in between.

Using the parameters S1 and S2 the chainage (or parametrisation) of the curve can be set explicitly. If nothing is given at S1 and/or S2 the parametrisation is de-fined according to the true (arc) length of the curve.

See also: GAX GAXN GAXP GAXS GAXV

4.6.

GAXC − 3D curve point data

ÄÄÄÄÄÄÄÄÄ ÄÄÄÄÄÄÄÄÄ ÄÄÄÄÄÄÄÄÄ

GAXC

Item Description Unit Default

X Y Z W S 3D coordinates

Weight of control point (NURBS) Station on point (for interpolation)

[m]1001 [m]₁₀₀₁ [m]₁₀₀₁ − − 0.0 0.0 0.0 1.0 − DX DY DZ NX NY NZ

Tangential direction (Type HINT)

Direction of local z−axis (not available)

− − − − − − − − − − − −

The geometry of arbitrary freeform curves can be defined with this record by ente-ring characteristic data points. Each record GAXC defines a single coordinate in 3D. The points always refer to the directly preceding geometry axis. The type and the degree of the curve is specified by the parameters TYPC and DEG within the main record GAX:

• POLY: Interpolation as polygonal sequence

The given points will be connected to a polygonal line. • SPLI: Spline interpolation

The given datapoints will be interpolated using a cubic B−Spline. The inter-polation is carried out curvature continuous at the definition points (C2− continuity).

The chainage (parametrisation) of the curve can be set explicitly at each datapoint using the parameter S. If no parameter values are given, SOFiMSHC assigns a parametrisation automatically. The end chainage corresponds to the geometric length of the axis in this case.

• HINT: Hermite interpolation

The given datapoints will be interpolated using piecewise cubic B−Spline segments. The interpolation is carried out tangentially continuous at the definition points (C1−continuity).

Using the parameters DX,DY,DZ, the tangential direction at certain points can be defined explicitly by the user. Similar to the spline interpolation, the parametrisation (chainage) along the curve can be set using the parameter S.

• NURB: NURBS−curve

A NURBS (Non Uniform Rational B−Spline) curve can be defined by ente-ring the euclidian coordinates of the control−points at X,Y,Z. If weights <> 1.0 are given, the input results in a true ’rational’ NURBS curve, which, for example, allows to describe also circle and ellipses. The degree of the NURBS curve can be set in record SLNN, when defining the knot vector. It is also possible to create curves relatively to an existing axis. If a reference axis REF is given in the main record GAX, the X−values are then interpreted as station value S on the reference axis and the values Y and Z as distances relatively to the local coordinate system of the referenced axis. The thus defined points are then interpolated by a cubic B−spline (TYPC SPLI). Contrary to secondary axes at GAXS, the reference is resolved explicitly, i.e. a new independent geometry is calculated based on the definition of the data points.

At NX,NY,NZ a user defined orientation of the local z−axis can be set for each point on the curve independantly. This allows to define, for example, arbitrarily ori-ented cross−sections along a curve or an axis. If no directions are given at all, the local z−axis is oriented towards the globally defined gravity direction.