3. GLOBAL AND LOCAL COORDINATE REFERENCE FRAMES 3-
3.3 Orientation of Local Member Reference Frame (The BETA Angle) 3-
Although the specification of joint coordinates and member incidences are necessary in order to uniquely and precisely describe the position of members of a structure in space, they are not sufficient specifications for the unique description of the orientation of a member's principal axes. In particular, specification of joint coordinates and member incidences describe only the precise position of a member's local x-axis, but do not describe the position of a member's local principal cross-section axes (i.e., the local member y and z axes) as shown in Figure 3.3. Rather, the precise position of a member's local y and z principal axes is defined relative to the global cartesian reference frame by an angle called the BETA angle. As shown in Section 8.4, the BETA angle is measured in the cross-section plane of the member from some initially assumed reference position (i.e., the BETA = 0.0° position). Sections 8.4, 8.5, and 8.6 describe the BETA angle in detail.
3.4
Local and Planar Finite Element Reference Frames
Two-dimensional (planar) finite elements in GTSTRUDL are associated with local, planar, and global reference frames, while three-dimensional (solid) finite elements are associated only with the global reference frame.
With the exception of the rigidity matrix property, finite element properties are independent of the local and planar finite element reference frames. However, the rigidity matrix property is always referenced to the planar reference frame for 2D planar finite elements, and referenced to the global reference frame for 3D solid finite elements. Finite element applied loads may be referenced to the local, planar, or global reference frames depending on the element type.
Finite element analysis results are output in the planar reference frame for 2D planar finite elements, and in the global reference frame for 3D solid finite elements.
Sections 3.4.1 and 3.4.2 provide a short description of the 2D finite element local and planar reference frames.
General Global and Local Coordinate Reference Frames
3.4.1
2D Finite Element Local Reference Frame
Each 2D (planar) finite element has a local reference frame (Figure 3.5) with which it is associated and which is defined as follows (where references to the order of the nodes of an element are based on the direction (i.e., clockwise or counterclockwise) in which the element nodes were specified when defining the incidences of the element):
1. The origin of the local reference frame is at the first node of the element, where the local x- and y-axes lie in the plane of the 2D element, and where the local z- axis is normal to the plane of the 2D element,
2. The positive direction of the local x-axis (xL) is from the first node to the second node of the element,
3. The positive direction of the local z-axis (zL) is determined by applying the right- hand rule to the order in which the element nodes were input, and
4. The positive direction of the local y-axis (yL) is determined by applying the right- hand rule to the xL and zL axes.
It is important to note the following regarding 2D finite element local reference frames: 1. The element's local x- and y-axes lie in the plane of the element, and their directions are dependent on the direction of the side of the element which goes from the first to the second node of the element (side 1).
2. For all 2D elements that lie in the same plane, the local axes are all parallel to each other and in the same positive directions only if side 1 of all the elements are parallel to each other, and only if the order of input of nodal incidences are the same.
3. It is often the case where the geometry of the finite element mesh is such that all 2D elements in the same plane do not have their first sides parallel to each other, resulting in local reference axes not being parallel to each other. In this case, it becomes extremely difficult to specify loadings applied to all elements which lie in the same plane, and to correctly interpret the finite element analysis results such as stresses (since stress results are referred to an element's reference axes). To solve this difficulty, GTSTRUDL provides a planar reference frame for
Global and Local Coordinate Reference Frames General
3.4.2
2D Finite Element Planar Reference Frame
Each 2D finite element has a planar reference frame (Figure 3.6) with which it is associated and which is defined as follows:
1. The origin of the planar reference frame is not of interest. Only the positive directions of the planar reference axes are of interest.
2. The positive direction of the planar z-axis (zp) is determined by applying the right- hand rule to the order (i.e., clockwise or counterclockwise) in which the element nodes were input (i.e., in the same positive direction as the local z-axis (zL)).
3. The direction of the planar x-axis (xp) lies along a line which is parallel to the line of intersection of the plane of the element and the Global XY plane. The positive direction of xp is determined as follows:
a. If the planar z-axis (zp) does not lie in a plane which is parallel to the
Global XZ plane, then the positive direction of the planar x-axis (xp) is such that its projection on the Global X-axis is in the positive direction of the Global X-axis.
b. If the planar z-axis (zp) does lie in a plane which is parallel to the Global XZ
plane, and if zp is parallel to the Global Z-axis, then the positive direction
of the planar x-axis (xp) is in the same positive direction as the Global X-
axis. If zp is not parallel to the Global Z-axis, then the positive direction of
the planar x-axis (xp) is in the same positive direction as the Global Y-axis.
4. The positive direction of the planar y-axis (yp) is determined by applying the right- hand rule to the xp and zp axes.
General Global and Local Coordinate Reference Frames
ELEMENT INCIDENCES 6 2 7 8 3
ELEMENT INCIDENCES 6 7 2 3 8
General Global and Local Coordinate Reference Frames
3.5
Local Joint Reference Frame
Each joint in a structure modeled with GTSTRUDL has a local joint reference frame and the global reference frame associated with it (Figures 3.7(a), (b), and (c)). Except for input describing certain structure boundary conditions, all other input joint data, and all output computed joint results, are referred to the global reference frame.
The only time the local joint reference frame is not parallel and in the same positive direction as the global reference frame is at a support joint where the displacement restraints and releases are not parallel to the global reference frame axes. In this case, the local reference frame is oriented parallel to the restraint and released directions. The orientation of a non-parallel local joint reference frame is given by the JOINT RELEASES command (Section 7.3).
Figure 3.7(d) shows a structure where only one support joint (joint 4) has a restraint direction non-parallel to global. Therefore, the only local joint reference frame which is non-parallel to global is at joint 4.
General General Commands and File Management
4.
General Commands and File Management
This Chapter describes the concept of "list" processing, default command file processing, general commands, and files created by GTSTRUDL, as follows:
Commands and Concepts Description 4.1 "list" Processing Forms of lists of names
4.2 STRUDL Initiate execution
4.3 FINISH Terminate execution and exit
4.4 CINPUT Read an external input file
4.5 COUTPUT Output to an external file
4.6 FLIST 1 and FLIST 2 Display system and user data files 4.7 SCAN Error Notice Error notification control
4.8 BYPASS Bypass following commands
4.9 UNITS Specify current units
4.10 QUERY Summarize current status
4.11 DEFINE GROUP Assigns collections of joint, member, finite element, or loading names to GROUP names
4.12 PRINT GROUP Print group data
4.13 DELETE GROUP Delete group data
4.14 PRINT GENERATE Controls output from automatic mesh generation commands
4.15. CONSISTENCY CHECK Perform a data consistency check 4.16 OPEN USERDATA FILE Open new or existing user data set
General Commands and File Management General
4.18 The GTSTRUDL Batch Processor Run one or more GTSTRUDL command files in a batch mode
4.19 LARGE PROBLEM SIZE Improve analysis performance for very large problems and speed of data base RESTORE processing
4.20 RUN Run DOS commands from a GTSTRUDL
command
4.21 ALIGN Adjust coordinates to assure members are parallel to the global Y-axis
4.22 NOTES Specify and store notes in connection with a structural model
4.23 PRINT COMMAND ARCHIVE Print commands and comments that are archived in files associated with data base SAVE files.
4.24 ACTIVE SOLVER Perform all subsequent static analyses using the GT64M or GTSES solvers, and Eigen solving using the GTSELANCZOS solver
4.25 DEFINE PHYSICAL MEMBER Define and smooth the design of physical SMOOTH PHYSICAL MEMBER members
General Commands "list" Options
4.1
"list" Options
Command elements:
"list" Options General Commands
Command elements:
alphalist = 'a1' ('a2'). . . integerlist = i1 (i2) . . .
'a1' ('a2')... = alphanumeric names each of from 1 to 8 characters enclosed in single quotes (apostrophes).
i1 (i2) ... = positive integer names
id1, id2 = first and last names (integer or alphanumeric) of a name
sequence.
n3 = integer increment used to generate the name sequence. If not specified, n3 = 1 or -1 depending on the value of id1 and id2. id4 = the name (integer or alphanumeric) of a previously defined
GROUP name (Chapter 4.13).
id5, id6 = first and last names (integer or alphanumeric) of a previously defined GROUP name (Chapter 4.13) sequence.
n7 = integer increment used to generate the GROUP name
sequence. If not specified, n7 = 1 or -1 depending on the value
of id5 and id6.
Example
DEFINE GROUP 'COLINE-A' MEMBERS 301 TO 320 DEFINE GROUP 'COLINE-B' MEMBERS 401 TO 420 MEMBER PROPERTIES
EXISTING AX 100 IZ 10000 $ For ALL currently active members CONSTANTS
BETA 90 MEMBERS 1 TO 31 BY 2
BETA 45 MEMBERS 101 107 200 TO 209 GRP LIST 'COLINE-A' 'COLINE-B' DENSITY EXISTING 490. BUT 301 305 GRP 'COLINE-B'
LOADING 1 'APPLIED MEMBER LOADS' MEMBER LOADS
EXISTING FOR Y UNIF W -1.5 $ Applied to all currently active members C
General Commands "list" Options
Explanation
In GTSTRUDL, all joints, members, finite elements, and independent and dependent loading conditions have names (id's) associated with them. These names can either be positive integer numbers, or they can be strings of from 1 to 8 alphanumeric characters (other than reserved characters such as the single quote or $ characters) enclosed in single quotes (apostrophes). The names are established and stored in the problem data base (Section 5.2) at the time a joint, member, finite element, or loading is referenced the first time in a GTSTRUDL execution, or during the creation of a finite element model using GTMenu.
Where the word "list" appears in a command description in this User Guide, and unless otherwise described, it means that a list of names may be given in the form described above.
Whenever a list of names is given in a command, the list may refer only to one type of entity (i.e., joints, members and finite elements, or loading conditions). Examples of different forms of "list" are presented after the following description of how the different forms of "list" operate:
1. alphalist:
This is a list of names where each name consists of a string of from 1 to 8 alphanumeric characters (other than reserved characters such as the single quote or $ characters) enclosed in single quotes (apostrophes).
2. integerlist:
This is a list of positive integer numbers in any sequence. 3. id1 TO id2 BY n3:
This is a list of consecutive names. The names are incremented or decremented as follows:
a. If the "BY n3" option is given, then n3 may be a positive or negative integer
and the names are incremented or decremented accordingly.
b. If the "BY n3" option is not given, then the names id1 TO id2 are incremented from id1 TO id2 by 1 if id1 is less than id2, or decremented from id1 TO id2 by -1 if id1 is greater than id2.
"list" Options General Commands
c. If id1 and id2 are alphanumeric names, then they are incremented or
decremented as follows:
(1) The alphanumeric name must be composed of two parts which are an alphanumeric prefix and an integer suffix. The alphanumeric prefix consists of the first string of characters in the name where the last character in the prefix is a character other than the integers 0 - 9. For example:
'BEAM10' 'COLA-15' 'ABC*100'
In the above names, the alphanumeric prefixes are "BEAM", "COLA- ", and "ABC*" respectively, while the integer suffixes are "10", "15", and "100" respectively.
(2) The integer suffix is then incremented/decremented according to the "BY n3" option.
4. GROUP or GRP:
A GROUP (Section 4.12) is associated with a list of joint, member and finite element, and/or loading condition names.
When the GROUP option is used, the group name is simply the name of a group which in turn is associated with a list of joint, member and finite element, and/or loading condition names. GROUP names may be specified as follows:
(a) id4:
Only one GROUP name may follow the word GROUP or GRP. The GROUP name may be a positive integer number or an alphanumeric string of from 1 to 8 characters enclosed in single quotes. If several GROUP names are to be given, then the LIST option must be used.
(b) LIST:
This option allows one or more GROUP names to be given as described by "group-list". If additional joint, member and finite element, or loading condition names are to be given in the "listi", then the list of GROUP names
must first be followed by the word JOINT, NODE, MEMBER, ELEMENT, or LOAD.
General Commands "list" Options
5. EXISTING:
The "alphalist", "integerlist", "id1 TO id2 BY n3", and GROUP options of specifying names requires using explicit names. For example, you cannot use the word "ALL" to mean all the joints, members, finite elements, or both members and finite elements. The "EXISTING" option provides a means of specifying "ALL". The word "ALL" is not permitted as part of a "list" since it will conflict with its use in certain other commands.
The use of EXISTING is context dependent. For example, it can mean all joints, or all members, or all finite elements, or all members and finite elements depending on the command in which EXISTING is used. Further, EXISTING only applies to the "structural components" referred to as joints, members, and finite elements, but not to loading conditions.
EXISTING operates as follows:
(a) If the MEMBERS, ELEMENTS, NLS or CABLES ONLY option is not given, then EXISTING refers to joint names, or member and finite element names. ACTIVE is the default.
(b) If the MEMBERS, ELEMENTS, NLS or CABLES ONLY option is given, then EXISTING refers ONLY to MEMBERS, ELEMENTS (i.e., finite elements), NLS (i.e., nonlinear springs), or CABLES (i.e., cable finite elements). ACTIVE is the default.
(c) Only ACTIVE, INACTIVE, or both ACTIVE and INACTIVE structural components will be referenced depending on the use of the respective word. ACTIVE is the default.
(d) Any name that is given in, or implied by, the "list2" or "BUT list3" options will
be used as long as the name exists in the current GTSTRUDL data base (i.e., it has been referenced in a previous command and has not been previously deleted). Any name given or implied by list2 and list3 that does not exist in the current data base is ignored during the processing of these lists (i.e., such nonexistent names are neither created nor added to the data base).
(e) If a "list2" has been given, then only the names that exist in the current
GTSTRUDL data base are used (i.e., the names that have been referenced in previous commands and which have not been previously deleted are used). The other names in the "list2" are ignored.
(f) If a "list2" has not been given, then all names that exist in the current GTSTRUDL data base for the particular structural component being
"list" Options General Commands
(g) Any name that is from the "BUT list3" option operates as follows:
(1) If a "list2" has been given, then the names used from "list3" are subtracted from the names used from "list2". The remaining names are then sorted in the same order as is ordered by the OUTPUT ORDERED command (Section 13.2).
(2) If a "list2" has not been given, then the names used from "list3" are
subtracted from all names that currently exist in the data base for the particular structural component being referenced by the command in which EXISTING is used. The remaining names are then sorted in the same order as is ordered by the OUTPUT ORDERED command (Section 13.2).
(h) Any name that is given in, or implied by, the "PLUS list4" option will be used if it exists in the current GTSTRUDL data base or, if it does not exist in the current data base, it will be created and placed in the data base as a new existing structural component.
Examples of Different Forms of "list"
4 or 'COLUMN1': A single name is a list.
'L2', 105, 'LOAD1' 'LOAD2' 4 5: Integer and alphanumeric names can be mixed, and spaces and commas are equivalent.
'J9' 6 TO 10 23 25: This list contains eight names which are: 'J9', 6, 7, 8, 9, 10, 23 and 25.
17, 18, 21, 2 TO 10 BY 2, 22 TO 13 BY -3, 33 TO 29:
This list contains seventeen names which are: 17, 18, 21, 2, 4, 6, 8, 10, 22, 19, 16, 13, 33, 32, 31, 30 and 29.
General Commands "list" Options
'JT-3' TO 'JT-7': This list contains seven names which are: 'JT-3' 'JT-4' 'JT-5' 'JT-6' 'JT-7'
GRP 1 GRP 2 GRP 3 10 TO 15
This list will contain the names associated with GROUP 1, 2 and 3, and the structural component names 10, 11, 12, 13, 14 and 15.
GRP LIST 1 TO 7 BY 2 4 10
This list will contain the names associated with GROUP 1, 3, 5, 7, 4 and 10. GROUP LIST 1 TO 4 7 JOINT 17 19
This list will contain the joint names associated with GROUP 1, 2, 3, 4 and 7, and the joint names 17 and 19 .
EXISTING
Depending on the context of the command, all names of currently active structural components are included in this list. For example, all active joints, or all active members and finite elements.
EXISTING 1 TO 100
This list will contain the names of all currently active structural components whose names lie in the range of 1 to 100. Any names in the range of 1 to 100 that are the names of inactive structural components, or which do not exist in the current GTSTRUDL data base are ignored. For example, all active members and finite elements whose names lie in the range 1 to 100.
EXISTING ELEMENTS ONLY
This list will only contain the names of all currently active finite elements. EXISTING MEMBERS ONLY
"list" Options General Commands
EXISTING INACTIVE
All names of currently inactive structural components are included in this list. EXISTING BUT 4 TO 12 BY 2
The names of all currently active structural components, except for those whose names are 4, 6, 8, 10, or 12, are included in this list.
EXISTING MEMBERS ONLY 1 TO 20 BUT 5 TO 17 BY 3
The names of all currently active members whose names lie in the range 1 to 20, except those whose names are 5, 8, 11, 14 or 17, are included in this list. EXISTING PLUS 201 to 231 by 2
The names of all currently active structural components, plus those structural components whose names lie in the range 201 to 231 by 2, are included in this list. In addition, any structural components whose names do not appear in the range 201 to 231 by 2 are created and added to the currently active GTSTRUDL data base, and they are included in this list of names.
1 TO 11 BY 3
The sequence 1, 4, 7, 10 is generated, but a warning message is issued stating that the incrementation sequence does not terminate on the number 11. In this case, the number 11 is ignored.
'A1' TO 'B5'
The alphanumeric prefixes in the range of names are not the same. The two names specified are ignored.
GROUP LIST 1 TO 5 10 15 MEMBER 54
If the GROUP option is given in a command that references JOINT names, the word MEMBER will cause list processing for the joint list to terminate. The joint