Assumption 2: The stress in the direction normal to the mi
2.5 Solid eleme
only b
the 4-node element is used in problems where bending effects are sig
• Fo tic
materi axisym eleme
2.5 Solid eleme
2.5.1 Gene
e CHEXA, CPENTA , TETRA and CPYRAM element connectivity entries. They
n
r all of the supported perelastic which uses PLSOLID.
•
e
edron, node brick elements).
dations on use of elements
e 9-node element is usually the most effe
The linear interpolation elements (3-node and 4-node) should e used in analyses when bending effects are not dominant. If nificant, incompatible modes should be activated.
r nearly incompressible elastic materials, elasto-plas als and creep materials, and when using plane strain or
metric elements, the use of the u/p mixed formulation nts is recommended.
nts – 3-D
ral considerations
3-D solid elements are generated using th
• C
ge erate 6-, 5- and 4-sided 3-D elements. Typical 3-D solid elements are shown in Fig 2.5-1.
• The PSOLID property ID entry is used fo materials, except hy
• 3-D solid elements in Advanced Nonlinear Solution are classified based on the number of nodes in the element, and the element shape.
Table 2.5-1 shows the correspondence between the different 3-D solid elements and the NX element connectivity entries. Not that the elements are frequently referred to just by their number of nodes.
• Solution 701 only supports linear elements (4-node tetrah 6-node wedge and
8-ll
(a) 8-, 20- and 27-node brick elements (CHEXA)
(b) 4-, 10- and 11-node tetrahedral elements (CTETRA)
ll
(c) 6-, 15-, and 21-node wedge elements (CPENTA)
l
(d) 5-, 13-, and 14-pyramid elements (CPYRAM)
Figure 2.5-1: 3-D solid elements
3-D solid element NX element connectivity entry 4-node tetrahedron CTETRA
10-11- TRA and ELCV = 1 in NXSTRAT
1 2
rick CHEXA
2
2 AT
5 13
14 RAM and ELCV = 1 in NXSTRAT
node tetrahedron1 CTETRA node tetrahedron1 CTE
6-node wedge CPENTA
5-node wedge1 CPENTA
1-node wedge1 CPENTA and ELCV = 1 in NXSTRAT 8-node b
0-node brick1 CHEXA
7-node brick1 CHEXA and ELCV = 1 in NXSTR
-node pyramid CPYRAM
-node pyramid1 CPYRAM
-node pyramid1 CPY Note:
1. Only for Solution 601
able 2.5-1: Correspondence between 3-D solid elements and NX element connectivity entries
T
lements.
id
elements are output in the element coordinate system. ELRESCS = stress/strain results in the material coordinate system. The option is
• Advanced Nonlinear Solution supports incomplete quadratic 3-D elements for tetrahedral and pyramid elements. Incomplete quadratic elements are not supported for brick and wedge e For example, a CHEXA entry can only have 8 nodes or 20 nodes.
Anything in between is not supported. Also, a CTETRA can have any of its midside nodes removed.
• For nonlinear analysis, stress/strain results for 3-D sol 1 in NXSTRAT may be used to request output of nonlinear useful for post-processors that do not perform any transformation of the stress/strain coordinate system when importing the op2 file.
olume and midsurface nodes in the 27-node, 1-node, 14-node and 11-node elements are automatically added by Advanced Nonlinear Solution when ELCV is set to 1 in the
NX at the added nodes are
predicted from the neighboring nodes.
• d Nonlinear Solution are
oparametric displacement-based elements, and their formulation is d
The basic finite element assumptions for the coordinates are
1
i i i
i i i
• Note that the mid-v 2
STRAT entry. The boundary conditions
The elements used in Advance is
escribed in ref. KJB, Section 5.3.
•
(see Fig. 2.5-2, for the brick element):
q q q
n for the displacements:
i Poisson's ratio is close to 0.5, for rubber-like materials and for elasto-plastic materials). Table 2.5-2 shows the number of pressure degrees of freedom for each 3-D element type. For more details on the mixed interpolation of pressure and displacement degrees of freedom for 3-D solids, see Section 4.4.3, p. 276, and Tables 4.6 and 4.7, pp. 292 - 295 in ref. KJB.
• In addition to the displacement-based elements, special mixed-interpolated elements are also available, in which the displacements and pressure are interpolated separately. These elements are effective and should be preferred in the analysis of incompress media and inelastic materials (specifically for materi
3
l
Figure 2.5-2: Conventions used for the nodal coordinates and displacements of the 3-D solid element
Number of 3-D solid element pressure DOFs
4-node tetrahedron -
10-node, 11-node tetrahedron 4
5-node pyramid 1
13-node, 14-node pyramid 1
6-node wedge 1
15-node, 21-node wedge 4
8-node brick 1
20-node, 27-node brick 4
Table 2.5-2: Mixed u/p formulations available for 3-D solid elements
• The mixed formulation is the default setting for hyperelastic materials, and it can be activated for other materials, such as elastic-plastic, creep, and elastic with high Poisson’s ratio, via the UPFORM flag in the NXSTRAT entry.
• The use of the 8-node (one pressure DOF) or 27-node (4 pressure DOFs) element is recommended with the mixed formulation.
• Note that 4 pressure degrees of freedom are used for the 10-node tetrahedron, the 15-10-node wedge and the 20-10-node brick element. Even though this setting does not satisfy the inf-sup test, the elements generally perform better than with a single pressure
egree of freedom. Still, it is better to add the midside nodes if
ee
element distortions deteriorate the element performance when incompatible modes are used.
The incompatible modes feature cannot be used in conjunction with the mixed-interpolation formulation
• Table 2.5-3 shows which elements support incompatible modes (bubble functions). The incompatible modes feature is only available for the 5-node pyramid, 6- node wedge and the 8-node brick elements.
d
possible. This is done by setting ELCV = 1 in the NXSTRAT entry.
• In addition to the displacement-based and mixed-interpolated elements, Advanced Nonlinear Solution also includes the
possibility of including incompatible modes (bubble functions) in the formulation of the 5-node pyramid, 6-node wedge and the 8-node brick element. Within this element, additional displacement degrees of freedom are introduced. These additional displacement degrees of freedom are not associated with nodes; therefore the condition of displacement compatibility between adjacent elements is not satisfied in general. The addition of the incompatible modes (bubble functions) increases the flexibility of the element,
especially in bending situations. For theoretical considerations, s reference KJB, Section 4.4.1. Note that these incompatible-mode elements are formulated to pass the patch test. Also note that
3-D solid element
Support for incompatible
modes
4-node tetrahedron No
5- to 11-node tetrahedron No
6-node wedge Yes
15-node, 21-node wedge No
8-node brick Yes
20-node, 27-node brick No
5-node pyramid Yes
6- to 14-node pyramid No
atible modes (bubble functions) available for 3-D lements
ifferent local node numbering convention).
d sides of rectangular elements. Spatially otropic 10-node and 11-node tetrahedra are used in Solution 601.
e 8-node rectangular element. This lement exhibits constant strain conditions.
ses/strains can be output either at the center and corner rid points (PSOLID STRESS=blank or GRID), or at the center
2.5.2 Mate
rial models that are ompatible with 3-D solid elements.
Table 2.5-3: Incomp solid e
• The interpolation functions used for 3-D solid elements for q ≤ 20 are shown in Fig. 5.5, ref. KJB, p. 345 (note that ref KJB uses a d
• The 10-node tetrahedron (see Fig. 2.5-1(c)) is obtained by collapsing nodes an
is
The 4-node tetrahedron (see Fig. 2.5-1(c)) is obtained by collapsing nodes and sides of th
e
• The stres g
and corner Gauss points (PSOLID STRESS=1 or GAUSS).
rial models and nonlinear formulations
• See Tables 2-2 and 2-3 for a list of the mate c
anced Nonlinear Solution automatically uses the mixed terpolation formulation for hyperelastic materials. The mixed
and . It can be tivated by setting UPFORM = 1 in the NXSTRAT entry.
ematics can be used with any of the compatible material models, except for the hyperelastic material. The use of a linear material with small
displacement/small strain kinematics corresponds to a linear formulation, and the use of a nonlinear material with the small displacement/small strain kinematics corresponds to a materially-nonlinear-only formulation.
The program uses the TL (total Lagrangian) formulation when large displacement/small strain kinematics is selected.
The large displacement/large strain kinematics can be used with plastic materials including thermal and creep effects, as well as hyperelastic materials. The ULH (updated
Lagrangian Hencky) formulation or the ULJ (updated Lagrangian Jaumann) formulation can be used for all compatible material models except the hyperelastic material.
For the hyperelastic material models, a TL (total Lagrangian) formulation is used. The ULFORM parameter in the
NXSTRAT entry determines the ULH/ULJ setting.
The basic continuum mechanics formulations are described in
ref. KJB Sections 6.
• Adv in
formulation is also recommended for elastic-plastic materials elastic materials with a Poisson ratio close to 0.5
ac
• The 3-D elements can be used with
- small displacement/small strain kinematics,
- large displacement/small strain kinematics, or - large displacement/large strain kinematics.
The small displacement/small strain and large displacement/small strain kin
•
ref. KJB, pp. 497-568. The finite element discretization is summarized in Table 6.6, p. 555, ref. KJB.
2 and 6.3.5
l .
2.5.3 Num
the lements
Tetrahedral elements are spatially isotropic with respect to tegration point locations and interpolation functions. For the 4-ode tetrahedral element, 1-point Gauss integration is used. For the 0-node tetrahedral element, 17-point Gauss integration is used,
al os
ion order is used for both Solution 601 and 01
2.5.4 Mas
• Note that all these formulations can be used in the same finite element model. If the elements are initially compatible, they wil remain compatible throughout the analysis
erical integration
• The 8-node brick element uses 2×2×2Gauss integration for calculation of element matrices. The 20-node and 27-node e use 3×3×3Gauss integration.
• in n 1
and 17-point Gauss integration is also used for the 11-node tetrahedral element.
• Note that in geometrically nonlinear analysis, the spati p itions of the Gauss integration points change continuously as the element undergoes deformations, but throughout the response the same material particles are at the integration points.
• The same integrat 7 .
s matrices
• The consistent mass matrix is always calculated using 3×3×3 Gauss integration except for the tetrahedral 4-node, 10-node and 11-node elements which use a 17-point Gauss integration.
• The lumped mass matrix of an element is formed by dividing the element’s mass M equally among each of its n nodal points.
Hence the mass assigned to each node is M n/ . No special distributory concepts are employed to distinguish between corner
nd midside nodes, or to account fo
a r element distortion.
ref. KJB Section 6.8.1
ref. KJB Sections 5.5.3, 5.5.4 and 5.5.
• The same lumped matrix is used for both Solution 601 and Solution 701.
5
2.5.5 Heat transfer capabilities
! Heat transfer capabilities are available for all 3-D solid lements.
tegration using the same integration order as the structural
an be calculated based on a lumped or onsistent heat capacity assumption.
The lumped heat capacity matrix of an element is formed by ding the element’s total heat capacity C equally among each of s n nodal points. Hence the mass assigned to each node is
guish etween corner and midside nodes, or to account for element
. 2.5.6 Reco
lation elements (4- to 8-node) usually perform etter in contact problems.
The linear interpolation elements (5-node, 6-node and 8-node ffects are not dominant. If bending ffects are insignificant, it is usually best to not use incompatible
n element, many lements (fine meshes) must usually be used in analyses.
e elastic materials, elasto-plastic materials and creep materials, the use of the u/p mixed formulation
odeled has a dimension which is xtremely small compared with the others, e.g., thin plates and e
! One temperature degree of freedom is present at each node.
! The element matrices are integrated numerically by Gauss in
No special distributory concepts are employed to distin b
distortion
mmendations on use of elements
• The linear interpo b
•
brick elements, without incompatible modes) should only be used in analyses when bending e
e modes.
• Since the 4-node tetrahedron is a constant strai e
• For nearly incompressibl elements is recommended.
• When the structure to be m e
use of the 3-D solid element usually results in too stiff a s, particularly the 4-node shell element (see ection 2.3), is more effective.
ecommendations specific to Solution 601
The 27-node element is the most accurate among all available e costly.
ially if
2.6 Scalar
2.6.1 CEL
r Solution either connect deg f freedom r or just a egree of fr to the ground. There are three forms of scalar elements: spri
masses, and dampers.
ring elements are defined using the CELAS1 and
ASS2 el connectivit es.
per element defined using CDAMP1 an
single degree of
model and a poor conditioning of the stiffness matrix. In this case, the use of shell element
S R
•
elements. However, the use of this element can b
• The 20-node element is usually the most effective, espec the element is rectangular (undistorted).