# Nonlinear finite elements/Homework 6/Solutions/Problem 2
## Problem 2: Exploring commercial software

Track down the different types of beam and shell elements that ANSYS and LS-DYNA provide. For each element that you find, answer the following
* What is the name of the element?
* How many nodes does the element have?
* How many displacement type (displacements, rotations) degrees of freedom are there at each node?List them.
* How many force type (forces, moments) boundary conditions can be applied at each node?List them.
* What is the form of the shape functions used by the element? (Alternatively, you may write down the approximate solutions assumed by the element.)
* Is the beam element a continuum-based one or one derived from the equations of beam theory?
* Does the element allow for full and reduced integration?
ANSYS Beam Elements :
| Element name | Description | Nodes | Degree of freedom | Load | Shape function | Theory | Full/reduced integration |
| BEAM3 | 2D elastic | 2 | $u_{x},u_{y},\theta _{z}$ | $F_{x},F_{y},M_{z}$ | $**$ | $*$ | no |
| BEAM4 | 3D elastic | 2 | $u_{x},u_{y},u_{z}$ $\theta _{x},\theta _{y},\theta _{z}$ | $F_{x},F_{y},F_{z}$ $M_{x},M_{y},M_{z}$ | $**$ | $*$ | no |
| BEAM23 | 2D plastic | 2 | $u_{x},u_{y},\theta _{z}$ | $F_{x},F_{y},M_{z}$ | $**$ | $*$ | no |
| BEAM24 | 3D thin-walled | 2 | $u_{x},u_{y},u_{z}$ $\theta _{x},\theta _{y},\theta _{z}$ | $F_{x},F_{y},F_{z}$ $M_{x},M_{y},M_{z}$ | $**$ | $*$ | no |
| BEAM44 | 3D elastic tapered unsymmetric | 2 | $u_{x},u_{y},u_{z}$ $\theta _{x},\theta _{y},\theta _{z}$ | $F_{x},F_{y},F_{z}$ $M_{x},M_{y},M_{z}$ | $**$ | $*$ | no |
| BEAM54 | 2D elastic tapered unsymmetric | 2 | $u_{x},u_{y},\theta _{z}$ | $F_{x},F_{y},M_{z}$ | $**$ | $*$ | no |
| BEAM161 | Explicit 3D | 2 | $u_{x},u_{y},u_{z}$ $v_{x},v_{y},v_{z}$ $a_{x},a_{y},a_{z}$ $\theta _{x},\theta _{y},\theta _{z}$ | $F_{x},F_{y},M_{z}$ | $**$ | $*$ | no |
| BEAM188 | 3D linear finite strain | 3 | $u_{x},u_{y},u_{z}$ $\theta _{x},\theta _{y},\theta _{z}$ | $F_{x},F_{y},F_{z}$ $M_{x},M_{y},M_{z}$ | $**$ | Beam | no |
| BEAM189 | 3D quadratic finite strain | 4 | $u_{x},u_{y},u_{z}$ $\theta _{x},\theta _{y},\theta _{z}$ | $F_{x},F_{y},F_{z}$ $M_{x},M_{y},M_{z}$ | $**$ | Beam | no |
| $*$ not specified by the software. ||||||||
| $**$ see ANSYS Theory Reference: Chapter 14. ||||||||
ANSYS Shell Elements :
| Element name | Description | Nodes | Degree of freedom | Load | Shape function | Full/reduced integration |
| SHELL28 | Shear/twisted panel | 4 | $u_{x},u_{y},u_{z}$ $\theta _{x},\theta _{y},\theta _{z}$ | $F_{x},F_{y},F_{z}$ $M_{x},M_{y},M_{z}$ | $**$ | no |
| SHELL41 | Membrane | 4 | $u_{x},u_{y},u_{z}$ | $F_{x},F_{y},F_{z}$ | $**$ | no |
| SHELL43 | Plastic large strain | 4 | $u_{x},u_{y},u_{z}$ $\theta _{x},\theta _{y},\theta _{z}$ | $F_{x},F_{y},F_{z}$ $M_{x},M_{y},M_{z}$ | $**$ | no |
| SHELL51 | Asymmetric | 2 | $u_{x},u_{y},\theta _{z}$ | $F_{x},F_{y},F_{z}$ $M_{z}$ | $**$ | no |
| SHELL57 | Thermal | 4 | Temperature | $T,q$ | $**$ | no |
| SHELL61 | Asymmetric- harmonic | 2 | $u_{x},u_{y},u_{z},\theta _{z}$ | $F_{x},F_{y},F_{z}$ $M_{z}$ | $**$ | no |
| SHELL63 | Elastic | 4 | $u_{x},u_{y},u_{z}$ $\theta _{x},\theta _{y},\theta _{z}$ | $F_{x},F_{y},F_{z}$ $M_{x},M_{y},M_{z}$ | $**$ | no |
| SHELL91 | Nonlinear layered | 8 | $u_{x},u_{y},u_{z}$ $\theta _{x},\theta _{y},\theta _{z}$ | $F_{x},F_{y},F_{z}$ $M_{x},M_{y},M_{z}$ | $**$ | no |
| SHELL99 | Linear layered | 8 | $u_{x},u_{y},u_{z}$ $\theta _{x},\theta _{y},\theta _{z}$ | $F_{x},F_{y},F_{z}$ $M_{x},M_{y},M_{z}$ | $**$ | no |
| SHELL143 | Plastic small strain | 4 | $u_{x},u_{y},u_{z}$ $\theta _{x},\theta _{y},\theta _{z}$ | $F_{x},F_{y},F_{z}$ $M_{x},M_{y},M_{z}$ | $**$ | no |
| SHELL150 | p-Element | 8 | $u_{x},u_{y},u_{z}$ $\theta _{x},\theta _{y},\theta _{z}$ | $F_{x},F_{y},F_{z}$ $M_{x},M_{y},M_{z}$ | $**$ | no |
| SHELL157 | Thermal | 4 | Temperature current | $T,q,I,V$ | $**$ | no |
| SHELL163 | Explicit thin | 4 | $u_{x},u_{y},u_{z}$ $v_{x},v_{y},v_{z}$ $a_{x},a_{y},a_{z}$ $\theta _{x},\theta _{y},\theta _{z}$ | $F_{x},F_{y},F_{z}$ $M_{x},M_{y},M_{z}$ | $**$ | no |
| SHELL181 | Finite strain layered | 4 | $u_{x},u_{y},u_{z}$ $\theta _{x},\theta _{y},\theta _{z}$ | $F_{x},F_{y},F_{z}$ $M_{x},M_{y},M_{z}$ | $**$ | yes |
| $^{**}$ see ANSYS Theory Reference: Chapter 14. |||||||
LS-DYNA BEAM Elements: ELFORM 1-9$^{**}$ :
| Element name | Nodes | Degree of freedom | Load | Shape function | Theory | Full/reduced integration |
| Belytschko | 2 | $u_{x},u_{y},u_{z}$ $\theta _{x},\theta _{y},\theta _{z}$ | $F_{x},F_{y},F_{z}$ $M_{x},M_{y},M_{z}$ | $*$ | C-B | $***$ |
| Hughes-Liu | 8 | $u_{x},u_{y},u_{z}$ $\theta _{x},\theta _{y},\theta _{z}$ | $F_{x},F_{y},F_{z}$ $M_{x},M_{y},M_{z}$ | $**$ | C-B | $***$ |
| $*$ see LS-DYNA Theory Manual: Chapter 4-5 |||||||
| $^{**}$ see LS-DYNA User Keyword Manual: Chapter 26: $^{*}$SECTION. |||||||
| $^{***}$ depends on chosen ELFORM. |||||||
LS-DYNA SHELL Elements: ELFORM 1-18,20-22,31,32,43,44,99$^{**}$ :
| Element name | Nodes | Degree of freedom | Load | Shape function | Theory |
| Belytschko-Lin-Tsay | 4 | $u_{x},u_{y},u_{z}$ $\theta _{x},\theta _{y},\theta _{z}$ | $F_{x},F_{y},F_{z}$ $M_{x},M_{y},M_{z}$ | $*$ | $***$ |
| C0 triangular | 3 | $u_{x},u_{y},u_{z}$ $\theta _{x},\theta _{y},\theta _{z}$ | $F_{x},F_{y},F_{z}$ $M_{x},M_{y},M_{z}$ | $*$ | $***$ |
| Marchertas-Belytschko Triangular | 3 | $u_{x},u_{y},u_{z}$ $\theta _{x},\theta _{y},\theta _{z}$ | $F_{x},F_{y},F_{z}$ $M_{x},M_{y},M_{z}$ | $*$ | $***$ |
| Hughes-Liu | 4 | $u_{x},u_{y},u_{z}$ $\theta _{x},\theta _{y},\theta _{z}$ | $F_{x},F_{y},F_{z}$ $M_{x},M_{y},M_{z}$ | $*$ | $***$ |
| 8-node solid | 8 | $u_{x},u_{y},u_{z}$ $\theta _{x},\theta _{y},\theta _{z}$ | $F_{x},F_{y},F_{z}$ $M_{x},M_{y},M_{z}$ | $*$ | $***$ |
| $^{*}$ see LS-DYNA Theory Manual: Chapter 6-10. ||||||
| $^{**}$ see LS-DYNA User Keyword Manual: Chapter 26: $^{*}$SECTION. ||||||
| $^{***}$ depends on chosen ELFORM. ||||||