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

1. What is the name of the element?
2. How many nodes does the element have?
3. How many displacement type (displacements, rotations) degrees of freedom are there at each node?List them.
4. How many force type (forces, moments) boundary conditions can be applied at each node?List them.
5. What is the form of the shape functions used by the element? (Alternatively, you may write down the approximate solutions assumed by the element.)
6. Is the beam element a continuum-based one or one derived from the equations of beam theory?
7. Does the element allow for full and reduced integration?

Element name Description Nodes Degree of freedom Load Shape function Theory Full/reduced integration ANSYS Beam Elements BEAM3 2D elastic 2 ${\displaystyle u_{x},u_{y},\theta _{z}}$ ${\displaystyle F_{x},F_{y},M_{z}}$ ${\displaystyle **}$ ${\displaystyle *}$ no BEAM4 3D elastic 2 ${\displaystyle u_{x},u_{y},u_{z}}$  ${\displaystyle \theta _{x},\theta _{y},\theta _{z}}$ ${\displaystyle F_{x},F_{y},F_{z}}$  ${\displaystyle M_{x},M_{y},M_{z}}$ ${\displaystyle **}$ ${\displaystyle *}$ no BEAM23 2D plastic 2 ${\displaystyle u_{x},u_{y},\theta _{z}}$ ${\displaystyle F_{x},F_{y},M_{z}}$ ${\displaystyle **}$ ${\displaystyle *}$ no BEAM24 3D thin-walled 2 ${\displaystyle u_{x},u_{y},u_{z}}$  ${\displaystyle \theta _{x},\theta _{y},\theta _{z}}$ ${\displaystyle F_{x},F_{y},F_{z}}$  ${\displaystyle M_{x},M_{y},M_{z}}$ ${\displaystyle **}$ ${\displaystyle *}$ no BEAM44 3D elastic tapered unsymmetric 2 ${\displaystyle u_{x},u_{y},u_{z}}$  ${\displaystyle \theta _{x},\theta _{y},\theta _{z}}$ ${\displaystyle F_{x},F_{y},F_{z}}$  ${\displaystyle M_{x},M_{y},M_{z}}$ ${\displaystyle **}$ ${\displaystyle *}$ no BEAM54 2D elastic tapered unsymmetric 2 ${\displaystyle u_{x},u_{y},\theta _{z}}$ ${\displaystyle F_{x},F_{y},M_{z}}$ ${\displaystyle **}$ ${\displaystyle *}$ no BEAM161 Explicit 3D 2 ${\displaystyle u_{x},u_{y},u_{z}}$  ${\displaystyle v_{x},v_{y},v_{z}}$  ${\displaystyle a_{x},a_{y},a_{z}}$  ${\displaystyle \theta _{x},\theta _{y},\theta _{z}}$ ${\displaystyle F_{x},F_{y},M_{z}}$ ${\displaystyle **}$ ${\displaystyle *}$ no BEAM188 3D linear finite strain 3 ${\displaystyle u_{x},u_{y},u_{z}}$  ${\displaystyle \theta _{x},\theta _{y},\theta _{z}}$ ${\displaystyle F_{x},F_{y},F_{z}}$  ${\displaystyle M_{x},M_{y},M_{z}}$ ${\displaystyle **}$ Beam no BEAM189 3D quadratic finite strain 4 ${\displaystyle u_{x},u_{y},u_{z}}$  ${\displaystyle \theta _{x},\theta _{y},\theta _{z}}$ ${\displaystyle F_{x},F_{y},F_{z}}$  ${\displaystyle M_{x},M_{y},M_{z}}$ ${\displaystyle **}$ Beam no ${\displaystyle *}$  not specified by the software. ${\displaystyle **}$  see ANSYS Theory Reference: Chapter 14.
Element name Description Nodes Degree of freedom Load Shape function Full/reduced integration ANSYS Shell Elements SHELL28 Shear/twisted panel 4 ${\displaystyle u_{x},u_{y},u_{z}}$  ${\displaystyle \theta _{x},\theta _{y},\theta _{z}}$ ${\displaystyle F_{x},F_{y},F_{z}}$  ${\displaystyle M_{x},M_{y},M_{z}}$ ${\displaystyle **}$ no SHELL41 Membrane 4 ${\displaystyle u_{x},u_{y},u_{z}}$ ${\displaystyle F_{x},F_{y},F_{z}}$ ${\displaystyle **}$ no SHELL43 Plastic large strain 4 ${\displaystyle u_{x},u_{y},u_{z}}$  ${\displaystyle \theta _{x},\theta _{y},\theta _{z}}$ ${\displaystyle F_{x},F_{y},F_{z}}$  ${\displaystyle M_{x},M_{y},M_{z}}$ ${\displaystyle **}$ no SHELL51 Asymmetric 2 ${\displaystyle u_{x},u_{y},\theta _{z}}$ ${\displaystyle F_{x},F_{y},F_{z}}$  ${\displaystyle M_{z}}$ ${\displaystyle **}$ no SHELL57 Thermal 4 Temperature ${\displaystyle T,q}$ ${\displaystyle **}$ no SHELL61 Asymmetric- harmonic 2 ${\displaystyle u_{x},u_{y},u_{z},\theta _{z}}$ ${\displaystyle F_{x},F_{y},F_{z}}$  ${\displaystyle M_{z}}$ ${\displaystyle **}$ no SHELL63 Elastic 4 ${\displaystyle u_{x},u_{y},u_{z}}$  ${\displaystyle \theta _{x},\theta _{y},\theta _{z}}$ ${\displaystyle F_{x},F_{y},F_{z}}$  ${\displaystyle M_{x},M_{y},M_{z}}$ ${\displaystyle **}$ no SHELL91 Nonlinear layered 8 ${\displaystyle u_{x},u_{y},u_{z}}$  ${\displaystyle \theta _{x},\theta _{y},\theta _{z}}$ ${\displaystyle F_{x},F_{y},F_{z}}$  ${\displaystyle M_{x},M_{y},M_{z}}$ ${\displaystyle **}$ no SHELL99 Linear layered 8 ${\displaystyle u_{x},u_{y},u_{z}}$  ${\displaystyle \theta _{x},\theta _{y},\theta _{z}}$ ${\displaystyle F_{x},F_{y},F_{z}}$  ${\displaystyle M_{x},M_{y},M_{z}}$ ${\displaystyle **}$ no SHELL143 Plastic small strain 4 ${\displaystyle u_{x},u_{y},u_{z}}$  ${\displaystyle \theta _{x},\theta _{y},\theta _{z}}$ ${\displaystyle F_{x},F_{y},F_{z}}$  ${\displaystyle M_{x},M_{y},M_{z}}$ ${\displaystyle **}$ no SHELL150 p-Element 8 ${\displaystyle u_{x},u_{y},u_{z}}$  ${\displaystyle \theta _{x},\theta _{y},\theta _{z}}$ ${\displaystyle F_{x},F_{y},F_{z}}$  ${\displaystyle M_{x},M_{y},M_{z}}$ ${\displaystyle **}$ no SHELL157 Thermal 4 Temperature current ${\displaystyle T,q,I,V}$ ${\displaystyle **}$ no SHELL163 Explicit thin 4 ${\displaystyle u_{x},u_{y},u_{z}}$  ${\displaystyle v_{x},v_{y},v_{z}}$  ${\displaystyle a_{x},a_{y},a_{z}}$  ${\displaystyle \theta _{x},\theta _{y},\theta _{z}}$ ${\displaystyle F_{x},F_{y},F_{z}}$  ${\displaystyle M_{x},M_{y},M_{z}}$ ${\displaystyle **}$ no SHELL181 Finite strain layered 4 ${\displaystyle u_{x},u_{y},u_{z}}$  ${\displaystyle \theta _{x},\theta _{y},\theta _{z}}$ ${\displaystyle F_{x},F_{y},F_{z}}$  ${\displaystyle M_{x},M_{y},M_{z}}$ ${\displaystyle **}$ yes ${\displaystyle ^{**}}$  see ANSYS Theory Reference: Chapter 14.
Element name Nodes Degree of freedom Load Shape function Theory Full/reduced integration LS-DYNA BEAM Elements: ELFORM 1-9${\displaystyle ^{**}}$ Belytschko 2 ${\displaystyle u_{x},u_{y},u_{z}}$  ${\displaystyle \theta _{x},\theta _{y},\theta _{z}}$ ${\displaystyle F_{x},F_{y},F_{z}}$  ${\displaystyle M_{x},M_{y},M_{z}}$ ${\displaystyle *}$ C-B ${\displaystyle ***}$ Hughes-Liu 8 ${\displaystyle u_{x},u_{y},u_{z}}$  ${\displaystyle \theta _{x},\theta _{y},\theta _{z}}$ ${\displaystyle F_{x},F_{y},F_{z}}$  ${\displaystyle M_{x},M_{y},M_{z}}$ ${\displaystyle **}$ C-B ${\displaystyle ***}$ ${\displaystyle *}$  see LS-DYNA Theory Manual: Chapter 4-5 ${\displaystyle ^{**}}$  see LS-DYNA User Keyword Manual: Chapter 26: ${\displaystyle ^{*}}$ SECTION. ${\displaystyle ^{***}}$  depends on chosen ELFORM.
Element name Nodes Degree of freedom Load Shape function Theory LS-DYNA SHELL Elements: ELFORM 1-18,20-22,31,32,43,44,99${\displaystyle ^{**}}$ Belytschko-Lin-Tsay 4 ${\displaystyle u_{x},u_{y},u_{z}}$  ${\displaystyle \theta _{x},\theta _{y},\theta _{z}}$ ${\displaystyle F_{x},F_{y},F_{z}}$  ${\displaystyle M_{x},M_{y},M_{z}}$ ${\displaystyle *}$ ${\displaystyle ***}$ C0 triangular 3 ${\displaystyle u_{x},u_{y},u_{z}}$  ${\displaystyle \theta _{x},\theta _{y},\theta _{z}}$ ${\displaystyle F_{x},F_{y},F_{z}}$  ${\displaystyle M_{x},M_{y},M_{z}}$ ${\displaystyle *}$ ${\displaystyle ***}$ Marchertas-Belytschko Triangular 3 ${\displaystyle u_{x},u_{y},u_{z}}$  ${\displaystyle \theta _{x},\theta _{y},\theta _{z}}$ ${\displaystyle F_{x},F_{y},F_{z}}$  ${\displaystyle M_{x},M_{y},M_{z}}$ ${\displaystyle *}$ ${\displaystyle ***}$ Hughes-Liu 4 ${\displaystyle u_{x},u_{y},u_{z}}$  ${\displaystyle \theta _{x},\theta _{y},\theta _{z}}$ ${\displaystyle F_{x},F_{y},F_{z}}$  ${\displaystyle M_{x},M_{y},M_{z}}$ ${\displaystyle *}$ ${\displaystyle ***}$ 8-node solid 8 ${\displaystyle u_{x},u_{y},u_{z}}$  ${\displaystyle \theta _{x},\theta _{y},\theta _{z}}$ ${\displaystyle F_{x},F_{y},F_{z}}$  ${\displaystyle M_{x},M_{y},M_{z}}$ ${\displaystyle *}$ ${\displaystyle ***}$ ${\displaystyle ^{*}}$  see LS-DYNA Theory Manual: Chapter 6-10. ${\displaystyle ^{**}}$  see LS-DYNA User Keyword Manual: Chapter 26: ${\displaystyle ^{*}}$ SECTION. ${\displaystyle ^{***}}$  depends on chosen ELFORM.