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?

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.

Nonlinear finite elements/Homework 6/Solutions