VM145

VM145
Stretching of an Orthotropic Solid

Overview

Reference:

S. H. Crandall, N. C. Dahl, An Introduction to the Mechanics of Solids, McGraw-Hill Book Co., Inc., New York, NY, 1959, pg. 225.

SOLID185 - 3D 8-Node Structural Solid in the Mechanical APDL Theory Reference

Analysis Type(s):

Static Analysis (ANTYPE = 0)

Element Type(s):

3D 8-Node Structural Solid or Layered Solid (SOLID185)

Input Listing:

vm145.dat

Test Case

A unit cube of side , having orthotropic material properties, is subjected to forces FX and FY as shown. Three orthogonal faces are supported and the opposite three faces are free. Determine the translational displacements (ΔX, ΔY, and ΔZ) of the free faces.

Figure 201: Orthotropic Solid Problem Sketch

Material Properties

Geometric Properties

E_x = 10 x 10⁶ psi

E_y = 20 x 10⁶ psi

E_z = 40 x 10⁶ psi

υ_xy = 0.1

υ_yz = 0.2

υ_xz = 0.3

G_xy = G_xz = G_yz = 10 x 10⁶ psi

= 1.0 in

FX = 100 lb

FY = 200 lb

Analysis Assumptions and Modeling Notes

Two independent one-element models are used. Element 1 uses the material property data input in the nonlinear material table (material 1) in a matrix form that is to be inverted by the program. Element 2 uses directly labeled material property input.

The matrix input is defined as shown in Equation 2–4 of the Mechanical APDL Theory Reference with matrix term numbers 1, 2, 3, 7, 8, 12, 16, 19 and 21. Set TBOPT = 1 on the TB command to input the stiffness matrix in flexibility form. The same terms are input with the TBDATA command as described in the Element Reference.

Results Comparison

	Target	Mechanical APDL [1]	Ratio
UX, in	0.9 x 10^-5	0.9 x 10^-5	1.000
UY, in	0.95 x 10^-5	0.95 x 10^-5	1.000
UZ, in	-0.175 x 10^-5	-0.175 x 10^-5	1.000

for Nodes 8 and 16