VM194

VM194
Element Birth/Death in a Fixed Bar

Overview

Reference:	Any standard mechanics of materials text
Analysis Type(s):	Static Analysis (ANTYPE = 0)
Element Type(s):	3D Spar (or Truss) LINK180
Input Listing:	vm194.dat

Test Case

A bar of uniform cross-section, fixed at both ends and subjected to a uniform thermal load (ΔT) has its center third removed. This is followed by replacing the removed part in a "strain-free" condition and then removing the uniform thermal load. Determine the axial stresses and the thermal strains in the three sections of the bar at the end of this sequence of loading operations.

Figure 298: Fixed Bar with Thermal Loading Problem Sketch

Material Properties

Geometric Properties

E = 30 x 10⁶ psi

α = 0.00005 in/in-°F

L = 10 in

b = 1 in

Load Step 1: ΔT = 100°F

Load Step 2: Elem 2 dead

Load Step 3: Elem 2 alive

Load Step 4: ΔT = 0°F

Analysis Assumptions and Modeling Notes

The REFT material property is used to model "rebirth" of the "dead" element such that no thermal strains exist at birth. This is achieved by specifying the value of REFT equal to the uniform temperature of the bar (100°F). Removing the thermal load in the subsequent final load step therefore results in relieving the thermal strains in elements 1 and 3. Element 2 on the other hand, experiences a thermal load of ΔT = -100°F resulting in a negative thermal strain.

Results Comparison

Load Step No. 4	Target	Mechanical APDL[1]	Ratio
Stress_x , psi	150,000[1]	150,000	1.000
Strain_th , (elem1, 3)	0.0	0.0	-
Strain_th , (elem 2)	-0.005	-0.005	1.000

Uniform for all elements.