VM35

VM35
Bimetallic Layered Cantilever Plate with Thermal Loading

Overview

Reference: R. J. Roark, W. C. Young, Formulas for Stress and Strain, 5th Edition, McGraw-Hill Book Co., Inc., New York, NY, 1975, pp. 113-114.
Analysis Type(s): Static Analysis (ANTYPE = 0)
Element Type(s): 8-Node Finite Strain Shell Elements (SHELL281)
Input Listing: vm35.dat

Test Case

A cantilever beam of length   , width w, and thickness t is built from two equal thickness layers of different metals. The beam is stress free at Tref. The beam is fixed at the centerline of one end (X = 0, Y = w/2), and subjected to a uniform temperature Ta. Determine the deflection at the centerline of the free end (X =  ) of the cantilever and the outer fiber bending stress at the fixed end.

Figure 47: Cantilever Plate Problem Sketch

Cantilever Plate Problem Sketch

Material PropertiesGeometric PropertiesLoading
E1 = E2 = 3 x 107 psi
υ 1 =  υ 2 = 0.0
α 1 = 1 x 10-5 in/in-°F
α 2 = 2 x 10-5 in/in-°F
= 10 in
t = 0.1 in
Tref = 70°F
Ta = 170°F

Analysis Assumptions and Modeling Notes

The width w is arbitrary for the solution of this problem and is chosen as 1 to produce reasonably-shaped elements. At the "fixed" end, only the center node is constrained to match the simple beam theory used in the reference, and allow unrestrained bending in the Y-Z plane.

The model is solved using layered finite-strain shell elements (SHELL281).

Results Comparison

TargetMechanical APDLRatio
SHELL281
free-end deflectionz, in0.7500.7501.000
free-end deflectionx, in0.0150.0151.000
fixed-end top stressx, psi750075001.000