VM34

VM34
Bending of a Tapered Plate (Beam)

Overview

Reference:C. O. Harris, Introduction to Stress Analysis, The Macmillan Co., New York, NY, 1959, pg. 114, problem 61.
Analysis Type(s):Static Analysis (ANTYPE = 0)
Element Type(s):
Elastic Shell Elements (SHELL63)
3D Elastic Tapered Unsymmetric Beam Element (BEAM188)
4-Node Finite Strain Shell Elements (SHELL181)
8-Node Structural Shell (SHELL281)
Input Listing:vm34.dat

Test Case

A tapered cantilever plate of rectangular cross-section is subjected to a load F at its tip. Find the maximum deflection δ and the maximum principal stress σ1 in the plate.

Figure 46: Beam Problem Sketch

Beam Problem Sketch

Material PropertiesGeometric PropertiesLoading
E = 30 x 106 psi
υ = 0.0
L = 20 in
d = 3 in
t = 0.5 in
F = 10 lbs

Analysis Assumptions and Modeling Notes

The problem is solved first using quadrilateral shell elements (SHELL63) and then using tapered beam elements (BEAM188). For the quadrilateral shell elements (used in triangular form), nodal coupling is used to ensure symmetry. Node 10 is arbitrarily located at Z = 1.0 in order to define the orientation of the beam. The problem is also solved using quadrilateral finite strain shell elements (SHELL181 and SHELL281).

Results Comparison

 TargetMechanical APDLRatio
SHELL63Deflection, in-0.042667-0.0426671.000
(Stress1)max, psi1600.001600.44961.000
BEAM188Deflection, in-0.042667-0.0427921.003
(Stress1)max, psi1600.001599.999951.000
SHELL181Deflection, in-0.042667-0.0427071.001
(Stress1)max, psi1600.0000001600.0000061.000
SHELL281Deflection, in-0.042667-0.0427321.002
(Stress1)max, psi1600.001604.3758801.003