VM42

VM42
Barrel Vault Roof Under Self Weight

Overview

Reference: R. D. Cook, Concepts and Applications of Finite Element Analysis, 2nd Edition, John Wiley and Sons, Inc., New York, NY, 1981, pp. 284-287.
Analysis Type(s): Static Analysis (ANTYPE = 0)
Element Type(s):
4-Node Finite Strain Shell Elements (SHELL181)
8-Node Finite Strain Shell Elements (SHELL281)
Input Listing: vm42.dat

Test Case

A cylindrical shell roof of density ρ is subjected to a loading of its own weight. The roof is supported by walls at each end and is free along the sides. Find the x and y displacements at point A and the top and bottom stresses at points A and B. Express stresses in the cylindrical coordinate system.

Figure 57: Barrel Vault Roof Problem Sketch

Barrel Vault Roof Problem Sketch

Material PropertiesGeometric PropertiesLoading
E = 4.32 x 108 N/m2
υ = 0.0
ρ = 36.7347 kg/m3
t = 0.25 m
r = 25 m
= 50 m
Θ = 40°
g = 9.8 m/s2

Analysis Assumptions and Modeling Notes

A one-fourth symmetry model is used. Displacements, UX and UY, and the longitudinal rotation, ROTZ, are constrained at the roof end to model the support wall.

Results Comparison

TargetMechanical APDLRatio
SHELL181
UYA, m-.3019-.3161.047
UXA, m-.1593-.16611.042
Stressz, Top @ A, Pa215570205333.28120.953
Stressz, Bot @ A, Pa340700336983.68750.989
Stressangle, Top @ B, Pa191230182418.85810.954
Stressangle, Bot @ B, Pa-218740-209768.54760.959
SHELL281
UYA, m-.3019-.30281.003
UXA, m-.1593-.15981.003
Stressz, Top @ A, Pa215570215625.93751
Stressz, Bot @ A, Pa340700341506.65621.002
Stressangle, Top @ B, Pa191230190332.58320.995
Stressangle, Bot @ B, Pa-218740-219199.28671.002