VM218

VM218
Hyperelastic Circular Plate

Overview

Reference:

J. T. Oden, Finite Elements of Nonlinear Continua, McGraw-Hill Book Co., Inc., New York, NY, 1972, pp. 318-321.

Analysis Type(s):

Static Analysis (ANTYPE = 0)

Element Type(s):

4-Node Finite Strain Shell Elements (SHELL181 )

2-Node Finite Strain Axisymmetric Shell Elements (SHELL208)

3-Node Axisymmetric Shell Elements (SHELL209)

8-Node Finite Strain Shell Elements (SHELL281)

Input Listing:

vm218.dat

Test Case

A flat circular membrane made of a rubber material is subjected to uniform water pressure. The edges of the membrane are fixed. Determine the response as pressure is increased to 50 psi.

Figure 354: Hyperelastic Circular Plate Project Sketch

Material Properties

Geometric Properties

C₁ = 80 psi

C₂ = 20 psi

R = 7.5 in

T = 0.5 in

Pres = 50.0 psi

Analysis Assumptions and Modeling Notes

The full circular plate is reduced to a 7.5° sector for analysis. The midplane of the outer edge of the circle is considered to be fixed. A pressure of 50 psi is applied to the bottom surface of the shell sector. The SHELL181 and SHELL281 models are solved using standard formulation using reduced integration.

Four different analyses are performed using SHELL181, SHELL208, SHELL209, and SHELL281 elements, respectively.

Results Comparison

Pressure	Target	Mechanical APDL	Ratio
SHELL181
4.0	2.250	2.292	1.019
24.0	6.200	5.715	0.922
38.0	10.900	10.093	0.926
SHELL208
4.0	2.250	2.301	1.023
24.0	6.200	5.730	0.924
38.0	10.900	10.079	0.925
SHELL209
4.0	2.250	2.288	1.017
24.0	6.200	5.704	0.920
38.0	10.900	10.118	0.928
SHELL281
4.0	2.250	2.261	1.005
24.0	6.200	5.544	0.894
38.0	10.900	9.847	0.903

Figure 355: Results Plot 1 - UZ vs. Thickness

Figure 356: Results Plot 2 - UZ vs. Pressure

Figure 357: Results Plot 3 - Displaced Shape