Overview

Test Case

A rectangular plate whose length is large compared to its width is subjected to a uniform pressure p as shown. The shorter edges are simply-supported. Determine the direct stress σ_x (MID) at the middle of the plate and the maximum combined stress (direct plus bending) σ_x (BOT) at the bottom of the plate.

Figure 193: Rectangular Plate Problem Sketch

Material Properties	Geometric Properties	Loading
E = 30 x 106 psi υ = 0.3	= 45 in w = 9 in t = 0.375 in	p = 10 lb/in2

Analysis Assumptions and Modeling Notes

Since the plate ends are immovable along the X-axis, a small lateral displacement caused by the pressure load induces membrane stresses. The geometric and loading symmetry is used to model only half of the plate with appropriate symmetry boundary conditions at the midspan.

Two analysis solutions are performed. The first solution is performed without large deflection results in a static solution with no coupling between in-plane and transverse deflections. The second solution is performed with large deflection results in a converged solution with the coupling effects. POST1 is used to report nodal stresses along the plate middle and bottom. Note that these stresses are based on the original geometry, and include the element rotations due to the large deflection option.

The two solutions above are repeated using 3D Solid Shell Elements (SOLSH190). Two layers of SOLSH190 elements are used across the thickness, and appropriate symmetry boundary conditions are applied at mid-thickness. The solid model adopts an approximate method for simulating shell simple support, resulting in differences in the stress Y component within a small boundary region.

Results Comparison