VM82

VM82
Simply Supported Laminated Plate Under Pressure

Overview

Reference:

J. N. Reddy, "Exact Solutions of Moderately Thick Laminated Shells", ASCE Journal Engineering Mechanics, Vol. 110 No. 5, 1984, pp. 794–809.

Analysis Type(s):

Static Analysis (ANTYPE = 0)

Element Type(s):

3D 8-Node Layered Solid Shell Elements (SOLSH190)

3D 20-Node Layered Structural Solid Elements (SOLID186)

4-Node Finite Strain Shell Elements (SHELL181)

8-Node Finite Strain Shell Elements (SHELL281)

3D 8-Node Structural Solid (SOLID185)

Input Listing:

vm82.dat

Test Case

A simply-supported square cross-ply laminated plate is subjected to a uniform pressure p_o. The stacking sequence of the plies is symmetric about the middle plane. Determine the center deflection δ (Z-direction) of the plate due to the pressure load.

Figure 114: Simply Supported Laminated Plate Problem Sketch

Material Properties

Geometric Properties

E_x = 25 x 10⁶ N/m²

E_y = 1 x 10⁶ N/m²

υ_xy = 0.25 (Major Poisson's ratio)

G_xy = G = 0.5 x 10⁶ N/m²

G_yz = 0.2 x 10⁶ N/m²

a = 10 m

h = 0.1 m

t = 0.025 m

p_o = 1.0 N/m²

Analysis Assumptions and Modeling Notes

A quarter of the plate is modeled due to symmetry in geometry, material orientation, loading, and boundary conditions. Five models using SHELL181, SOLID185, SOLID186, SOLSH190, and SHELL281 elements, respectively, are analyzed. The transverse shear stiffness values are calculated using the 5/6 shear correction factor and are input with SHELL181 and SHELL281 elements using the SECCONTROL command. Note that PRXY is used to directly input the major Poisson's ratio. EZ (explicitly input) is assumed to be equal to EY.

Results Comparison

	Target	Mechanical APDL	Ratio
Deflection, m (SOLID185)	0.0683	0.0677	0.991
Deflection, m (SOLSH190)	0.0683	0.0682	0.998
Deflection, m (SOLID186)	0.0683	0.0683	1.000
Deflection, m (SHELL181)	0.0683	0.0683	1.000
Deflection, m (SHELL281)	0.0683	0.0683	1.000