Shell15 – Orthotropic Plate X

Example Description

This example uses a flat, circular plate to test orthotropic plate behavior. The plate has a 48 inch radius, is 2 inches thick and is fixed (clamped) around the perimeter. The plate is meshed 8x16 (radial by tangential). A uniform vertical (out-of-plane) load of 0.2 kips per square inch is applied to the plate. The results for the vertical deflection at the center of the plate and bending moments at selected points on the edge of the plate are compared with independent hand calculated results based on theory presented in Chapter 6 of Ugural 1981. Similar theory is presented in Chapter 11 of Timoshenko and Woinowsky-Krieger 1959.

The orthotropic behavior for this example is defined by equations 6.1 on page 141 in Ugural 1981:

From reviewing the preceding equations it is apparent that for this plate bending problem the material properties are defined by four constants, namely, , E'x , E'y ,Vy and G.

For this example the stiffness of the plate spanning in the X-direction is assumed to be twice that of the plate spanning in the Y-direction. In other words, the stiffness for bending about the Y-axis is twice that for bending about the X-axis. Thus E'x is equal to 2E'y. For this example these constants are taken as:

The orthotropic behavior is modeled using two different methods in two different models. In Model A orthotropic material properties are used. In Model B isotropic material properties are used together with appropriate stiffness modifiers for the shell elements. The calculation of the properties and modifiers used for those two models are described later in this example.

The local axes of the shell elements are oriented in their default orientation such that the positive local 1-axis is in the same direction as the positive global X-axis and the positive local 2-axis is in the same direction as the positive global Y-axis.

MATERIAL PROPERTIES FOR ORTHOTROPIC MODEL (MODEL A)

In Model A orthotropic material properties are used. Here the constants , E'x , E'y, Vy and G are input directly into the material properties definition for the model. In this model those constants are referred to as modulus of elasticity for direction 1 (e1), modulus of elasticity for direction 2 (e2), Poisson’s ratio for plane12 (u12) and shear modulus for plane12 (g12), respectively. For the thick plate model the out-of-plane shear moduli, g13 and g23, are set equal to the G used in the thick plate isotropic model and then, similar to the thick plate isotropic model, the v13 and v23 area object stiffness modifiers are set to 1E+04 so that out-of-plane shear deformations are ignored. This is consistent with the thin plate solution and with the independent results.

Tested Features

•  Plate bending analysis of shells
•  Orthotropic material properties
•  Area object stiffness modifiers