Application of Equivalent Elastic Methods in Three-Dimensional Finite Element Structural Analysis

Abstract

This paper describes use of equivalent solid (EQS) modeling to obtain efficient solutions to perforated material problems using three-dimensional finite element analysis (3-D-FEA) programs. It is shown that EQS modeling in 3-D-FEA requires an EQS constitutive relationship with a sufficient number of independent constants to allow the EQS material to respond according to the elastic symmetry of the penetration pattern. It is also shown that a 3-D-FEA submodel approach to calculate peak stresses and ligament stresses from EQS results is very accurate and preferred over more traditional stress multiplier approaches. The method is demonstrated on the problem of a transversely pressurized simply supported plate with a central divider lane separating two perforated regions with circular penetrations arranged in a square pattern. A 3-D-FEA solution for a model that incorporates each penetration explicitly is used for comparison with results from an EQS solution for the plate. Results for deflection and stresses from the EQS solution are within 3 percent of results from the explicit 3-D-FE model. A solution to the sample problem is also provided using the procedures in the ASME B&PV Code. The ASME B&PV Code formulas for plate deflection were shown to overestimate the stiffening effects of the divider lane and the outer stiffening ring.