Structural Ritz-Based Simple-Polynomial Nonlinear Equivalent Plate Approach: An Assessment

Abstract

Thelinearequivalentplateapproachdevelopedandusedfortheaeroelasticoptimizationofcompositewingsatthe conceptual design stage is a Ritz approach based on simple polynomial functions as generalized coordinates. Generalization to the case of geometrically nonlinear structural behavior is presented here in an effort to assess accuracy and performance of the method in the nonlinear static and linear dynamic cases. Using the von Karman plate formulation for moderately large deformations, three-dimensional assemblies of thin-plate segments are modeled using a penalty function approach to impose boundary conditions and compatibility of motion between adjacent segments. Closed-form expressions for mass and stiffness terms (linear and nonlinear) make numerical integration unnecessary. Numerical results obtained by the present method for a variety of plate structures, in both static anddynamic cases, show good correlation with published results andresults by othercomputer codes.Results by the present formulation are also compared with large-deformation results. Limits of applicability, in terms of the range of deformations still captured accurately by the equivalent plate method, are studied in all test cases.