An analysis capability for predicting the nonlinear behavior of elastic structural systems that can be adequately idealized with rectangular plate and cylindrical shell discrete elements is reported. The displacement patterns in each element are approximated in terms of products of one-dimension al, first-order Hermite interpolation polynomials and undetermined nodal displacement parameters. Geometric admissibility of the displacement state for an assembled set of these discrete elements can be readily assured. Incorporation of geometric nonlinearities in the strain-displacement relations permits the prediction of finite displacements. For example, elastic postbuckling behavior can be analyzed using this method. The option to impose a prescribed end-shortening and then determine the boundary-force distribution required to maintain the resulting displacement pattern is a valuable feature of this capability. Numerical solutions are obtained by direct minimization of the total potential energy. The elastic postbuckling behavior of a flat-plate panel and a cylindrical shell panel are presented as examples. The applicability of these discrete elements to predicting the elastic postbuckling behavior of integrally stiffened plate and cylindrical shell panels is provided by the assumed element displacement patterns.
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Schmit et al. (1968) studied this question.