Response of Plates of Arbitrary Shape Subject to Static Loading

The paper presents the static analysis of arbitrarily shaped plates. The analysis is performed using the principle of minimum potential energy with the admissible pb‐2 Ritz functions. The pb‐2 Ritz functions consist of the product of a two‐dimensional polynomial (p‐2) and a basic function (b). The basic function is defined by the product of equations of the specified continuous piecewise boundary shape, each raised to the power of 0, 1, or 2 corresponding to free, simply supported, or clamped edge, respectively; thus satisfying the kinematic boundary conditions at the outset. Based on the proposed approach, deflections and bending moments for several plate problems having different combinations of free, simply supported, and clamped edges are obtained. The present solutions, where possible, are verified with those published values from the open literature.

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