Buckling and vibration of in-plane loaded plates treated by a unified Ritz approach

Abstract

The problem of the buckling and lateral vibration of rectangular plates subject to in-plane loads is treated by using a Ritz approach for both the determination of the middle surface stresses caused by the in-plane loading and the analysis of the consequent out-of-plane buckling and vibrational characteristics of the plates. Since the stress function formulation of the middle surface stress problem is formally analogous to the plate bending problem, the same type of admissible functions—ordinary and degenerated beam vibration mode shapes—are employed in the Ritz series for both parts of the problem. The approach permits the accurate treatment of plates subject to real in-plane loads, where the middle surface stresses may not be realistically representable by simple polynomials as has been assumed in earlier studies. Several numerical examples are presented, illustrating the applicability of the approach and giving an indication of the order of errors that may result in the determination of the out-of-plane characteristics of plates when using simplifying assumptions for the in-plane stress field.