A Variational Approach to Plates on Elastic Foundations

Abstract

Approximate methods may have to be adopted for the solution of complex problems in solid mechanics. Vlasov’s variational method (1,2) is considered in this context because of its simplicity, computational economy and efficiency. The method simplifies the continuum problem into a discrete-continuum problem thus reducing the governing equations to ordinary differential equations (which can be easily solved), without losing any of the physical characteristics in the process of mathematical simplification. Further, the method is versatile enough to tackle problems involving non-homogeneity, anisotropy, arbitrary boundary conditions besides being computationally economic as compared to the Finite Element Method. The bending theory of plates on generalised elastic foundations is presented using this method. The elastic foundation is modelled as a discrete-continuum and general solutions of finite plates on such foundations have been obtained in terms of initial parameters. Application of the method of initial parameters to general plate configurations carrying arbitrary external loads and moments is discussed, thus emphasising the versatality, computational efficiency and adaptability of the same. Both static and dynamic analyses are discussed and few results are presented in non-dimensional form.