Hypar Shell on Pasternak Foundation

Abstract

This paper deals with nonlinear static and dynamic analysis of hyperbolic paraboloid shells on Pasternak foundations. The governing differential equation of a hypar shell on a Pasternak foundation is reduced to that of a plate on a double elastic foundation. Moduli of double elastic foundations are presented in terms of a geometric parameter of the hypar shell and the two parameters of the Pasternak model. Nonlinear differential equations are obtained in decoupled form, using Berger's approximation. In the first part, the effects of the geometry of the shell and foundation moduli on load‐deflection characteristics for the simply supported edges are investigated. Effects of shell geometry and foundation modulus are found to be significant, but changes in shear modulus are not. In the second part, the effects of geometric and foundation parameters on time period‐amplitude relationship are studied. Application of the proposed nonlinear static and dynamic analysis method may lead to a better, more efficient design of hypar shell foundations.