Effect of large deflections and initial imperfections on buckling of flexible shallow hyperbolic paraboloid shells

Abstract

The present paper gives the results of numerical solutions for non-linear problems concerning transverse bending of flexible shallow hyperbolic paraboloid shells with elastic edge elements and tie-connecting lower corners. Perfect and imperfect shells are analysed. To solve the system of non-linear differential equations, the method of finite differences combined with the method of differentiation with respect to a parameter is used. These methods reduce the boundary value problem to Cauchy's problem which is solved with the use of Runge-Kutta's method. It has been shown that the buckling of a flexible shallow hypar under transverse load occurs in the vicinity of the upper corner zones under the effect of principal compressive membrane forces caused by surface shear. The values of critical loads are given here. They depend significantly on the surface curvature and stiffness of the edge elements and tie. For imperfect shells the position and shape of the initial irregularities influence greatly the value of the critical load.