Shallow Shell Finite Element for the Large Deflection Geometrically Nonlinear Analysis of Shells and Plates

摘要

An investigation into the large deflection, geometrically nonlinear behaviour of shells is carried out in the present paper. The finite element method is used in conjunction with linearised incrementation and the Newton-Raphson iterative technique. The finite element used is based on independent strain assumptions insofar as it is allowed by the compatibility equations. Strain—displacement relationships based on shallow shell formulation are used and applied to an element having three principal curvatures. The resulting element has the only essential external degrees of freedom, satisfies the exact requirement of strain-free rigid body modes of displacements and can be used for the representation of cylindrical, spherical and hyperbolic paraboloid shells. Complex load-deflection curves are obtained for cylindrical and spherical shells by incrementing loads as well as deflections. The relative behaviour of cylindrical and spherical panels having the same overall dimensions are also discussed in terms of stiffness, instability and snap-through phenomena.