MATHEMATICAL FINITE ELEMENT MODEL FOR GENERAL ANALYSIS OF DOUBLE CURVED SHELL ACCORDING TO STRAIN BASED APPROACH

Abstract

A new mathematical finite element model suitable for the general bending analysis of double-curved shell structures depending on the strain-based approach has been derived. The element is simple and contains only the essential degrees of freedom. The element has the advantage over the other available double-curved shell elements. The improvement obtained is due to the fact that all the displacement fields of the present element satisfy the exact representation of rigid body modes of displacements then the shape function error due to rigid body modes becomes zero. Also, the present element satisfies the full geometry of the double-curved shell due to this point discretization error becomes zero. Finally, the error due to strain mode becomes very small because the present element satisfies the compatibility equations of strains and the 19 coefficients of strain mode are derived exactly from partial differential equations of strains. The numerical solution of several problems by using the present element proved to be powerful in the structural analysis of double-curved shells, such as cylindrical shells. Its results are better than the solution of other elements and packages with respect to analytical solutions.