Linear and non-linear analysis of thin shallow shells by mixed finite elements

Abstract

Two triangular mixed finite elements are developed for the linear and non-linear analysis of thin shallow shells. The unknown variables at the finite element nodes include not only the three displacements and bending stress resultants, but also the membrane stress resultants. The theory of thin shallow shells based on Kirchhoff-Love's hypothesis, and Reissner's principle have been used to obtain explicitly the finite element matrices. The interpolation functions used for the nodal variables are linear for the first finite element and quadratic for the second one. The non-linear problem is solved by the method of Newton-Raphson and the results are compared to those obtained by exact and approximate methods.