Equilibrium Finite Elements of Spherical Shells in Analysis Problems

In this paper, the problems of analysis of flat spherical shells modelled by equilibrium finite elements are formulated and solved. A new second-order equilibrium finite element developed by the method of Bubnov-Galerkin is suggested. Equilibrium and geometrical equations are created for this element and, based on these equations, the mathematical models of the analysis problem of internal forces and displacements, as well as the limit external load optimization problem for the shell structures are constructed. These are nonlinear mathematical programming problems. The methodology is illustrated by the numerical examples. The solution results are obtained for the finite elements of various sizes and show very high accuracy of the suggested element and convergence of the results.