Joint finite elements with vector approximation of unknowns for the calculation of thin shells of complex geometry

Abstract

The formulation of boundaryvalue problems for thin shells of complex shape under the action of a static load is given. The basic equations are given on the basis of the theory of shells, in which the Kirchhoff—Love hypotheses hold. The geometric relationships are written in the vector form, and the physical ones are based on Hooke’s law for isotropic materials. Using the finiteelement method, a technique has been developed for numerically solving twodimensional static problems for thin shells of complex geometry. The resolving equations in displacements are obtained from the stationary conditions of a discrete analog of the Lagrange functional. Two variants of joint finite elements with 36 and 20 degrees of freedom are proposed. A feature of the developed modifications of the finiteelement method is the vector form of approximation of the sought quantities and the discrete execution of the geometric part of the Kirchhoff—Love hypotheses. The finite elements of thin shells of complex shape constructed in this way satisfy the continuity conditions for the displacement vectors and rotation angles and accurately describe the translational part of the movements of the finite elements as rigid bodies.