An equilibrium segmental finite element for plane elasticity problems

The displacements of structural elements due to environmental changes and or due to externally applied loads are made up of two major components. The first component is due to the strain free-rigid body modes and the second is due to straining of the elements and the final displacements are obtained by adding the corresponding two components for each of the various fields. This fact is inherent in any analytical solution for such problems. For in such an analysis the displacements are usually obtained by integrating the relevant strain-displacement equations. If the equations for the various components of strains in terms of the displacements are put to zero the resulting solutions for the various components of the displacements are due to strain free-rigid body modes. In mathematical terms these are referred to as the complementary functions of the solutions to the differential equations. The complete solution is obtained by adding the particular integrals to the complementary functions and hence the particular integrals are the displacements corresponding to straining of the element. In the present paper, a sector inplane element having the only essential degrees of freedom, satisfying the strain free-rigid body and compatibility requirements and based on strain assumptions satisfying the equilibrium equations is developed. The performance of this new equilibrium sector element is compared with a previous sector element to show the degree of improvement of convergence of the results. (orig./GL)