Bulk theory elasticity finite element based on piecewise constant approximations of stresses

The solution of the volume theory elasticity problem was obtained on the basis of the additional energy functional and the possible displacements principle. On the basis of the possible displacements’ principle, equilibrium equations for grid nodes are compiled, which are added to the additional energy functional using Lagrange multipliers. Linear functions are taken as possible displacements. The volumetric finite element based on piecewise constant approximations of stresses is presented. The stress fields are continuous along finite element boundaries and discontinuous inside ones. The calculation results of a cantilever beam and a bending plate are presented. The obtained solutions are compared with the solutions by the finite element method in displacements. The proposed finite element makes it possible to obtain more accurate stress values.