The hybrid-stress finite element model is used to develop a 20-node, isoparametric, quadratic displacement, three dimensional element. Linear elastic, elastoplastic, visco-plastic and creep analyses of three dimensional and axisymmetric structures subject to arbirary loads are considered. The results for axisymmetric structures subject to arbitrary loads, obtained by the semi-analytic finite element developed elsewhere, are compared with those obtained by using the three dimensional hybrid-stress element developed in this work.
The hybrid-stress functional requires both a continuous displacement field and an appropriate stress field interpolation in the element interior. The stress field is further required to satisfy the set of equilibrium equations. To develop the 20- node element displacement is interpolated in terms of the nodal displacements. The stress field for the element is developed using the complete cubic polynomials for each of the six stress components. In addition to satisfying the equilibrium equations, the complete set of stress compatibility equations is enforced on the stress field to reduce the number of stress parameters. The element thus obtained possesses correct rank, is invariant under translation and rotation and shows better displacement and stress accuracy than an analogous assumed displacement element.
Axisymmetric structures subject to arbitrary loads can be analyzed in two ways. The conventional approach is to use the solid elements. An alternative approach is to use the semi-analytic finite element approach. It is confirmed in this work through several examples that in the linear elastic range the semi-analytic method yields reasonably accurate results in comparison with a 3-D solution.
For elasto-plastic solution of three dimensional structures a hybrid-stress formulation based on the "initial stress" approach is presented. The semi-analytic technique of linear elastic analysis is extended to the elasto-plastic range using this hybrid-stress functional. Numerical examples are presented to compare the accuracy of the semi-analtyic solution to the 3-D elastoc-plastic solution of axisymmetirc structures subject to arbitrary loadr. A reasonable agreement between the two solution is observed along with savings in computational effort and time through the semi-analytic approach.
A visco-plasticity based method is an efficient approach to solve elasto-plastic and phenomenological creep problems. A hybrid-stress finite element formulation of visco-plastic and creep problems using the "initial strain" approach is presented. The semi-analytic method is extended to visco-plastic and creep analysis of axisymmetric strucutres subject to arbitrary loads.
Through a numerical example, accuracy of semi-analytic method of visco-plastic analysis when compared with a 3-D solution is found to be of the same order as in elasto-plastic formulation. The visco-plastic approach is found to be computationally more efficient than the conventional incremental plasticity approach in solution of elasto-plastic problems.
Formulation of the creep problem is verified by comparing the analysis results with an available exact solution of a selected example. When applied to creep analysis of axisymmetric structures subject to aribtary loads, the semi-analytic approach is found to produce poor results in comparison to the 3-D solution due to the higher order of nonlinearity present in the constitutive relations of the creep phenomenon.