A finite element method for two-dimensional quasi-static elasto-perfectly plasticity problems, employing the stress-based approach, is presented. The HCT6 element, 6-node 12-d.o.f. Hsieh-Clough-Tocher triangle, is used to approximate Airy stress function which is applied to construct the self equilibrating fields of stresses, so it needs $C^1$ continuity. The HCT6 is made of three sub-elements in which shape functions are defined as complete cubic ploynomials and $C^1$ continuity is satisfied in an element.
Two examples are solved by using three types of finite elements. The first is the HCT3 element : the 3-node 9-d.o.f. Hsieh-Clough-Tocher triangle. The second is the HCT6 that is the modification of HCT3. The third is the TRI6 : the 6-node 12-d.o.f. triangle which uses the displacement-based FEM. The technique to calculate a shape function value of HCT6 is shown. Traction boundary conditions are imposed by the use of Lagrange's multipliers method, which employs an additional boundary element. The procedure of calculating shape function along boundary is described.
For each example, results are obtained with three types of elements and convergence is shown to be achived in each element as the mesh is refined. In the case of stress-based FEM, better results are obtained with HCT6 than HCT3 for the similar number of nodal degrees of freedom. The lower load bound obtained from the stress-based FEM is compared with the upper one obtained from the displacement-based FEM.
