A compatible and complete six-noded element to model singularity

Abstract

The shape functions of a six-noded triangular element are developed to model power type singularities which satisfy all the convergence criteria—the rigid body mode, the interelement continuity and the constant strain condition. Hence this provides a unique tool to model power type singularities under mechanical and thermal loads. Three case studies are presented. The first case study deals with the comparison of the present element with the existing singular elements. The convergence studies are done for this case study by refining the mesh and also by increasing the order of integration. The second and the third case studies deal with real life problems, namely, the analysis of a cracked bimaterial strip and the analysis of a power plant nozzle with a kinked crack under mechanical and thermal loads. These case studies show the usefulness of the element.