Finite Element Solutions to Point-Load Problems

The numerical solution is presented for a point load problem obtained by various types of finite element meshes. The types of meshes used include standard element configurations with and without special singular elements under the load, and element configurations obtained by the use of grid optimization procedures with and without special singular elements under the loads. Standard meshes with singular elements yield results which are comparable to those obtained by a mesh obtained by a grid optimization procedure without singular elements. However, substantially better results were obtained by employing singular elements, which possess the proper order singularity, in an element mesh obtained by a grid optimization procedure.