A new MLPG method for elastostatic problems

This paper introduces a novel meshless local Petrov–Galerkin (MLPG) method by presenting a new test function as a schema to solve the elasto-static problems. It is seen that the four ordinary MLPG methods can also be approached using the present test function. Both the moving least square (MLS) and the direct method have been applied to the method to estimate the shape function and to impose the essential boundary conditions. The results of three studied elasto-static cases; “two dimensional cantilever beam”, “first mode fracture of a center-cracked strip” and “edge-cracked functionally graded strip” show that by using less number of nodes, the present work gives sufficiently more accurate results. Meanwhile the method can also unify various kinds of MPLGs and one may conclude that the model is a good replacement for other common approaches.

► A new meshless local Petrov–Galerkin method has been introduced using the Gaussian test function.
► By this method, four common types of MLPGs can also be approached, and it may unify its various kinds.
► The main benefit of the work is to improve the efficiency of the MLPG method by presenting a new, single and subtle test function.
► The method may be substituted with common MLPG approaches to solve the elasto-static problems.