Development of meshfree techniques for analyzing Smart/FGM structures and nonlinear problems

Abstract

Mesh-based numerical methods, such as finite element method (FEM), set an artificial constraint to ensure a physical compatibility that a continuum possesses. To overcome this difficulty, meshfree methods have been proposed recently. This thesis aims to develop some new meshfree techniques and apply them to solve relatively complicated structures and systems. In the study a meshfree interpolation scheme is proposed and developed based on moving Kriging formulation. Then the method is devoted to the numerical analysis and active control of complex structures including smart structures, shear deformable laminated composite plates, functionally graded material (FGM) plates. The last part deals with the nonlinear static and dynamic structural analysis considering both material and geometrical nonlinearities. A large number of numerical experiments are conducted to demonstrate the validity and efficiency of the proposed meshfree models. It is found the developed meshfree techniques are successful and versatile for solving a variety of engineering problems.