Advanced composite materials are increasingly used in a variety of fields due to their desirable properties. The use of these advanced materials in different applications requires a thorough understanding of the effect of their complex microstructures and the effect of the operating environment on the materials. This requires an efficient, robust and powerful tool that is able to predict the behavior of composites under a variety of loading conditions. This research addresses this problem and develops a new convenient numerical method and framework for users to perform such analyses of composites.
In this thesis, the hybrid fundamental solution based finite element method (HFS-FEM) is developed and applied to model composite materials across microscale and macroscale and from single field to multi-field. The basic idea and detailed formulations of the HFS-FEM for elasticity and potential problems are first presented. Then this method is extended to solve general three-dimensional (3D) elasticity problems with body forces and to model anisotropic materials encountered in composite analysis. Standard tests for proposed elements are carried out to assess their performance. Further, an efficient numerical homogenization method based on HFS-FEM is applied to predict the macroscopic elasticity properties and thermal conductivity of heterogeneous composites in micromechanical analysis. The effect of material parameters, such as fiber volume fractions, inclusion shapes and arrangements on the effective coefficients of composites are investigated by means of the proposed micro.
mechanical models. Meanwhile, special elements are also proposed for mesh reduction and efficiency improvement in the analyses.
Finally, the HFS-FEM method is developed for modeling two-dimensional (2D) and 3D thermoelastic problems. The particular solutions related to the body force and temperature change are approximated using the radial basis function interpolation. The new HFS-FEM is also developed for modeling plane piezoelectric materials in two different formulations: Lekhnitskii formalism and Stroh formalism. Numerical examples are provided for each kind of problems to demonstrate the accuracy, efficiency and versatility of the proposed method
