202 / 2019-08-27 15:07:51

Special n-sided hybrid finite element for thermal analysis of cellular materials with elliptic holes

Cellular materials; elliptic holes; hybrid finite element; fundamental solution

计算力学在工程中的应用 > 复合材料力学

As an alternative to the traditional finite element method and boundary element method, the hybrid finite element method based on fundamental solution kernels has been well developed for thermal and elastic analysis in isotropic and anisotropic media recently. In this study, the hybrid finite element formulation is extended to solve two-dimensional heat conduction in cellular materials including multiple elliptic holes. In order to achieve the balance of computational efficiency and accuracy, special n-sided hybrid finite element with fundamental solution kernels of problem are developed to enclose an elliptic hole so that the meshing effort around this elliptic hole is greatly reduced. For such special element, two independent approximations are assumed: (1) The intra-element temperature field defined inside the special element which is approximated by the linear combination of the fundamental solution of problem to achieve the local satisfaction of the governing equations of problem and the elliptic boundary condition, but not the specific boundary conditions and the inter-element continuity conditions; (2) The inter-element temperature field defined over the entire element boundary which is approximated by means of the conventional shape function to satisfy the conformity requirement of temperature. Combining with the two-variable hybrid functional, the element stiffness equation can be obtained, in which only line integrals along the element boundary are involved with one-dimension reduction, compared to domain integral in the conventional finite element. Finally, the accuracy and efficiency of the present special n-sided elements are demonstrated by three examples involving one, two and multiple randomly dispersed elliptic holes, respectively.