CTE傾斜機能材料設計

Design of functionally graded materials (FGM) with spatially varying coefficient of thermal expansion for thermal stress reduction. Ceramic-metal system.

We use spatial discretization by the Finite Element Method (FEM). We assemble the element stiffness matrices and construct the global stiffness equation.

We perform transformation to the weak form (variational form) and use formulation by the Galerkin method using test functions and shape functions. The choice of element type (low-order elements vs. high-order elements, full integration vs. reduced integration) directly affects the trade-off between solution accuracy and computational cost.

We solve the simultaneous equations by direct methods (LU decomposition, Cholesky decomposition) or iterative methods (CG method, GMRES method). For large-scale problems, preconditioned iterative methods are effective.

Developed in 1970 by Swanson Analysis Systems Inc. (SASI). Based on APDL (Ansys Parametric Design Language).

Developed in 1978 by HKS (Hibbitt, Karlsson & Sorensen). Acquired by Dassault Systèmes in 2005 and integrated into the SIMULIA brand.

A nonlinear FEA solver developed by MARC Analysis Research Corp. Acquired by MSC Software. Strong in large deformation and contact.

When converting models between different solvers, attention must be paid to the correspondence of element types, compatibility of material models, and differences in the representation of loads and boundary conditions. Especially high-order elements and special elements (cohesive elements, user-defined elements, etc.) often cannot be directly converted between solvers.