Analysis of Heat Treatment for Strengthened Glass

Formation of residual compressive stress on the glass surface through rapid cooling. Safety design of air-quenched strengthened glass. Prediction of fracture patterns.

We use spatial discretization by the Finite Element Method (FEM). We assemble the element stiffness matrix 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. higher-order elements, full integration vs. reduced integration) is directly linked to the trade-off between solution accuracy and computational cost.

Solve the simultaneous equations by direct methods (LU decomposition, Cholesky decomposition) or iterative methods (CG method, GMRES method). Preconditioned iterative methods are effective for large-scale problems.

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

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. Particularly, higher-order elements and special elements (cohesive elements, user-defined elements, etc.) often cannot be directly converted between solvers.

Verifying mesh convergence, validating the appropriateness of boundary conditions, and performing sensitivity analysis of material parameters are extremely important.