Читать книгу Finite Element Analysis - Barna Szabó - Страница 34

Following assembly of the coefficient matrix and enforcement of the essential boundary conditions (when applicable) the resulting system of simultaneous equations is solved by one of several methods designed to exploit the symmetry and sparsity of the coefficient matrix. The solvers are classified into two broad categories; direct and iterative solvers. Optimal choice of a solver in a particular application is based on consideration of the size of the problem and the available computational resources.

At the end of the solution process the finite element solution is available in the form

(1.81)

where the indices reference the global numbering and Nu is the number of degrees of freedom plus the number of Dirichlet conditions.

The basis functions are decomposed into their constituent shape functions and the element‐level solution records are created in the local numbering convention. Therefore the finite element solution on the kth element is available in the following form:

(1.82)