What Can Go Wrong

This article focuses on some aspects of the reliability of finite-element methods and their accurate use. In order to illustrate, linear elastic solutions are considered and assumed that the algebraic finite-element equations are solved exactly. The mathematical model is based on assumptions made regarding the geometry, material conditions, loading, and displacement boundary conditions. The analysis problem is obtained by specifying the geometry and dimensions, support conditions, material constants, and loading. As a remedy in displacement-based finite-element methods, reduced integration is employed. This means that in the numerical integration of the element stiffness matrices, the exact matrices are not evaluated. The method is simple to program and requires less computation time to establish the matrices, and with experience acceptable results are frequently obtained. However, the technique can also lead to very large errors. As a conclusion, finite-element methods can now be employed with great confidence, however, only the methods considered reliable should be used.