Issues In Convergence Improvements For Nonlinear Finite Element Programs
Esche, S. K., Kinzel, G. L. & Altan, T.
International Journal for Numerical Methods in Engineering, Vol. 40, No. 24, pp. 4577-4594, 1997.
Abstract
Systems of nonlinear equations as they arise when analyzing various physical phenomena and technological processes by the implicit Finite Element Method (FEM) are commonly solved by the Newton-Raphson method. The modeling of sheet metal forming processes is one example of highly nonlinear problems where the iterative solution procedure can become very slow or diverge. This paper focuses on techniques to overcome these numerical difficulties. Several methods to generate initial guesses within the radius of convergence are proposed. Appropriate stopping criteria for the iterative procedure are discussed. A combination of various line search methods with the continuation method is proposed. The efficiency and robustness of these numerical procedures are compared based on a set of test examples. A particular form of line search was identified which allows the stable and efficient solution of highly nonlinear sheet metal forming problems. Even though the present investigations were motivated by the application of the implicit FEM to the simulation of sheet metal forming processes, the findings are general enough to be applicable to a wide spectrum of nonlinear FEM applications.