Adaptive Through-Thickness Integration Strategy for Shell Elements

Abstract

Reliable numerical prediction of springback in sheet metal forming is essential for the automotive industry. There are numerous factors that influence the accuracy of springback prediction by using the finite element method. One of the reasons is the through‐thickness numerical integration of shell elements. It is known that even for simple problems the traditional integration schemes may require up to 50 integration points to achieve a high accuracy of springback analysis. An adaptive through‐thickness integration strategy can be a good alternative. The strategy defines abscissas and weights depending on the integrand’s properties and, thus, can adapt itself to improve the accuracy of integration. A concept of the adaptive through‐thickness integration strategy for shell elements is presented. It is tested using a simple problem of bending of a beam under tension. Results show that for a similar set of material and process parameters the adaptive Simpson’s rule with 7 integration points performs better than the traditional trapezoidal rule with 50 points. The adaptive through‐thickness integration strategy for shell elements can improve the accuracy of springback prediction at minimal costs.