Stabilized reduced integration and sequentially linear analysis on the approximation of the non-linear behaviour of structures

In this paper, a computationally efficient strategy for the approximation of the non-linear behaviour of structures through the finite element method is proposed. This proposal is based on the execution of a set of linear analyses in which the strength of the elements where the damage occurs is sequentially degraded and, in addition, complemented with a stabilized reduced numerical integration scheme for solid finite elements. Thus, the stiffness matrix only contains information of one integration point and, consequently, the stresses are computed only at that point. Also, due to the stabilization, it is possible to use reduced integration not only in the elements where the damage is assumed to occur, but in all the elements, guaranteeing a greater reduction in the computational cost. In this paper, the strategy of sequentially linear analysis with stabilized reduced integration is applied to several validation as well as application examples in which the quality of the approximation and the computational efficiency achieved are discussed. Finally, some future developments for the strategy are proposed.