Nonlinear Substructuring Analysis Expedited by Clustering Analysis Method with Applications to Elastoplasticity

ABSTRACT Finite element method for complex structures usually leads to high numerical costs due to a large number of degrees of freedom, especially when nonlinearities exist. Substructuring techniques can significantly reduce the numerical costs by retaining only a limited number of nodes while eliminating most degrees of freedom. Nevertheless, the resulting nonlocalized nonlinearities impose considerable challenges to conventional substructuring techniques. In this work, we propose a novel cluster‐based substructuring analysis (CSA) algorithm to address such challenges in simulating elastoplastic material. First, clustering analysis accounting for boundary conditions is introduced for relating the boundary conditions to cluster‐wise stress/strain fields in a single substructure. Perturbation analysis is then performed to reconstruct the nodal forces at retained nodes. Finally, substructures are coupled through nodal displacements and forces at their shared nodes. Four numerical examples are presented to demonstrate the efficiency and accuracy of the proposed method, in particular, how the clustering analysis method expedites the nonlinear substructuring analysis.