Mortar Method With Interpolative Mapping Displacement for Nonmatching Mesh Problems

In this paper, an interpolative mapping mortar method (IM‐mortar) is proposed for nonmatching finite element meshes. Displacement continuity is enforced weakly using a Lagrange multiplier field. An intermediate frame is introduced, on which the interface displacement field is reconstructed from the adjoining bodies through interpolative mapping. All interface integrals are then evaluated on the frame mesh, avoiding direct integration over element‐to‐element overlap regions. The proposed method satisfies patch tests to machine precision for the regular configurations considered, whereas exact satisfaction of the patch test is not achieved for the distorted three‐dimensional configuration. Nevertheless, approximately first‐order convergence is observed under mesh refinement. The accuracy and computational performance of the proposed method are further examined through a series of numerical examples.