A new approach for nonmatching interface construction by the method of localized Lagrange multipliers

A new frame discretization method for treating non-matching discrete interfaces is presented based on the method of localized Lagrange multipliers, which introduces the frame domain lying between the two interfacing parts. The required interface compatibility conditions are then enforced independently between the master domain interface nodes and the frame nodes, and the slave domain interface nodes and the same frame nodes. The frame nodes are determined so as to satisfy the mean coordinates, including the frame node to be determined, of the nearest interface element of the master domain for each of the slave domain interface nodes. The roles of the two domains may interchange, resulting in a unique determination of the frame elements for each case. The interface compatibility conditions thus obtained satisfy energy conservation, especially when the interface gaps are unavoidable while requiring no special treatments for the boundary nodes that are often required in mortar and allied methods. Consequently, the proposed method can effectively deal with the non-matching interface regardless of the geometric complexity and element type. Numerical examples illustrate the simplicity of the proposed method and offer improved accuracy for interfaces with gaps and as good of an accuracy as other methods when there are no gaps, while preserving implementation simplicity. •A new frame-discretization method that used in the method of localized Lagrange multipliers for the non-matching interface problems is proposed.•Mean-value points are used as the frame node to properly impose the interface compatibility condition and to precisely apply them.•The accuracy is analytically confirmed through the error analysis and the satisfaction of the frame equilibrium equation.•Several numerical examples are presented to verify the validity of the proposed method.