복합재료의 멀티스케일 해석을 위한 직접 FE2 방법의 개선

This paper proposes a method to reduce shear locking in the direct FE² method for multiscale analysis of composite materials. The direct FE² method connects macroscopic and microscopic scale finite elements through a linear relationship using multipoint constraints to obtain solutions to multiscale problems. Unlike conventional FE² methods, this method does not require a complex program and iterative calculations between macroscopic and microscopic problems. Since the boundary conditions applied to microscale elements are based on macroscopic deformations, shear locking can occur when macroscopic elements are under bending deformations. To resolve this problem, analytic solutions for bending deformations are added to the boundary conditions of microscopic elements as additional deformation components, which improves the performance of the direct FE² method.