Extended multiscale FEM for design of beams and frames with complex topology

A numerical method for design of beams and frames with complex topology is proposed. The method is based on extended multi-scale finite element method where beam finite elements are used on coarse scale and continuum elements on fine scale. A procedure for calculation of multi-scale base functions, up-scaling and downscaling techniques is proposed by using a modified version of window method that is used in computational homogenization. Coarse scale finite element is embedded into a frame of a material that is representing surrounding structure in a sense of mechanical properties. Results show that this method can capture displacements, shear deformations and local stress-strain gradients with significantly reduced computational time and memory comparing to full scale continuum model. Moreover, this method includes a special hybrid finite elements for precise modelling of structural joints. Hence, the proposed method has a potential application in large scale 2D and 3D structural analysis of non-standard beams and frames where spatial interaction between structural elements is important.