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

Abstract

• 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 . • This finite element technology is validated and tested using beam and frame structures. • By reducing length of extra window, the displacement continuity increases and stress fields are more accurate. 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.