Optimum Substitution of Complicated Profiles

Special aluminium profiles (BOSCH, ITEM, MAYTEC, LIPRO, MINITEC, ALUSIC, etc) are widely applied in several fields of everyday life. When constructing items such as tables, cupboards, instrument boards, shelves, etc., it could be necessary to use several metres of beams having these profiles. During an optimisation procedure of these structures (for minimum weight or minimum cost), finite element (FE) method may be necessary to verify the stress, deformation or eigenfrequency constraints. Finite element meshing (using solid hexahedron or tetrahedron finite elements) of beams several metres in length and structures containing these special complicated profiles will give a high number of nodes and elements, which will result in too high a computational cost for the solution. Beam and truss finite elements with no physical cross-sectional dimensions sometimes are not sufficient for an accurate and realistic approximation of the 3D behaviour of the real structure. In this paper a procedure is proposed for the optimal substitution of these complicated profiles for quicker FE analysis, using three-dimensional tetrahedron or hexahedron elements during static and dynamic analysis. The finite element mesh of the substituting profiles contains 96% less nodes and elements than the original complicated profiles. This method permits considerably shorter computational time for optimisation programs for these profiles.