Three Different Methods for Approximate Analysis of Bar Structures

In this paper, modified solutions were compared through utilizing three different approximate methods for bar structures. The modifications considered various changes in the initial design. To authors' best of knowledge, the studies have carried out on this matter so far are not broad enough and have considerred the simeltaneous variations of size, geometry and topology on the bar structures. In this study, three well-known methods, including combined approximation, rational approximation and the approximate inversion of stiffness matrix methods are formulated. A large variety of problems will be performed with different characteristics to compare the ability of these approaches in determining the suitable approximate modified displacements. Cross sectional properties and nodal coordinates are considered as design variables. Displacement errors and computational efforts of the processes considered as comparison factors. It is shown that the approximate inversion of the stiffness matrix method cannot solve the problems, which requires the modification of structural geometry. Furthermore, the combined approximation and rational approximation methods have the ability of reaching displacements with suitable quality in the problems with a moderate size.