Computational Methods in Engineering

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Due to their dual behavior under tension and compression, structures with tension-only members show non-linear behavior. To analize such structures, it is necessary to use a nonlinear analysis scheme. Nonlinear analysis methods generally use gradual loading techniques with/without modification of stiffness matrix of the structure. These methods, in addition to being time consuming algorithms, are iterative and may not always lead to exact results. In this paper, an innovative technique is presented that conducts the nonlinear analysis in one step without any modification in stiffness matrix and/ or load vector and gives exact results. The proposed method conducts nonlinear analysis via solution of a Quadratic Programming problem that, in turn, is established based on some simple static rules and superposition principle. It superimposes the results of linear elastic analysis for external loads and some weighted (yet unknown) self-equilibrating unit loads. The outcome of QP problem is the unknown weights of unit loads from which internal forces are obtained. Two solved examples have been provided to show the capabilities of the proposed method in doing nonlinear analysis and in obtaining exact and accurate results.

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In this paper, first the theory of Improved Applied Element Method (IAEM) is proposed and then an appropriate algorithm and software are developed for analyzing structures behavior until collapse by this method. Then, some examples of structural analysis by the above method and a software developed for this study are presented. The results show that IAEM has the ability to solve the discussed problems more accurately in less time than Finite Element Method (FEM). Moreover, the efficiency of the method for solving large displacements problems is enhanced in this research by introducing nonlinear response indicators. For modification of the stiffness matrix in the nonlinear range, a new method is presented that increases the accuracy of calculation up to 30%.