Investigations in structural optimization of nonlinear problems using the finite element method




Sedaghati, Ramin

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Structural optimization is an important field in engineering with a strong foundation on continuum mechanics, structural finite element analysis, computational techniques and optimization methods. Research in structural optimization of linear and geometrically nonlinear problems using the force method has not received appropriate attention by the research community. The present thesis constitutes a comprehensive study in the area of structural optimization. Development of new methodologies for analysis and optimization and their integration in finite element computer programs for analysis and design of linear and nonlinear structural problems are among the most important contributions. For linear problems, a force method formulation based on the complementary energy is proposed. Using this formulation, the element forces are obtained without the direct generation of the compatibility matrix. Application of the proposed method in structural size optimization under stress, displacement and frequency constraints has been investigated and its efficiency is compared with the conventional displacement formulation. Moreover, an efficient methodology based on the integrated force method is developed for topology optimization of adaptive structures under static and dynamic loads. It has been demonstrated that structural optimization based on the force method is computationally more efficient. For nonlinear problems, an efficient methodology has been developed for structural optimization of geometrical nonlinear problems under system stability constraints. The technique combines the nonlinear finite element method based on the displacement control technique for analysis and optimality criterion methods for optimization. Application of the proposed methodology has been investigated for shallow structures. The efficiency of the proposed optimization algorithms are compared with the mathematical programming method based on the Sequential Quadratic Programming technique. It is shown that structural design optimization based on the linear analysis for structures with intrinsic geometric nonlinearites may lead to structural failure. Finally, application of the group theoretic approach in structural optimization of geometrical nonlinear symmetric structures under system stability constraint has been investigated. It has been demonstrated that structural optimization of nonlinear symmetric structures using the group theoretic approach is computationally efficient and excellent agreement exists between the full space and the reduced subspace optimal solutions.



Structural optimization, Nonlinear functional analysis