Tese: Topology optimization of geometrically nonlinear structures based on an energy interpolation scheme
Aluno(a) : André Xavier LeitãoOrientador(a): Anderson Pereira
Área de Concentração: Mecânica Aplicada
Data: 03/05/2019
Link para tese/dissertação: http://doi.org/10.17771/PUCRio.acad.48287
Resumo: In many engineering problems, e.g., design of flexible biomedical prostheses or energy absorption devices, structures undergo large displacements. In those problems, the structural response must take into account the geometric nonlinearity. However, topology optimization algorithms regarding nonlinearities, and based on the finite element method, typically suffer from numerical instabilities caused by excessive distortions of low-density regions within the design domain. In particular, the stiffness matrix may be no longer positive definite, which can jeopardize the convergence of the optimization process. This dissertation aims to study an energy interpolation scheme based on the St. Venant-Kirchhoff material model to alleviate this convergence issue. At each step of the optimization, the nonlinear state equation is solved by the Newton-Raphson procedure to determine the equilibrium configuration. Making use of the gradient information computed from the adjoint method, the Method of Moving Asymptotes is employed to update the design variables. Through several benchmark problems considering large displacements, it is demonstrated the effectiveness and efficiency of this energy interpolation scheme. More specifically, the optimized designs are in agreement with those obtained in the literature and exhibit correct load-level dependence. The investigated energy interpolation scheme plays a crucial in the solution of nonlinear problems with high load levels, allowing the optimization routine to converge and to obtain the optimal material arrangement.