SummaryTopology optimization using stress constraints and considering uncertainties is a serious challenge, since a reliability problem has to be solved for each stress constraint, for each element in the mesh. In this paper, an alternative way of solving this problem is used, where uncertainty quantification is performed through the first-order perturbation approach, with proper validation by Monte Carlo simulation. Uncertainties are considered in the loading magnitude and direction. The minimum volume problem subjected to local stress constraints is formulated as a robust problem, where the stress constraints are written as a weighted average between their expected value and standard deviation. The augmented Lagrangian method is used for handling the large set of local stress constraints, whereas a gradient-based algorithm is used for handling the bounding constraints. It is shown that even in the presence of small uncertainties in loading direction, different topologies are obtained when compared to a deterministic approach. The effect of correlation between uncertainties in loading magnitude and direction on optimal topologies is also studied, where the main observed result is loss of symmetry in optimal topologies.

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One of the most widely employed models to evaluate ductile damage and fracture is due to Gurson. An inconvenience of the model is that several material parameters must be determined in order to represent adequately a given experimental behavior. Determination of such parameters is not trivial but can be performed by means of inverse analyses using optimization procedures. In this work, the material parameters are sought by fitting force vs. displacement curves computed using finite element simulation to experimental curves obtained from tensile tests. The resulting optimization problem is nonconvex and may present several local minima, thereby posing some difficulties to gradient-based optimization procedures due to the strong dependence on initial estimates of the design variables (the material parameters in this case). An approach based on a genetic algorithm is used in an attempt to avoid this problem. This strategy makes also possible to exploit the parallel nature of evolutionary algorithms as, at each generation, the evaluation of the fitness function of one individual is independent of the fitness of the rest of the population. In this particular implementation, each individual is represented by a gray encoding sequence of genes, the parental selection is performed by means of a tournament selection, the crossover probability is 0.8 and the probability of mutation is 0.05.

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A general mesh independent filter as a mean to control the complexity of topology optimization designed structures is discussed. A new mesh-independent filter, applied over the move-limits of the sequential linear programming is proposed, and it is shown that its use alleviates common problems in the continuum topology optimization, like checkerboarding, mesh dependency, as well as effects associated to non-structured meshes, like numerical anisotropy. The structural optimization formulation adopted in this work is the minimization of a penalized function of the volume, with constraints on the compliance of each load case. Aspects of this penalized objective function are discussed, and several numerical examples are shown