In this paper, optimization approaches for the numerical design of structures are presented. The uncertainty of structural parameters is considered by means of random variables and interval design parameters within the optimization. A new space subdividing technique is introduced to substitute time-consuming failure probability constraint evaluations. In order to solve optimization problems with polymorphic uncertain parameters, surrogate objectives are formulated and solved by means of a particle swarm optimization (PSO) approach in combination with Monte Carlo simulation and interval analysis. Two computational schemes are presented and verified by a benchmark example. Finally, an application is shown, where the reinforcement layout of a reinforced concrete bridge structure is optimized by minimizing the crack widths at the reinforcement layers in order to improve the durability of the structure. A nonlinear finite element (FE) model is used to compute the uncertain crack patterns and the load bearing capacity. The stochastic objective function and the failure probability constraint are approximated by neural network based surrogate models.
In this contribution, a numerical design strategy for the optimization under polymorphic uncertainty is introduced and applied to a self‐weight minimization of a framework structure. The polymorphic uncertainty, which affects the constraint function of the optimization problem, is thereby modeled in terms of stochastic variables, fuzzy sets, and intervals to account for variability, imprecision and insufficient information. The stochastic quantities are computed using polynomial chaos expansion resulting in a purely fuzzy‐valued formulation of the constraint functions which can be computed using α‐cut optimization. Afterward, the constraint function can be interpreted in a possibilistic manner, resulting in a flexible formulation to include expert knowledge and to achieve a robust design.
The durability of reinforced concrete structures is dominated by steel reinforcement corrosion and uncertain service loads, which have to be considered in the lifetime oriented structural design. The transport of corrosive substances into the structure is considerably influenced by load induced cracking. The crack width therefore is a major controlling factor for the lifetime of reinforced concrete structures. To improve the design for durability, finite element models in combination with optimization approaches for polymorphic uncertain data are presented. Here, the crack width at the reinforcement layer is used as the optimization objective to be minimized. The structural reliability is treated as a constraint of the optimization task in terms of the accepted failure probability. The concrete covers of the reinforcement layers are chosen as interval design parameters, with midpoints to be optimized and a given radius to take construction imprecision into account. The structural loading, the Young's modulus of concrete and the corresponding tensile strength are considered as stochastic a priori parameters within the optimization, which is solved by a particle swarm optimization approach in combination with an artificial neural network surrogate model. The polymorphic uncertain structural response is computed by a combination of Monte Carlo simulations and optimization-based interval analysis to consider the stochastic and interval parameters within the optimization task, respectively. An application example demonstrates the performance of the proposed approach.
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