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Robust topology optimization under multiple independent uncertainties of loading positions
Author(s) -
Wang Dong,
Gao Weifeng
Publication year - 2020
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.6503
Subject(s) - topology optimization , mathematical optimization , position (finance) , quadratic equation , topology (electrical circuits) , mathematics , optimization problem , benchmark (surveying) , bounded function , control theory (sociology) , computer science , finite element method , engineering , structural engineering , geometry , mathematical analysis , control (management) , finance , geodesy , combinatorics , artificial intelligence , economics , geography
Summary The topology optimization problem of a continuum structure is further investigated under the independent position uncertainties of multiple external loads, which are now described with an interval vector of uncertain‐but‐bounded variables. In this study, the structural compliance is formulated with the quadratic Taylor series expansion of multiple loading positions. As a result, the objective gradient information to the topological variables can be evaluated efficiently upon an explicit quadratic expression as the loads deviate from their ideal application points. Based on the minimum (largest absolute) value of design sensitivities, which corresponds to the most sensitive compliance to the load position variations, a two‐level optimization algorithm within the non‐probabilistic approach is developed upon a gradient‐based optimization method. The proposed framework is then performed to achieve the robust optimal configurations of four benchmark examples, and the final designs are compared comprehensively with the traditional topology optimizations under the loading point fixation. It will be observed that the present methodology can provide a remarkably different structural layout with the auxiliary components in the design domain to counteract the load position uncertainties. The numerical results also show that the present robust topology optimization can effectively prevent the structural performance from a noticeable deterioration than the deterministic optimization in the presence of load position disturbances.