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Topology optimization for reliable micro mechanical structures with respect to geometric uncertainties during etching process is presented by using the level-set method. The etching uncertainty is treated as the bounded-but-unknown parameter and the performance drops by the worst etched micro structures are limited as the constraint form of optimization. To this end, models of the over-or under-etched structures should be consistently built from the nominal models during the whole optimization process, which is very hard by using conventional SIMP-based topology optimization methods. By using the level-set method, due to the implicit boundary representation and the signed distance property of the level-set function, models according to the uncertain etching parameter can be easily constructed. The effectiveness of the proposed approach is verified through design examples for mean compliance minimization problems and compliant mechanism problems.
In this investigation, thin-walled closed beams are modeled by a higher-order beam theory that incorporates warping and distortional degrees of freedom in addition to the standard Timoshenko degrees of freedom. In the proposed approach, no artificial spring is inserted between beams connected at an angled joint, but a systematic technique to match all degrees of freedom of the connected beams is employed. Although specific numerical examples consist of relatively simple thin-walled box beams, the present analysis suggests a possibility to handle arbitrarily-cross-sectioned closed beams meeting at multiple joints by a higher-order beam theory without using joint springs. Two cases were investigated: two box beams connected at an angled joint and a box beam forming a closed loop. The predicted vibration results by the developed approach were compared with shell analysis results.
Based on finite element method, topology optimization is applied to design optimal shape of a given design space. In this study, the multilayer plate structures are analyzed and extended to topology optimization design. In order to solving shear locking problem of thin plate caused by Mindlin-Reissner plate model, P1-nonconforming element and selective reduced integration are employed. P1 quadrilateral element is one kind of discontinuous and Poisson' locking-free element. Furthermore, P1-nonconforming element has linear shape functions that are defined at middle point of each edge. Here, Darcy-Stokes fluid model and reinforcement plate model are applied on different layers. By calculating sensitivity analysis of multiobjective function, the minimum compliance and dissipated power of the model with given mass is obtained by method of moving asymptotes (MMA). Some numerical examples of multilayer plate structure are studied and compared with the reference results.