A new reliability-based topology optimization method for compliant mechanisms with geometrical nonlinearity is presented. The aim of this paper is to integrate reliability and geometrical nonlinear analysis into the topology optimization problems. Firstly, geometrical nonlinear response analysis method of the compliant mechanisms is developed based on the Total-Lagrange finite element formulation, the incremental scheme and the Newton-Raphson iteration method. Secondly, a multi-objective topology optimal model of compliant mechanisms considering the uncertainties of the applied loads and the geometry descriptions is established. The objective function is defined by minimum the compliance and maximum the geometric advantage to meet both the stiffness and the flexibility requirements, and the reliabilities of the compliant mechanisms are evaluated by using the first order reliability method. Thirdly, the computation of the sensitivities is developed with the adjoint method and the optimization problem is solved by using the Method of Moving Asymptotes. Finally, through numerical calculations, reliability-based topology designs with geometric nonlinearity of a typical compliant micro-gripper and a multi-input and multi-output compliant sage are obtained. The importance of considering uncertainties and geometric nonlinearity is then demonstrated by comparing the results obtained by the proposed method with deterministic optimal designs, which shows that the reliability-based topology optimization yields mechanisms that are more reliable than those produced by deterministic topology optimization.

In this paper, we prove topology dependent bounds on the number of rounds needed to compute Functional Aggregate eries (FAQs) studied by Abo Khamis et al. [PODS 2016] in a synchronous distributed network under the model considered by Cha opadhyay et al. [FOCS 2014, SODA 2017. Unlike the recent work on computing database queries in the Massively Parallel Computation model, in the model of Cha opadhyay et al., nodes can communicate only via private point-to-point channels and we are interested in bounds that work over an arbitrary communication topology. is model, which is closer to the well-studied CONGEST model in distributed computing and generalizes Yao's two party communication complexity model, has so far only been studied for problems that are common in the two-party communication complexity literature.is is the rst work to consider more practically motivated problems in this distributed model. For the sake of exposition, we focus on two special problems in this paper: Boolean Conjunctive ery (BCQ) and computing variable/factor marginals in Probabilistic Graphical Models (PGMs). We obtain tight bounds on the number of rounds needed to compute such queries as long as the underlying hypergraph of the query is O(1)-degenerate and has O(1)-arity. In particular, the O(1)-degeneracy condition covers most well-studied queries that are e ciently computable in the centralized computation model like queries with constant treewidth. ese tight bounds depend on a new notion of 'width' (namely internal-node-width) for Generalized Hypertree Decompositions (GHDs) of acyclic hypergraphs, which minimizes the number of internal nodes in a sub-class of GHDs. To the best of our knowledge, this width has not been studied explicitly in the theoretical database literature. Finally, we consider the problem of computing the product of a vector with a chain of matrices and prove tight bounds on its round complexity (over the nite eld of two elements) using a novel min-entropy based argument.

Homogenization or material distribution method based topology optimization will create final topologies in grey level image and saw tooth jump discontinuity boundaries that are not suitable for direct engineering practice, so it is necessary to extract the topological diagram. And a new topology extraction method for compliant mechanisms is presented. In the fist stage, the grey image is transferred into the black-and white finite element topology optimization results. The threshold value meeting to objective function is obtained so that each element is either empty or solid; in the second stage, the density contour approach is used by redistributing nodal densities to generate the smooth boundaries; in the third stage, Smooth boundaries are represented by parameterized B-spline curves whose control points selected from the viewpoint of stiffness and flexibility constitute the parameters ready to undergo shape optimization; Then shape optimization is executed to improve stress-based local performance, The parameters that present the outer shape of the compliant mechanism are used as design variables; In the final stage, simulations of numerical examples are presented to show the validity of the proposed method.