Abstract
This paper concentrates on finding the optimal distribution for continuum structure such that the structural weight with stress constraints is minimized where the physical design domain is discretized by finite elements. A novel Independent-Continuous-Mapping (ICM) method is proposed to convert equivalently the binary design variables which is used to indicate material or void in the various elements to independent continuous design variables. Moreover, three smooth mappings about weight, stiffness, and stress of the structural elements are introduced to formulate the objective function based on the so-called concepts of polish function and weighting filter function. A new general continuous approach for topology optimization is given which can eliminate the stress singularity phenomena more efficiently than the traditionalε-relaxation method, and an alternative strain energy method for the stress constraints is proposed to overcome the difficulty in stress sensitivity analyses. Mathematically, by means of a generalized aggregation KS-like function defined as the parabolic aggregation function, a topology optimization model is formulated with the weight objective and single parabolic global strain energy constraints. The numerical examples demonstrate that the proposed methods effectively remove the stress concentrations and generate black-and-white designs for practically sized problems.
Highlights
Topology optimization is one of the most challenging research topics and a research focus in the current structural optimization design field, which has been rapidly developed with a lot of fruitful research work in the past two decades, and the development of topology optimization can be found in the monographs [1,2,3] and references therein
By transforming the difficult structural topology optimization model into a relatively easier sizing optimization model based on the microstructural parameters of composite materials, the approach of homogenization is capable of finding the optimum topologies of the structures
From the ICM method point of view, as long as the physical or geometric parameters change in the structural topology optimization process, the related weighting filter function should be considered as not limiting to the stiffness matrix
Summary
Topology optimization is one of the most challenging research topics and a research focus in the current structural optimization design field, which has been rapidly developed with a lot of fruitful research work in the past two decades, and the development of topology optimization can be found in the monographs [1,2,3] and references therein. Denote as τi/τi0 = s−1(ti), which is a 0-1 binary multivalued function that cannot indicate the size of the physical or geometric parameter τi when the independent topological design variables ti = s(τi/τi0) take intermediate values between 0-1 To overcome this difficulty, we introduce the concept of weighting filter function f(ti) = τi/τi0 = p−1(ti) which continuously approximates the inverse mapping of the step-up function τi/τi0 = s−1(ti), and it points out the proximity degree that τi closes to τi0 and 0. From the ICM method point of view, as long as the physical or geometric parameters change in the structural topology optimization process, the related weighting filter function (or interpolation scheme in terms of the SIMP method) should be considered as not limiting to the stiffness matrix. The method is implemented in the topology optimization procedure to overcome the difficulty in stress sensitivity analyses
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