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基于SIMP和SSV的結(jié)構(gòu)與支撐拓撲優(yōu)化設(shè)計
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    摘要:

    針對SIMP方法中,存在中間支撐密度單元,且對拓撲分布有一定影響的情況,引入SSV約束,提出了一種基于SIMP方法和SSV約束的方法即SIMP-SSV方法,其思路是用SIMP的優(yōu)化結(jié)果初始化SSV方法中的設(shè)計變量,再用SSV方法得到最終的優(yōu)化目標。用SIMP-SSV方法同時進行了具有最小柔度的結(jié)構(gòu)與支撐的拓撲優(yōu)化設(shè)計。算例表明,SIMP-SSV方法不僅使拓撲分布更加清晰,有效消除了中間支撐變量對結(jié)構(gòu)與支撐拓撲分布的影響,而且可使最小柔度比

    Abstract:

    SIMP的更小。 In the results of topology optimization with SIMP(solid isotropic material with penalization model), there are always some grey areas with intermediate densities. The intermediate densities of supports will have an effect on the topologies of structure and support. In order to drive the solution to a 0/1 layout a new constraint, labeled the sum of squares of the variables (SSV) was introduced for the first time. The constraint stipulated that the SSV must be larger or equal to its value at a discrete design for a specified amount of material. Based on the SIMP approach and the SSV constraint, a two-pass method has been proposed, where SIMP was employed to generate an intermediate solution to initialize the design variables and SSV was then adopted to produce the final design. In SSV stage, the design variables were still the densities of the finite elements but Young's modulus was a linear function of these densities (in some sense, a SIMP material without penalty). The potential of the present method has been demonstrated by simultaneous topological design of structure and support for minimum compliance. The examples showed that the hybrid technique could effectively remove all intermediate densities of support, whose effects were eliminated accordingly, and generate stiffer optimal designs characterized with a sharper boundary in contrast to SIMP.

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周向陽,陳立平,黃正東.基于SIMP和SSV的結(jié)構(gòu)與支撐拓撲優(yōu)化設(shè)計[J].農(nóng)業(yè)機械學(xué)報,2008,39(6):137-141.[J]. Transactions of the Chinese Society for Agricultural Machinery,2008,39(6):137-141.

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