本文選題：連續(xù)體結(jié)構(gòu)拓?fù)鋬?yōu)化 + 應(yīng)力約束��； 參考：《應(yīng)用力學(xué)學(xué)報(bào)》2017年05期

【摘要】：針對(duì)受應(yīng)力約束的連續(xù)體結(jié)構(gòu)拓?fù)鋬?yōu)化問(wèn)題,推導(dǎo)了應(yīng)力敏度分析的伴隨法公式;并以算例形式,將伴隨法計(jì)算的應(yīng)力敏度結(jié)果與差分法結(jié)果進(jìn)行對(duì)比,驗(yàn)證了所推導(dǎo)公式的準(zhǔn)確性,應(yīng)力敏度分析結(jié)果表明了應(yīng)力對(duì)設(shè)計(jì)變量的偏導(dǎo)數(shù)具有局部性特點(diǎn)。在此基礎(chǔ)上,以受應(yīng)力約束重量極小化為目標(biāo)的結(jié)構(gòu)拓?fù)鋬?yōu)化為例,對(duì)比分析了應(yīng)力一階Taylor近似與滿應(yīng)力法的優(yōu)化效果。結(jié)果表明:相比滿應(yīng)力法,應(yīng)力一階近似能使結(jié)構(gòu)應(yīng)力在更多的部分達(dá)到許用應(yīng)力,得到的最優(yōu)結(jié)構(gòu)重量更輕。對(duì)設(shè)計(jì)變量數(shù)目巨大的應(yīng)力約束連續(xù)體結(jié)構(gòu)拓?fù)鋬?yōu)化問(wèn)題,由于應(yīng)力約束數(shù)目可以通過(guò)準(zhǔn)有效約束初選及不考慮刪除單元的應(yīng)力約束等方式減少,通常比設(shè)計(jì)變量數(shù)目小很多,應(yīng)用應(yīng)力敏度分析伴隨法可以顯著提高計(jì)算效率。
[Abstract]:In order to solve the topological optimization problem of continuum structure constrained by stress, the adjoint method formula of stress sensitivity analysis is derived, and the stress sensitivity results calculated by the adjoint method are compared with the results of the difference method in the form of an example. The results of stress sensitivity analysis show that the partial derivative of stress to design variables is local. On this basis, the optimization results of stress first order Taylor approximation and full stress method are compared and analyzed with the example of structural topology optimization in which the weight is minimized by stress constraints. The results show that compared with the full stress method, the stress first order approximation can make the stress reach the allowable stress in more parts, and the weight of the optimal structure is lighter. For the problem of topological optimization of continuum structures with large number of design variables, the number of stress constraints can be reduced by means of quasi-effective constraints and stress constraints without consideration of deleted elements, which is usually much smaller than the number of design variables. The adjoint method of stress sensitivity analysis can significantly improve the computational efficiency.
【作者單位】： 湖南城市學(xué)院土木工程學(xué)院;北京工業(yè)大學(xué)工程數(shù)值模擬中心;
【基金】：國(guó)家自然科學(xué)基金(11672103) 湖南省自然科學(xué)基金(2016JJ6016)
【分類號(hào)】：O302

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