發(fā)布時間：2018-08-06 19:31

【摘要】：近來提出的一致性高階無單元伽遼金法通過導(dǎo)數(shù)修正技術(shù)大幅度減少了所需積分點(diǎn)數(shù)目,并能夠精確地通過線性和二次分片試驗(yàn),顯著改善標(biāo)準(zhǔn)無單元伽遼金法的計算效率、精度和收斂性.本文在此基礎(chǔ)之上,充分利用無單元法易于在局部區(qū)域添加節(jié)點(diǎn)的優(yōu)勢,發(fā)展了一致性高階無單元伽遼金法的h型自適應(yīng)分析方法.根據(jù)應(yīng)變能密度梯度該方法自適應(yīng)地確定需節(jié)點(diǎn)加密的區(qū)域,基于背景積分網(wǎng)格的局部多層細(xì)化要求生成新的計算節(jié)點(diǎn),同時考慮了節(jié)點(diǎn)分布由密到疏漸進(jìn)過渡的情形.采用相鄰兩次計算的應(yīng)變能的相對誤差作為自適應(yīng)過程的停止準(zhǔn)則,將所發(fā)展自適應(yīng)無網(wǎng)格法應(yīng)用于由幾何外形、邊界外載和體力等因素造成的應(yīng)力集中問題的計算分析.數(shù)值結(jié)果表明,所發(fā)展方法能夠自適應(yīng)地對高應(yīng)力梯度區(qū)域進(jìn)行節(jié)點(diǎn)加密,自動給出合理的計算節(jié)點(diǎn)分布.與已有的標(biāo)準(zhǔn)無網(wǎng)格法的自適應(yīng)分析相比,所發(fā)展方法在計算效率、精度和應(yīng)力場光滑性等方面均展現(xiàn)出顯著優(yōu)勢.與采用節(jié)點(diǎn)均勻分布的一致性高階無單元伽遼金法相比,它大幅度地減少了計算節(jié)點(diǎn)數(shù)目,有效提高了一致性高階無單元伽遼金法在分析應(yīng)力集中等存在局部高梯度問題時的計算效率和求解精度.
[Abstract]:Recently, the consistent higher-order element-free Galerkin method has greatly reduced the number of integral points required by derivative correction, and has been able to improve the computational efficiency of the standard element-free Galerkin method by linear and quadratic piecewise experiments. Accuracy and convergence. On the basis of this, this paper makes full use of the advantage of element free method which is easy to add nodes in the local region, and develops an h type adaptive analysis method of consistent higher order element free Galerkin method. According to the strain energy density gradient this method adaptively determines the region requiring node encryption and generates a new computational node based on the local multi-layer refinement requirement of background integral grid. At the same time the case of node distribution transition from dense to sparsely progressive is considered. Using the relative error of the strain energy calculated by the adjacent two times as the stopping criterion of the adaptive process, the developed adaptive meshless method is applied to the calculation and analysis of the stress concentration caused by the factors such as geometric shape, external load and physical force. Numerical results show that the developed method can adaptively encrypt nodes in high stress gradient region and automatically give reasonable node distribution. Compared with the existing standard meshless adaptive analysis, the developed method shows significant advantages in computational efficiency, accuracy and stress field smoothness. Compared with the uniform higher-order element-free Galerkin method with uniform distribution of nodes, it greatly reduces the number of nodes. The computational efficiency and accuracy of the consistent higher-order element-free Galerkin method for the analysis of locally high gradient problems such as stress concentration are effectively improved.
【作者單位】： 大連理工大學(xué)工業(yè)裝備結(jié)構(gòu)分析國家重點(diǎn)實(shí)驗(yàn)室;成都理工大學(xué)地質(zhì)災(zāi)害防治與地質(zhì)環(huán)境保護(hù)國家重點(diǎn)實(shí)驗(yàn)室;武漢大學(xué)水資源與水電工程科學(xué)國家重點(diǎn)實(shí)驗(yàn)室;
【基金】：國家自然科學(xué)基金(11232003,11372066) 中央高�；究蒲袠I(yè)務(wù)費(fèi)專項(xiàng)資金(DUT15LK07) 遼寧省教育廳重點(diǎn)實(shí)驗(yàn)室基礎(chǔ)研究(LZ2014002) 水資源與水電工程科學(xué)國家重點(diǎn)實(shí)驗(yàn)室開放基金(2015SGG03) 地質(zhì)災(zāi)害防治與地質(zhì)環(huán)境保護(hù)國家重點(diǎn)實(shí)驗(yàn)室開放基金(SKLGP2016K007)資助項(xiàng)目
【分類號】：O241.8

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