本文選題：移動(dòng)最小二乘插值 + 數(shù)值流形法　； 參考：《巖土工程學(xué)報(bào)》2017年10期

【摘要】：由于基于單位分解的無網(wǎng)格法,如無網(wǎng)格伽遼金法等,所構(gòu)造的形函數(shù)往往不具有?插值屬性,因此難以準(zhǔn)確施加本質(zhì)邊界條件和材料邊界的連續(xù)性條件。而采用傳統(tǒng)的罰函數(shù)法和拉氏乘子法,分別有合適罰因子的選取和需滿足inf-sup條件等問題。所以,利用"局部解滿足了要求,則由單位分解所構(gòu)造的整體解會(huì)自動(dòng)滿足要求"的單位分解法的求解性質(zhì),通過構(gòu)造不同類型物理片上的局部解,提出了改進(jìn)的基于移動(dòng)最小二乘插值的數(shù)值流形法(MLS-NMM),并將其應(yīng)用于穩(wěn)定滲流問題的求解中。該方法不僅能直接準(zhǔn)確施加本質(zhì)邊界和材料邊界條件,而且能精確地求解奇異角點(diǎn)問題。典型算例的計(jì)算結(jié)果表明,我們所建議的方法是可行的、有效的,可為工程滲流分析提供參考。
[Abstract]:Because of the meshless method based on unit decomposition, such as the meshless Galerkin method, the shape functions constructed often do not have? Interpolation attribute makes it difficult to apply the essential boundary condition and the continuity condition of material boundary accurately. The traditional penalty function method and Lagrangian multiplier method are used to select the appropriate penalty factors and to satisfy the inf-sup condition respectively. Therefore, by using the solution property of the unit decomposition method, which "the local solution satisfies the requirement, the global solution constructed by the unit decomposition will automatically meet the requirement", by constructing the local solution on different types of physical slices, An improved MLS-NMMM method based on moving least square interpolation is proposed and applied to the solution of steady seepage problem. This method can not only directly and accurately apply essential boundary and material boundary conditions, but also solve singularity corner problem accurately. The results of typical numerical examples show that the proposed method is feasible and effective and can be used as a reference for engineering seepage analysis.
【作者單位】： 中國科學(xué)院武漢巖土力學(xué)研究所巖土力學(xué)與工程國家重點(diǎn)實(shí)驗(yàn)室;中國科學(xué)院大學(xué);北京工業(yè)大學(xué)建筑工程學(xué)院;
【基金】：國家自然科學(xué)基金項(xiàng)目(11172313,11572009,51538001) 國家基礎(chǔ)研究計(jì)劃(“973”計(jì)劃)項(xiàng)目(2014CB047100)
【分類號(hào)】：O357.3

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