【摘要】：無網(wǎng)格局部彼得洛夫-伽遼金(meshless local Petrov-Galerkin,MLPG)法是一種具有代表性的無網(wǎng)格方法,在計(jì)算力學(xué)領(lǐng)域得到廣泛應(yīng)用.然而,這種方法在邊界上需執(zhí)行積分運(yùn)算,通常很難處理不規(guī)則求解域問題.為了克服MLPG法的這種局限性,提出了無網(wǎng)格局部強(qiáng)弱(meshless local strong-weak,MLSW)法.MLSW法采用MLPG法離散內(nèi)部求解域,采用無網(wǎng)格介點(diǎn)(meshless intervention-point,MIP)法施加自然邊界條件,并采用配點(diǎn)法施加本質(zhì)邊界條件,避免執(zhí)行邊界積分運(yùn)算,可適用于求解各類復(fù)雜的不規(guī)則域問題.從理論上講,這種結(jié)合式方法,既保持了MLPG法穩(wěn)定而精確計(jì)算的優(yōu)勢(shì),同時(shí)兼?zhèn)渑潼c(diǎn)型方法在處理復(fù)雜結(jié)構(gòu)問題時(shí)簡(jiǎn)潔而靈活的優(yōu)勢(shì),實(shí)現(xiàn)了弱式法和強(qiáng)式法的優(yōu)勢(shì)互補(bǔ).此外,MLSW法采用移動(dòng)最小二乘核(moving least squares core,MLSc)近似法來構(gòu)造形函數(shù),是對(duì)傳統(tǒng)移動(dòng)最小二乘(moving least squares,MLS)近似法的一種改進(jìn).MLSc使用核基函數(shù)代替通常的基函數(shù),有利于數(shù)值求解的精確性和穩(wěn)定性,而且其導(dǎo)數(shù)近似計(jì)算變得更為簡(jiǎn)單.數(shù)值算例結(jié)果初步表明:這種新方法實(shí)施簡(jiǎn)單,求解穩(wěn)定、精確,表現(xiàn)出適合工程運(yùn)用的潛力.
[Abstract]:The meshless local Petrov-Galerkin (meshless local (meshless local) method is a representative meshless method, which is widely used in the field of computational mechanics. However, this method needs to perform integral operations on the boundary, and it is usually difficult to deal with irregular domain problems. In order to overcome the limitation of the MLPG method, a meshless local strong / weak (meshless local strong-weak MLSW method is proposed. The MLPG method is used to discretize the internal solution domain, the meshless intervention-point MLPG method is used to impose the natural boundary condition, and the collocation method is used to impose the essential boundary condition. It can be used to solve all kinds of complex irregular domain problems by avoiding boundary integral operation. Theoretically speaking, this combined method not only maintains the advantages of MLPG method in stable and accurate calculation, but also has the advantages of simplicity and flexibility in dealing with complex structural problems. The weak method and the strong method complement each other. In addition, the moving least square kernel (moving least squares coreSc approximation method is used to construct the shape function, which is an improvement of the traditional moving least squares (moving least squares MLS approximation method. MLSc uses kernel basis function instead of the usual basis function. It is advantageous to the accuracy and stability of the numerical solution, and the approximate calculation of its derivative becomes more simple. The results of numerical examples show that the new method is simple, stable and accurate, and shows the potential for engineering application.
【作者單位】： 長(zhǎng)沙理工大學(xué)道路結(jié)構(gòu)與材料交通行業(yè)重點(diǎn)實(shí)驗(yàn)室;長(zhǎng)沙理工大學(xué)交通運(yùn)輸工程學(xué)院;
【基金】：國家自然科學(xué)基金(51478053) 交通行業(yè)重點(diǎn)實(shí)驗(yàn)室(長(zhǎng)沙)開放基金(KFJ120201)資助項(xiàng)目
【分類號(hào)】：O241.82

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