本文選題：等參圓單元　切入點(diǎn)：等參管單元　出處：《大連理工大學(xué)》2015年碩士論文

【摘要】：隨著現(xiàn)代工程應(yīng)用對(duì)結(jié)構(gòu)的性能要求越來(lái)越高,使得結(jié)構(gòu)呈現(xiàn)出越來(lái)越復(fù)雜的外貌形狀。基于此背景,孔狀與管狀結(jié)構(gòu)因具有優(yōu)良的熱學(xué)與力學(xué)性能而得到廣‘泛應(yīng)用。由于孔狀與管狀結(jié)構(gòu)幾何外形的特殊性與復(fù)雜性,在采用有限元法求解時(shí),需要?jiǎng)澐执罅康木W(wǎng)格,導(dǎo)致建模與計(jì)算工作量很大。邊界元法作為繼有限元法之后又一重要的數(shù)值方法,因其具有降低問(wèn)題維數(shù)、求解精度高等優(yōu)點(diǎn)而在工程中得到廣泛應(yīng)用。但是,在邊界元法中采用常規(guī)單元求解此類問(wèn)題時(shí),為了保證計(jì)算精度、減少離散誤差,仍需要布置較密的單元來(lái)模擬結(jié)構(gòu)的幾何外形。這樣,邊界元法就無(wú)法體現(xiàn)自身的優(yōu)勢(shì)。為了克服傳統(tǒng)邊界元法中采用常規(guī)單元計(jì)算孔狀結(jié)構(gòu)時(shí)出現(xiàn)的計(jì)算節(jié)點(diǎn)多、離散誤差大的缺點(diǎn),本文基于Lagrange插值原理,構(gòu)造了二維邊界元法中的等參圓單元。該單元能很好地模擬孔狀結(jié)構(gòu)的光滑封閉曲線邊界,并能對(duì)單元內(nèi)的物理量進(jìn)行高階插值。另外,在二維邊界元法中使用等參圓單元時(shí),本文還提出了一種隔離對(duì)數(shù)奇異項(xiàng)、采用對(duì)數(shù)高斯積分來(lái)計(jì)算奇異積分的方法。對(duì)熱傳導(dǎo)問(wèn)題的算例分析表明,基于等參圓單元的邊界元算法在處理孔狀結(jié)構(gòu)時(shí)具有離散網(wǎng)格少、計(jì)算精度高的優(yōu)點(diǎn)。另外,在等參圓單元的基礎(chǔ)上,基于Lagrange插值原理,本文還提出了一種基于三維等參管單元的邊界元算法。等參管單元能很好地模擬工程問(wèn)題中結(jié)構(gòu)的內(nèi)外管狀壁面,并實(shí)現(xiàn)物理量的高階插值。在三維熱傳導(dǎo)問(wèn)題中,使用基于等參管單元的邊界元法求解時(shí),提出了一種在等參平面內(nèi)消除積分奇異性的方法。算例分析表明,本文所述方法能計(jì)算三維空間中沿任意方向彎曲的管狀結(jié)構(gòu),且具有計(jì)算節(jié)點(diǎn)少、求解精度高的優(yōu)點(diǎn)。
[Abstract]:As modern engineering applications become more and more demanding for the performance of structures, the structure presents more and more complex appearance shapes. Porous and tubular structures have been widely used because of their excellent thermal and mechanical properties. Due to the particularity and complexity of the geometrical shapes of porous and tubular structures, a large number of meshes are needed to be solved by finite element method (FEM). Boundary element method (BEM), as an important numerical method after finite element method, is widely used in engineering because of its advantages of reducing the dimension of the problem and high accuracy. In order to ensure the accuracy of the calculation and reduce the discrete error, it is necessary to arrange more dense elements to simulate the geometric shape of the structure when the conventional element is used to solve this kind of problem in the boundary element method. In order to overcome the disadvantages of traditional boundary element method, in which there are many nodes and large discrete errors, this paper is based on the principle of Lagrange interpolation. The isoparametric circular element in the two-dimensional boundary element method is constructed. The element can well simulate the smooth and closed curve boundary of the porous structure, and can interpolate the physical quantities in the element by higher order. In addition, when the isoparametric circular element is used in the two-dimensional boundary element method, In this paper, an isolated logarithmic singular term is proposed, and the method of calculating singular integral with logarithmic Gao Si integral is presented. The boundary element algorithm based on isoparametric circular element has the advantages of less discrete meshes and higher calculation accuracy in dealing with the hole structure. In addition, on the basis of isoparametric circular element, the method is based on the principle of Lagrange interpolation. In this paper, a boundary element algorithm based on 3-D isoparametric element is proposed. The isoparametric element can well simulate the inner and outer wall of the structure in engineering problems, and realize the high-order interpolation of physical quantities. A method to eliminate integral singularity in isoparametric plane is proposed when the boundary element method based on isoparametric element is used. The numerical examples show that the method presented in this paper can be used to calculate the tubular structures bending in any direction in three dimensional space. It has the advantages of less nodes and higher accuracy.
【學(xué)位授予單位】：大連理工大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2015
【分類號(hào)】：TK124

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相關(guān)期刊論文 前1條

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本文編號(hào)：1669518