本文選題：無網(wǎng)格方法 + 共軛復(fù)變量無單元Galerkin方法��； 參考：《湖北工業(yè)大學(xué)》2017年碩士論文

【摘要】：無網(wǎng)格方法是上個世紀(jì)九十年代中期興起的一種數(shù)值方法,由于不需要網(wǎng)格,只需要節(jié)點信息,不存在網(wǎng)格移動和網(wǎng)格畸變,因此具有適用范圍廣和計算精度高等優(yōu)點,已成為科學(xué)和工程計算方法研究的熱點,也是科學(xué)和工程計算發(fā)展的趨勢。將共軛復(fù)變量移動最小二乘法引入無單元Galerkin方法而形成的共軛復(fù)變量無單元Galerkin方法,可有效地解決無單元Galerkin方法存在的配點過多、計算量大等問題。共軛復(fù)變量無單元Galerkin方法的優(yōu)點是采用一維基函數(shù)建立二維問題的試函數(shù),使得試函數(shù)中所含的待定系數(shù)減少,從而提高了計算效率。本文將共軛復(fù)變量無單元Galerkin方法應(yīng)用于彈性力學(xué)問題,結(jié)合彈性力學(xué)問題的Galerkin積分弱形式,采用罰函數(shù)法施加本質(zhì)邊界條件,建立了彈性力學(xué)問題的共軛復(fù)變量無單元Galerkin方法,推導(dǎo)了相應(yīng)的計算公式,編制了相應(yīng)的計算程序,對三個彈性力學(xué)問題的算例進(jìn)行了數(shù)值分析,并對數(shù)值方法中的計算參數(shù)進(jìn)行了分析,確定了合理的參數(shù)范圍。該方法的優(yōu)點是具有較高的精度和較好的穩(wěn)定性。此外,采用外包線圖方法,綜合考察和評價了相關(guān)數(shù)值方法的計算精度和計算效率,直觀地比較了不同數(shù)值方法的優(yōu)劣。本文將共軛復(fù)變量無單元Galerkin方法應(yīng)用于溫度場問題,結(jié)合溫度場問題的Galerkin積分弱形式,使用罰函數(shù)法施加本質(zhì)邊界條件,采用兩種場變量表示方法,其中方法I中的場變量采用形函數(shù)的實部表示,方法II中的場變量采用試函數(shù)的實部或虛部表示,建立了兩種溫度場問題的共軛復(fù)變量無單元Galerkin方法,推導(dǎo)了相應(yīng)的計算公式,編制了相應(yīng)的計算程序,對三個溫度場問題的算例進(jìn)行了數(shù)值分析,并對數(shù)值方法中的計算參數(shù)進(jìn)行了分析,確定了合理的參數(shù)范圍。兩種方法均具有求解精度高、穩(wěn)定性好等優(yōu)點,其中方法II相對于方法I具有更高的精度。
[Abstract]:Meshless method is a numerical method developed in the middle of 1990s. Because it does not need mesh, only node information, mesh movement and mesh distortion, it has the advantages of wide application range and high calculation accuracy. It has become a hot spot in the research of scientific and engineering computing methods, and is also the trend of the development of science and engineering computing. The conjugate complex variable moving least square method is introduced into the element free Galerkin method, which can effectively solve the problems of too many collocation points and large computational costs in the element free Galerkin method. The advantage of the element free Galerkin method for conjugate complex variables is that a wiki function is used to establish the trial function of the two-dimensional problem, which reduces the undetermined coefficients in the trial function and improves the computational efficiency. In this paper, the conjugate complex variable element free Galerkin method is applied to the elastic mechanics problem. Combining the weak form of Galerkin integral of the elastic mechanics problem, using penalty function method to apply essential boundary conditions, the conjugate complex variable element free Galerkin method for the elastic mechanics problem is established. The corresponding calculation formula is derived and the corresponding calculation program is worked out. The numerical analysis of three examples of elastic mechanics problems is carried out, and the calculation parameters in the numerical method are analyzed, and the reasonable parameter range is determined. The advantage of this method is that it has higher accuracy and better stability. In addition, the calculation accuracy and efficiency of the relevant numerical methods are comprehensively investigated and evaluated by using the outsourced graph method, and the advantages and disadvantages of different numerical methods are compared intuitively. In this paper, the element free Galerkin method for conjugate complex variables is applied to the temperature field problem. Combining with the weak form of Galerkin integral of the temperature field problem, the penalty function method is used to impose essential boundary conditions, and two kinds of field variable representation methods are adopted. The field variables in method I are represented by the real part of the shape function, and the field variables in method II are represented by the real part or the imaginary part of the trial function. The element free Galerkin method of conjugate complex variables for two kinds of temperature field problems is established, and the corresponding calculation formulas are derived. The corresponding calculation program is compiled and the numerical analysis of three examples of temperature field problems is carried out. The calculation parameters in the numerical method are analyzed and the reasonable range of parameters is determined. Both methods have the advantages of high accuracy and good stability, among which method II has higher accuracy than method I.
【學(xué)位授予單位】：湖北工業(yè)大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：TU43

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