本文選題：哈密頓體系 + 壓電/電磁彈性材料��； 參考：《大連理工大學(xué)》2016年博士論文

【摘要】：隨著材料科學(xué)和電子技術(shù)的發(fā)展,具有良好力、電、磁耦合效應(yīng)的壓電／電磁等功能復(fù)合材料,被廣泛用于制造傳感器、探測(cè)器、超聲成像器等智能器件。然而,由于材料性質(zhì)間的不匹配及自身的脆性,該類(lèi)器件在制作和使用過(guò)程中,不可避免會(huì)產(chǎn)生裂紋或孔洞,從而導(dǎo)致缺陷附近的物理場(chǎng)奇異(力、電和磁場(chǎng)集中現(xiàn)象),影響結(jié)構(gòu)的完整性,并可能引發(fā)結(jié)構(gòu)功能失效。因此,研究壓電／電磁復(fù)合結(jié)構(gòu)的斷裂問(wèn)題,具有重要的理論和實(shí)際意義,是智能結(jié)構(gòu)設(shè)計(jì)和評(píng)估的重要基礎(chǔ)和前提。本博士論文通過(guò)哈密頓體系辛方法,建立了統(tǒng)一形式的有限尺寸壓電／電磁彈性智能復(fù)合材料界面斷裂問(wèn)題的對(duì)偶控制方程,獲得了以本征解展開(kāi)形式表示的裂紋尖端物理場(chǎng)的解析表達(dá)式,以及表征力、電、磁場(chǎng)奇異程度的物理場(chǎng)強(qiáng)度因子。此外,基于本征解函數(shù)和傳統(tǒng)有限元方法構(gòu)造出一種能夠克服網(wǎng)格敏感和路徑敏感的辛離散有限元方法。本文主要研究工作如下：(1)建立了有限尺寸壓電／電磁彈性智能復(fù)合材料界面斷裂問(wèn)題的哈密頓求解體系在哈密頓理論體系下,壓電／電磁智能材料的位移和應(yīng)力、電勢(shì)和電位移、磁勢(shì)和磁感應(yīng)強(qiáng)度互為對(duì)偶變量。將上述變量構(gòu)成的全狀態(tài)向量作為基本未知量,構(gòu)造出具有統(tǒng)一形式的力、電、磁智能復(fù)合材料的哈密頓正則方程。利用分離變量法,原問(wèn)題歸結(jié)為辛空間下的本征值和本征解問(wèn)題。各物理場(chǎng)的解通過(guò)辛本征解的線性組合表示,其中本征解的待定系數(shù)可以利用邊界條件和辛共軛正交關(guān)系求解�？紤]四種理想電磁裂紋面條件,利用斷裂力學(xué)公式獲得裂紋強(qiáng)度因子和能量釋放率的解析表達(dá)式。該方法突破了傳統(tǒng)半逆法的局限,是一種理性的直接求解方法。研究結(jié)果表明,裂紋尖端物理場(chǎng)均具有-1/2奇異性,應(yīng)力、電位移、磁感應(yīng)強(qiáng)度因子和能量釋放率與材料常數(shù)相關(guān)并可由廣義位移強(qiáng)度因子線性組合表示；而應(yīng)變、電場(chǎng)和磁場(chǎng)強(qiáng)度因子與材料常數(shù)無(wú)關(guān),只與本征值為1/2的本征解系數(shù)相關(guān)。該方法適用于不同類(lèi)型邊界條件,包括復(fù)雜的混合邊界條件。數(shù)值計(jì)算表征出裂紋尖端的機(jī)械場(chǎng)、電場(chǎng)和磁場(chǎng)特性,揭示了材料參數(shù)、幾何尺寸和外加荷載對(duì)斷裂參數(shù)的影響。(2)提出一種針對(duì)壓電／電磁彈性復(fù)合材料斷裂問(wèn)題的辛離散有限元方法利用裂紋尖端附近的解析辛本征解函數(shù)結(jié)合傳統(tǒng)有限元方法構(gòu)造出適用于壓電／電磁彈性復(fù)合材料斷裂分析的辛離散有限元方法。首先,將裂紋結(jié)構(gòu)整體劃分為含裂紋尖端的近場(chǎng)奇異區(qū)域和以及不含裂紋尖端的遠(yuǎn)場(chǎng)非奇異區(qū)域,并對(duì)整體結(jié)構(gòu)進(jìn)行有限元網(wǎng)格劃分。其次,在近場(chǎng)中以辛本征解展開(kāi)作為全局函數(shù),將近場(chǎng)內(nèi)大量廣義節(jié)點(diǎn)位移未知量轉(zhuǎn)化為辛本征解展開(kāi)系數(shù),而遠(yuǎn)場(chǎng)中的節(jié)點(diǎn)未知量保持不變。最后,通過(guò)求解出的本征解待定系數(shù)直接獲得近場(chǎng)內(nèi)物理場(chǎng)的顯式表達(dá)式以及裂紋的斷裂參數(shù)。與其它數(shù)值方法相比,辛離散有限元方法具有三點(diǎn)優(yōu)勢(shì)：(i)計(jì)算過(guò)程中,無(wú)需引入特殊的奇異單元和網(wǎng)格加密,消除傳統(tǒng)有限元對(duì)網(wǎng)格敏感問(wèn)題；(ii)近場(chǎng)內(nèi)大量的節(jié)點(diǎn)位移轉(zhuǎn)化為少量的本征解待定系數(shù),極大程度縮小了剛度矩陣的維度,從而大幅提高了計(jì)算效率和精度。(iii)無(wú)需額外的后處理程序,斷裂參數(shù)可以直接通過(guò)求解出來(lái)的辛本征解系數(shù)表示,消除路徑敏感問(wèn)題。數(shù)值結(jié)果驗(yàn)證了辛離散有限元方法的精確性。給出的數(shù)值算例,包括含有多裂紋,分叉裂紋和橢圓孔邊緣開(kāi)裂裂紋等問(wèn)題,計(jì)算結(jié)果為壓電、電磁智能復(fù)合材料的研發(fā)、設(shè)計(jì)、制造、可靠性分析及壽命評(píng)估提供直接的理論指導(dǎo)和技術(shù)支持。
[Abstract]:With the development of material science and electronic technology, the piezoelectric / electromagnetic composite materials with good force, electricity and magnetic coupling effect are widely used in the manufacture of sensors, detectors, ultrasonic imagers and other intelligent devices. However, because of the mismatch between material properties and their own brittleness, this kind of device can not be avoided in the process of production and use. The crack or hole can be avoided, which leads to the singularity of the physical field near the defect (force, electricity and magnetic field), which affects the integrity of the structure and may cause the failure of the structural function. Therefore, it is of great theoretical and practical significance to study the fracture of the piezoelectric / electromagnetic composite structure, which is an important basis for the design and evaluation of the intelligent structure. By means of the Hamilton system symplectic method, this thesis establishes a unified form of the dual control equation for the interfacial fracture problem of a finite size piezoelectric / electromagnetic elastic composite material, and obtains an analytic expression of the crack tip physical field expressed in the form of eigensolution, as well as the properties of the singularity of the force, electricity and magnetic field. In addition, based on the eigensolution function and the traditional finite element method, a symplectic discrete finite element method can be constructed to overcome the sensitivity of the grid and the path sensitivity. The main research work of this paper is as follows: (1) the Hamilton solution system of the interface fracture of the finite size piezoelectric / electromagnetic elastic intelligent composite material is established in Hazakhstan. The displacement and stress of piezoelectric / electromagnetic intelligent materials, potential and potential shift, magnetomotive force and magnetic induction intensity are dual variables under the system of the mill theory, and the whole state vector made up of the above variables is used as the basic unknown quantity to construct a Hamiltonian regular equation with a unified form of force, electric and magnetic compound material. The original problem is attributed to the eigenvalue and the eigensolution under the symplectic space. The solutions of the physical fields are represented by the linear combination of the symplectic eigensolutions. The undetermined coefficients of the eigensolutions can be solved by the boundary conditions and the symplectic conjugate orthogonal relations. The crack strength factors and energy are obtained by using the fracture mechanics formula to consider the four ideal surface conditions for the electromagnetic crack. This method breaks through the limitations of the traditional semi inverse method and is a rational direct solution. The results show that the physical field of the crack tip has -1/2 singularity, stress, potential shift, magnetic induction intensity factor and energy release rate related to the material constant and can be linear combination of generalized displacement intensity factors. The strain, the electric field and the magnetic field intensity factor are independent of the material constants, which are only related to the eigenvalues of the eigenvalues of 1/2. This method is suitable for different types of boundary conditions, including complex mixed boundary conditions. The numerical calculation shows the mechanical field, the electric field and magnetic field characteristics at the crack tip, and reveals the material parameters, geometry size and addition. The effect of load on the fracture parameters. (2) a symplectic discrete finite element method for the fracture problem of piezoelectric / electromagnetic elastic composite materials is proposed. The symplectic discrete finite element method is constructed by using the analytic symplectic intrinsic solution function near the crack tip and the traditional finite element method. First, a symplectic discrete finite element method is constructed for the fracture analysis of piezoelectric / electromagnetic elastic composite material. The crack structure is divided into the near field singular region with the crack tip and the nonsingular region of the far field without the crack tip, and the finite element mesh of the whole structure is divided. Secondly, in the near field, the symplectic intrinsic solution is used as a global function, and the unknown displacement of a large number of wide sense nodes in the field is transformed into the symplectic expansion system. The unknown quantity of the nodes in the far field remains unchanged. Finally, the explicit expressions of the near field physical fields and the fracture parameters are obtained by the undetermined coefficients of the eigensolutions. In comparison with other numerical methods, the symplectic discrete finite element method has three advantages: (I) no special singular elements need to be introduced in the (I) calculation process. The grid is encrypted to eliminate the sensitive problem of the traditional finite element to the grid. (II) the displacement of a large number of nodes in the near field is converted into a small number of eigenvalues, which greatly reduces the dimension of the stiffness matrix, thus greatly improves the computational efficiency and accuracy. (III) no additional post-processing program is needed, and the fracture parameters can be solved directly through the solution. The Xin Benzheng solution coefficient is expressed and the path sensitivity is eliminated. The numerical results verify the accuracy of the symplectic discrete finite element method. The numerical examples are given, including the problems of multiple cracks, bifurcation cracks and the edge cracks on the edge of the elliptical hole. The calculation results are the research, design, manufacture, reliability analysis and life of the piezoelectric, electromagnetic intelligent composite materials. The assessment provides direct theoretical guidance and technical support.
【學(xué)位授予單位】：大連理工大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2016
【分類(lèi)號(hào)】：O346.1

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