發(fā)布時間：2018-06-18 18:54

  本文選題：多孔介質(zhì) + 多場耦合問題�。� 參考：《中國農(nóng)業(yè)大學》2017年博士論文

【摘要】：多孔材料現(xiàn)已在汽車、醫(yī)學、環(huán)保、原子能等工程領(lǐng)域得到了廣泛的應(yīng)用。目前對于多孔介質(zhì)的理論研究得到了一定的發(fā)展。然而,多孔材料復雜的結(jié)構(gòu)以及各向異性的特點及其多場耦合效應(yīng),使得對多孔材料多場耦合問題的求解變得更加復雜。由于多孔介質(zhì)獨特的結(jié)構(gòu)和優(yōu)越的力學性能,對其力學行為的研究無疑在實踐應(yīng)用和理論研究中都具有重要的意義。對于穩(wěn)態(tài)下的平面問題,利用Lur'e算子方法推導出正交各向異性(橫觀各向同性)多孔熱彈性介質(zhì)平面問題的通解。利用推導出的通解,獲得多孔熱彈性無限大平面、半無限大平面和雙材料受線液源和線熱源作用時的基本解,然后利用數(shù)值算例,給出各場分量的等值線曲線。通過不斷改變Biot有效應(yīng)力系數(shù),研究流固耦合特性對多孔介質(zhì)力學行為的影響。對于穩(wěn)態(tài)下的三維問題:1.利用多孔介質(zhì)的基本方程,給出各向同性多孔彈性介質(zhì)的軸對稱Timpe通解。利用該通解對各向同性多孔彈性圓柱進行精化分析。引入Bessel函數(shù)表示,獲得圓柱柱面受外載作用時的精化方程和耦合場的近似表達式。2.從橫觀各向同性多孔熱彈性介質(zhì)的軸對稱通解出發(fā),給出了橫觀各向同性多孔熱彈性圓柱的精化理論。同時,利用該通解并引入勢函數(shù),獲得多孔熱彈性實心圓錐體和空心圓錐體在點液源和點熱源作用下的基本解,并給出不同載荷條件下的數(shù)值結(jié)果。3.根據(jù)橫觀各向同性多孔熱彈性介質(zhì)非軸對稱問題的三維通解,推導出無限大多孔熱彈性雙材料在任一點受點液源和點熱源的基本解。對于準靜態(tài)問題,根據(jù)微分算子方法,求解出多孔熱彈性介質(zhì)耦合問題的準靜態(tài)通解。利用該通解,獲得了無限大多孔熱彈性體分別在階躍點熱源和諧波點熱源作用下耦合場的表達式,繪制出各場分量的等值線圖。對于動力學問題,根據(jù)基于Nunziato-Cowin理論的雙重孔隙介質(zhì)的基本方程,利用Cramer法則,推導出該動力學問題的解。將無網(wǎng)格局部Petrov-Galerkin法應(yīng)用到壓電壓磁多孔熱彈性介質(zhì)的研究中,且對該問題的方程進行積分運算時無需背景網(wǎng)格。針對該多孔介質(zhì)的平面問題和軸對稱問題,首先給出壓電壓磁多孔熱彈性介質(zhì)的基本方程,根據(jù)控制方程的弱形式表達,并利用高斯散度定理分解,獲得子域下的積分方程,在子集中選取單位階躍函數(shù)作為試驗函數(shù)。利用移動最小二乘法引入空間變量的近似表達式,并代入到積分方程的弱形式中,根據(jù)本質(zhì)邊界的離散形式,獲得離散形式的積分方程,最后利用Houbolt法求得數(shù)值結(jié)果。
[Abstract]:Porous materials have been widely used in automotive, medical, environmental protection, atomic energy and other engineering fields. At present, the theoretical research on porous media has been developed to a certain extent. However, the complex structure, anisotropy and multi-field coupling effect of porous materials make the solution of multi-field coupling problem more complicated. Due to the unique structure and superior mechanical properties of porous media, the study of its mechanical behavior is undoubtedly of great significance in practical application and theoretical research. For the plane problem in steady state, the general solution of the plane problem of orthotropic (transversely isotropic) porous thermoelastic medium is derived by using the Lurne operator method. By using the derived general solution, the basic solutions of porous thermoelastic infinite plane, semi-infinite plane and bimaterial under the action of line liquid source and line heat source are obtained. Then, the isoline curves of each field component are given by numerical examples. By changing the Biot effective stress coefficient, the influence of fluid-solid coupling characteristics on the mechanical behavior of porous media is studied. For three dimensional steady state problem: 1. The axisymmetric Timpe general solution of isotropic porous elastic media is obtained by using the basic equations of porous media. This general solution is used to refine the isotropic porous elastic cylinder. The Bessel function representation is introduced to obtain the refined equation and the approximate expression of coupling field. Based on the general axisymmetric solution of transversely isotropic porous thermoelastic medium, the refined theory of transversely isotropic porous thermoelastic cylinder is presented. At the same time, by using the general solution and introducing the potential function, the basic solutions of the porous thermoelastic solid cone and hollow cone under the action of point liquid source and point heat source are obtained, and the numerical results under different loading conditions are given. Based on the three-dimensional general solution of the non-axisymmetric problem of transversely isotropic porous thermoelastic media, the basic solutions of the point liquid source and the point heat source for infinite porous thermoelastic bimaterials at any one point are derived. According to the differential operator method, the quasi-static general solution of the coupling problem in porous thermoelastic media is obtained for quasi-static problems. By using this general solution, the expressions of coupling fields of infinite porous thermoelastic bodies under the action of step point heat source and harmonic point heat source are obtained, respectively, and the isoline diagrams of each field component are drawn. According to the basic equations of dual porous media based on Nunziato-Cowin 's theory, the solution of the dynamic problem is derived by using Cramer's rule. The meshless local Petrov-Galerkin method is applied to the study of voltage-voltage magnetic porous thermoelastic media. Aiming at the plane problem and axisymmetric problem of the porous medium, the basic equations of the pressure-voltage magnetic-porous thermoelastic medium are first given. The integral equations under the subdomain are obtained by using the weak form of the governing equation and the decomposition of the Gao Si divergence theorem. The unit step function is selected as the test function in the subset. The approximate expression of spatial variables is introduced by the moving least square method, and is substituted into the weak form of the integral equation. According to the discrete form of the essential boundary, the discrete integral equation is obtained. Finally, the numerical results are obtained by using the Houbolt method.
【學位授予單位】：中國農(nóng)業(yè)大學
【學位級別】：博士
【學位授予年份】：2017
【分類號】：TB383.4

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