多孔介质若干多场耦合问题的基本解

发布时间：2018-06-18 18:54

本文选题：多孔介质 + 多场耦合问题　；参考：《中国农业大学》2017年博士论文

【摘要】：多孔材料现已在汽车、医学、环保、原子能等工程领域得到了广泛的应用。目前对于多孔介质的理论研究得到了一定的发展。然而,多孔材料复杂的结构以及各向异性的特点及其多场耦合效应,使得对多孔材料多场耦合问题的求解变得更加复杂。由于多孔介质独特的结构和优越的力学性能,对其力学行为的研究无疑在实践应用和理论研究中都具有重要的意义。对于稳态下的平面问题,利用Lur'e算子方法推导出正交各向异性(横观各向同性)多孔热弹性介质平面问题的通解。利用推导出的通解,获得多孔热弹性无限大平面、半无限大平面和双材料受线液源和线热源作用时的基本解,然后利用数值算例,给出各场分量的等值线曲线。通过不断改变Biot有效应力系数,研究流固耦合特性对多孔介质力学行为的影响。对于稳态下的三维问题:1.利用多孔介质的基本方程,给出各向同性多孔弹性介质的轴对称Timpe通解。利用该通解对各向同性多孔弹性圆柱进行精化分析。引入Bessel函数表示,获得圆柱柱面受外载作用时的精化方程和耦合场的近似表达式。2.从横观各向同性多孔热弹性介质的轴对称通解出发,给出了横观各向同性多孔热弹性圆柱的精化理论。同时,利用该通解并引入势函数,获得多孔热弹性实心圆锥体和空心圆锥体在点液源和点热源作用下的基本解,并给出不同载荷条件下的数值结果。3.根据横观各向同性多孔热弹性介质非轴对称问题的三维通解,推导出无限大多孔热弹性双材料在任一点受点液源和点热源的基本解。对于准静态问题,根据微分算子方法,求解出多孔热弹性介质耦合问题的准静态通解。利用该通解,获得了无限大多孔热弹性体分别在阶跃点热源和谐波点热源作用下耦合场的表达式,绘制出各场分量的等值线图。对于动力学问题,根据基于Nunziato-Cowin理论的双重孔隙介质的基本方程,利用Cramer法则,推导出该动力学问题的解。将无网格局部Petrov-Galerkin法应用到压电压磁多孔热弹性介质的研究中,且对该问题的方程进行积分运算时无需背景网格。针对该多孔介质的平面问题和轴对称问题,首先给出压电压磁多孔热弹性介质的基本方程,根据控制方程的弱形式表达,并利用高斯散度定理分解,获得子域下的积分方程,在子集中选取单位阶跃函数作为试验函数。利用移动最小二乘法引入空间变量的近似表达式,并代入到积分方程的弱形式中,根据本质边界的离散形式,获得离散形式的积分方程,最后利用Houbolt法求得数值结果。
[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.
【学位授予单位】：中国农业大学
【学位级别】：博士
【学位授予年份】：2017
【分类号】：TB383.4

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