基于格林函数的涂层结构精细计算方法及其仿真平台设计
发布时间：2018-09-14 08:22
【摘要】：涂层结构(由涂层和被涂层所覆盖的基体共同组成的结构)使得各种工程装备具有了耐磨、耐腐蚀、耐高温等各种优异性能,广泛应用于机械、电子、航空航天和生物医学等各高科技领域。涂层结构普遍具有五个特点：(1)涂层越来越薄,很多涂层的厚度在微米级；(2)服役状态下,大量的机械能和热能会贮存在涂层中,而且机械场和温度场在薄薄的涂层中以极高的梯度变化；(3)涂层结构是多相结构,涂层和基体的界面会产生复杂的界面效应；(4)随着新材料不断投入使用,各向异性涂层结构越来越多；(5)涂层结构常处于热、力、化学等多场耦合工作状态。这些特点使得对于涂层结构的准确分析,无论是基于解析求解还是数值求解都面临着困难,普遍存在着算不准的问题。而对于先进涂层结构的分析和设计又迫切需要一种高效稳定的精细计算方法和专用仿真平台。本学位论文即是在这一背景下,开展了以下三方面的工作：首先,针对工程中常见的正交各向异性和横观各向同性涂层结构,分别利用由调和函数表示的二维和三维通解,系统地给出了在法向和切向点力作用下涂层和基体内弹性场的二维和三维格林函数,并基于所得格林函数揭示了材料的各向异性属性与涂层结构弹性场的关系。首先综合考虑通解的形式、载荷的类型、涂层和基体内场的分布特点、涂层和基体在界面的相互影响和制约关系、以及便于进一步的应用和计算机程序实现等多个因素,利用试错的方法,以初等函数的形式,系统地构造了含有待定常数的调和函数。然后将该调和函数代入通解,并通过表面边界条件和界面连续条件确定待定常数,得到了涂层和基体内弹性场的格林函数。最后基于所得格林函数,分析了材料的各向异性参数与涂层结构弹性场之间的变化规律。其次,基于各向同性热弹性材料的三维控制方程,利用微分算子理论、Almansi定理以及各种变换方法,推导得到了用四个调和函数表示的各向同性热弹性材料的三维完备通解。利用该通解,针对工程中常见的热阻涂层结构,给出了在点热源作用下涂层和基体内热弹性场的三维格林函数,并基于所得格林函数揭示了材料的力热属性与涂层结构热弹性场的关系以及该型涂层结构的失效机理。通解是求解偏微分耦合方程组的重要一环,通解的形式是否简洁直接影响到后面的求解方法和难度。本论文获得的各向同性热弹性材料的三维通解均由调和函数来表达,便于进一步用来求解各种工程问题。由于热阻涂层的研究涉及到热力耦合效应,在基于所得通解构造调和函数时所需要考虑的因素更为丰富,也同时涉及到机械场和温度场的边界条件和界面连续条件,这增加了问题的复杂性。本论文充分考虑这些综合因素,构造了点热源作用下的调和函数,获得了相应的格林函数。并基于所得格林函数揭示了热阻涂层结构热弹性场的耦合机理以及该型涂层结构的失效机理。最后,基于本论文所得涂层结构的一系列格林函数,并利用叠加原理,给出了能对任意分布载荷作用下的涂层结构进行全场精细求解的计算方法—BGM算法(Based on Green's Function Method),并以BGM算法为内核,依托MATLAB GUI编程平台,设计开发了涂层结构的专用数值仿真平台,为工程界对各种先进涂层结构进行精细分析和设计提供了有力的工具。BGM算法充分发挥了格林函数精细求解的优势,使得涂层内部剧烈变化的机械场和温度场以及界面上的复杂的应力分布都得以准确的计算和描述。本文通过Scarborough准则对BGM算法的计算精度进行了控制,通过消除冗余计算和只考虑格林函数对计算目标贡献的方法对BGM算法进行了优化。给出了典型的接触问题(包括椭圆接触、锥形接触和圆柱接触)以及分布热载荷作用下涂层结构全场各分量的精细计算结果,显示了BGM算法在工程应用中具有高精度、高效率和高稳定性。依托BGM算法开发的涂层结构的专用数值仿真平台界面简洁友好,易于学习和操作,非常方便于工程界的应用。
[Abstract]:Coating structure (composed of coating and substrate covered by coating) makes all kinds of engineering equipment have excellent properties such as wear resistance, corrosion resistance, high temperature resistance and so on. It is widely used in mechanical, electronic, aerospace and biomedical fields. The thickness of multi-coatings is in the micron level; (2) In service, a large amount of mechanical and thermal energy will be stored in the coatings, and the mechanical and temperature fields in the thin coatings with a very high gradient; (3) coating structure is multiphase structure, coating and matrix interface will produce complex interface effects; (4) with the continuous input of new materials. More and more anisotropic coatings have been used. (5) Coating structures are often in thermal, mechanical, chemical and other coupled working conditions. These characteristics make the accurate analysis of coatings structure, whether based on analytical or numerical solutions are faced with difficulties, there is a general problem of inaccuracy. This dissertation is devoted to the following three aspects: Firstly, two-dimensional and three-dimensional general solutions expressed by harmonic functions are used for orthotropic and transversely isotropic coatings, which are commonly used in engineering. The two-dimensional and three-dimensional Green's functions of elastic field in coating and substrate under normal and tangential point forces are given systematically, and the relationship between anisotropic properties of materials and elastic field of coating structure is revealed based on the obtained Green's functions. By means of trial and error, the harmonic function with undetermined constants is constructed systematically in the form of elementary functions. Then the harmonic function is substituted into the general solution, and the surface boundary conditions and the interface continuity are obtained. The Green's function of the elastic field in the coating and substrate is obtained. Finally, based on the Green's function, the variation law between the anisotropic parameters of the material and the elastic field of the coating structure is analyzed. Secondly, based on the three-dimensional governing equation of the isotropic thermoelastic materials, the differential operator theory, Almansi theorem and various properties are used. A three-dimensional complete general solution of isotropic thermoelastic materials expressed by four harmonic functions is derived by means of the transformation method. Based on the general solution, the three-dimensional Green's function of the thermoelastic field in the coating and substrate under the action of point heat source is given for the common thermal resistive coating structures in engineering, and the force of the materials is revealed based on the obtained Green's function. The relationship between thermal properties and thermoelastic field of coatings and the failure mechanism of the coatings are discussed. The general solution is an important step in solving the coupled partial differential equations. As the study of thermal resistive coatings involves the thermo-mechanical coupling effect, the factors needed to be considered in constructing the harmonic function based on the obtained general solution are more abundant, and the boundary conditions and interface continuity conditions of mechanical and temperature fields are also involved, which adds to the complexity of the basic theory. Considering these comprehensive factors, the harmonic function under the action of point heat source is constructed, and the corresponding Green's function is obtained. Based on the Green's function, the coupling mechanism of thermoelastic field and the failure mechanism of the coating structure are revealed. Finally, a series of Green's functions of the coating structure obtained in this paper are used and the corresponding Green's function is obtained. Based on the superposition principle, the BGM (Based on Green's Function Method) algorithm, which can be used to solve the coating structure under arbitrarily distributed loads, is presented. With the BGM algorithm as the kernel and the MATLAB GUI programming platform as the support, a special numerical simulation platform for the coating structure is designed and developed, which can provide advanced information for the engineering community. The BGM algorithm gives full play to the advantages of the fine solution of Green's function, so that the drastically changed mechanical field and temperature field inside the coating and the complex stress distribution on the interface can be accurately calculated and described. The accuracy is controlled, and the BGM algorithm is optimized by eliminating redundant calculation and considering only the contribution of Green's function to the calculation objective. Typical contact problems (including elliptical contact, conical contact and cylindrical contact) and precise calculation results of the whole field components of the coating structure under distributed thermal load are given, which show the BGM. The algorithm has high precision, high efficiency and high stability in engineering application. The special numerical simulation platform for coated structure based on BGM algorithm has simple and friendly interface, is easy to learn and operate, and is very convenient for engineering application.
【学位授予单位】：湖南大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：O302;O174
本文编号：2242118
[Abstract]:Coating structure (composed of coating and substrate covered by coating) makes all kinds of engineering equipment have excellent properties such as wear resistance, corrosion resistance, high temperature resistance and so on. It is widely used in mechanical, electronic, aerospace and biomedical fields. The thickness of multi-coatings is in the micron level; (2) In service, a large amount of mechanical and thermal energy will be stored in the coatings, and the mechanical and temperature fields in the thin coatings with a very high gradient; (3) coating structure is multiphase structure, coating and matrix interface will produce complex interface effects; (4) with the continuous input of new materials. More and more anisotropic coatings have been used. (5) Coating structures are often in thermal, mechanical, chemical and other coupled working conditions. These characteristics make the accurate analysis of coatings structure, whether based on analytical or numerical solutions are faced with difficulties, there is a general problem of inaccuracy. This dissertation is devoted to the following three aspects: Firstly, two-dimensional and three-dimensional general solutions expressed by harmonic functions are used for orthotropic and transversely isotropic coatings, which are commonly used in engineering. The two-dimensional and three-dimensional Green's functions of elastic field in coating and substrate under normal and tangential point forces are given systematically, and the relationship between anisotropic properties of materials and elastic field of coating structure is revealed based on the obtained Green's functions. By means of trial and error, the harmonic function with undetermined constants is constructed systematically in the form of elementary functions. Then the harmonic function is substituted into the general solution, and the surface boundary conditions and the interface continuity are obtained. The Green's function of the elastic field in the coating and substrate is obtained. Finally, based on the Green's function, the variation law between the anisotropic parameters of the material and the elastic field of the coating structure is analyzed. Secondly, based on the three-dimensional governing equation of the isotropic thermoelastic materials, the differential operator theory, Almansi theorem and various properties are used. A three-dimensional complete general solution of isotropic thermoelastic materials expressed by four harmonic functions is derived by means of the transformation method. Based on the general solution, the three-dimensional Green's function of the thermoelastic field in the coating and substrate under the action of point heat source is given for the common thermal resistive coating structures in engineering, and the force of the materials is revealed based on the obtained Green's function. The relationship between thermal properties and thermoelastic field of coatings and the failure mechanism of the coatings are discussed. The general solution is an important step in solving the coupled partial differential equations. As the study of thermal resistive coatings involves the thermo-mechanical coupling effect, the factors needed to be considered in constructing the harmonic function based on the obtained general solution are more abundant, and the boundary conditions and interface continuity conditions of mechanical and temperature fields are also involved, which adds to the complexity of the basic theory. Considering these comprehensive factors, the harmonic function under the action of point heat source is constructed, and the corresponding Green's function is obtained. Based on the Green's function, the coupling mechanism of thermoelastic field and the failure mechanism of the coating structure are revealed. Finally, a series of Green's functions of the coating structure obtained in this paper are used and the corresponding Green's function is obtained. Based on the superposition principle, the BGM (Based on Green's Function Method) algorithm, which can be used to solve the coating structure under arbitrarily distributed loads, is presented. With the BGM algorithm as the kernel and the MATLAB GUI programming platform as the support, a special numerical simulation platform for the coating structure is designed and developed, which can provide advanced information for the engineering community. The BGM algorithm gives full play to the advantages of the fine solution of Green's function, so that the drastically changed mechanical field and temperature field inside the coating and the complex stress distribution on the interface can be accurately calculated and described. The accuracy is controlled, and the BGM algorithm is optimized by eliminating redundant calculation and considering only the contribution of Green's function to the calculation objective. Typical contact problems (including elliptical contact, conical contact and cylindrical contact) and precise calculation results of the whole field components of the coating structure under distributed thermal load are given, which show the BGM. The algorithm has high precision, high efficiency and high stability in engineering application. The special numerical simulation platform for coated structure based on BGM algorithm has simple and friendly interface, is easy to learn and operate, and is very convenient for engineering application.
【学位授予单位】：湖南大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：O302;O174
【参考文献】
相关期刊论文 前2条
1 王建国,于传君,蒋南;多层框架分析的状态变量传递法[J];合肥工业大学学报(自然科学版);1998年04期
2 雷晓燕;不同材料交界面上接触应力的有限元分析[J];应用力学学报;1995年03期
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