多层结构界面耦合场高效精细格林函数方法的研究

Since many physical problems can be modeled as a multilayered system, a lot of research has been carried out related to multilayered structures. These studies cover the areas of piezoelectricity, thermomechanics, microelectronics, electronomagnetics, poroelasticity, viscoelasticity, elastostatics, and finally, elastodynamics. Because the stress concentrations often happen in the interface, the failures is very easy to begin along or near the interface of multilayered system. In addition, the multilayered structures in engineering are often consisted of various structural materials, electric materials and functional materials; the constitutive relationships of these materials are often in forms of isotropy or anisotropy; there are cracks in the interface of multilayered structures etc. All these characteristics will lead more difficulties to study the coupled field in multilayered structures. In this project, the efficient and refined method for the two-dimensional and three-dimensional coupled fields in interface of multilayered structures are studied. Two parts are included. (1) Search for the Green’s functions: Green’s functions for coupled fields of multilayered structures will be derived in form of elementary functions. The multilayered structures include those which consisted of various structural materials, electric materials and four kinds of functional materials (piezoelectric materials, pyroelectric materials, electro-magneto-elastic materials and electro-magneto-thermo-elastic materials). The interface cracks can exist in the multilayered structures and the concentrated loads can be acted on the surface or in the interior of multilayered structures. (2) Studies on the efficient and refined Green’s function method: The new and efficient analysis and numerical methods which are based on the Green's functions are studied, and the obtained Green's functions will be used to construct a efficient and refined calculation soft for multilayered structures. And then, based on this calculation soft, a lot of problems connected with the structural design, craft improvement, strength analysis and effective application for multilayered structures can be solved. The studies of this project is a deeply exploration for the analysis method of coupled field in structures. It will improve the development of mechanics of coupled field and interface and have high theoretical and engineering values.

本项目以工程中广泛应用的各种多层结构为研究对象。从二维和三维的角度，对由各种材料构成的多层结构界面耦合场的高效精细计算方法进行研究。工作包括两个部分：一、多层结构耦合场格林函数的求解。即对于由各种材料按相应顺序排列构成的常见多层结构，考虑不含界面裂纹和含界面裂纹两种情况，求解各种集中载荷作用在其表面或内部时用初等函数表示的耦合场格林函数。二、高效精细格林函数方法的研究。在探索新方法的同时，综合利用各种基于格林函数的解析求解和数值计算方法，构建一个能对各种载荷作用下的多层结构耦合场进行精细计算的高效仿真平台。以此为工程领域里大量出现的与多层结构界面耦合场分析密切相关的结构设计、工艺提高、强度评估和高效使用等问题的解决做一些基础性的工作。本项目是对结构耦合场分析方法的深度探索，将丰富和发展结构耦合场力学和界面力学，具有大的理论意义和工程应用价值。

本项目以工程中广泛应用的各种多层结构为研究对象。从二维和三维的角度，对由各种材料构成的多层结构界面耦合场的高效精细计算方法进行研究。完成的工作包括两个部分：一、多层结构耦合场格林函数的求解。即对于由各种材料按相应顺序排列构成的常见多层结构，求解各种集中载荷作用在其表面或内部时用初等函数表示的耦合场格林函数。二、高效精细格林函数方法的研究。在探索新方法的同时，综合利用各种基于格林函数的解析求解和数值计算方法，构建了一个能对各种载荷作用下的多层结构耦合场进行精细计算的高效仿真平台。以此为工程领域里大量出现的与多层结构界面耦合场分析密切相关的结构设计、工艺提高、强度评估和高效使用等问题的解决做一些基础性的工作。本项目对结构耦合场分析方法进行了深度探索，丰富和发展结构耦合场力学和界面力学，具有大的理论意义和工程应用价值。