Radial Integration Boundary Element Method For Transient Thermal- Mechanics Analysis Of FGM And Its Application

Functionally graded material (FGM) has good mechanical properties in high temperature environment, which can effectively relieve the thermal stress and residual stress, and it has been widely used in aviation, aerospace and other high-tech fields. In the process of service, the functionally graded material is often subjected to thermal and mechanical shock loadings. So the study of dynamic response and fracture behavior of functionally graded material in the thermal and mechanical shock loadings is very important for the safety use of functionally graded material and the design and optimization of its structures.Boundary element method has unique advantages in the numerical simulation of fracture mechanics problems, which is one of the common methods in science and engineering computation. Since the fundamental solutions of corresponding problems are lacking, the employment of boundary element method to analyze the problems of transient simulation of non-homogeneous materials will lead to the introduction of the domain integrals in the boundary integral equation. Thus, it will result in losing the meshing advantage and reducing the computational efficiency. The radial integration method (RIM) is an effective method to transform the domain integral into equivalent boundary integrals. Combining the radial integration method with the boundary element method, a meshless boundary element method is established to solve the heat impact problem of FGM in this paper. With a further study of the transient heat conduction problem of FGM, the elastic dynamic problem and the dynamic coupled thermoelasticity, the corresponding radial integration methods are established respectively. Furthermore, the present method is used to perform the dynamic fracture analysis of the FGM. Based on the above mentioned theories, a general method of the radial integration boundary element program code is developed in this thesis, which can be applied to several problems of FGM, such as dynamic thermal-mechanical coupling analysis and dynamic fracture mechanics problems. The contents of this paper are organized as follows:Using the fundamental solution of the potential problem, a meshless boundary element method is developed for the transient heat conduction problem of FGM, and the discretized differential equations are solved by the finite difference method. The present method is also can be used to solve the transient heat conduction problem of soild structures with a crack. and the influence of time step size on the accuracy of the transient heat conduction problem is studied. Numerical examples are proved the effectiveness of the method.A meshless radial integration boundary element method is developed for the dynamics problem of functionally graded material, which is based on the Kelvin fundamental solution. The second order ordinary differential equations are solved by the standard Newmark numerical integration method. Modal analysis and dynamic response analysis of the structure of functionally graded material are carried out. The effect of time step size on the dynamic response of the structure is studied, and several numerical examples are proved the effectiveness of the method.On the base of the transient heat conduction problem and the elastic dynamic problem of the FGM, considering the inertia term and the coupling term, the radial integration boundary element method is developed for the dynamic coupled thermoelasticity problem of FGM. The Houbolt numerical integration method is used to solve the system of ordinary differential equations. A compiled program is used to analyze the influence of inertia and coupling terms on the temperature field and displacement field under thermal-mechanical shock loadings. These results will provide a theoretical foundation of simplifying the thermodynamics problems.The radial integration boundary element method is further applied to dynamic fracture mechanics analysis of functionally graded materials. The dynamic stress intensity factor (DSIF) of the crack tip is defined by the crack open displacement (COD) near the crack tip. The stress intensity factor as the fracture parameter is studied for two- and three-dimensional crack structures under thermal-mechanical shock loadings. It provides theoretical basis for engineering design, and extends the application range of the boundary element method.The results show that the RIBEM program is reliable and has good stability and high accuracy. The program not only can be suitable for the coupled thermoelasticity and dynamic fracture mechanics problems of homogeneous and heterogeneous materials, but also can be reduced to a variety of special conditions, such as transient heat conduction problems, elastic dynamic problems and quasi static coupled thermoelasticity problems. The objects of the study include two- and three-dimensional crack bodies and continuous bodies.