Unconventional Hamilton Variational Principles And Finite Element Method For Functionally Graded Material Structures

Functionally graded materials (FGMs) which have become a mechanical research focus are a new kind of composite materials that can alleviate the inside thermal stress effectively in ultra-high-temperature environment. In this thesis unconventional Hamilton variational principles and unconventional Hamilton variational principle in phase space for dynamics of FGMs structures are established systematically. Moreover based on such variational principles, Symplectic Space Finite Element- Time Subdomain Method (SSFE-TSM) for FGMs structures is proposed. Graded finite element is used to study the mechanical behavior of FGMs structures from three-dimensional perspective. The researches include static and dynamic analyses of FGMs plates with arbitrary variations of material properties, several boundary conditions and load conditions.According to the material properties of FGMs are functions of position instead of constants, eight-node hexahedron isoparametric graded element is employed for spatial mesh. The numerical solutions of simply supported rectangular plates are very close to analytical solutions. Static analyses of rectangular FGMs plates with arbitrary variations of material properties, several boundary conditions indicate that the simplified theories of homogeneous plates are almost proper for FGMs plates.Based on three-dimensional elasticity theory, the unconventional Hamilton variational principles and unconventional Hamilton variational principle in phase space for dynamics of FGMs structures are established systematically. These variational principles fully characterize the initial-boundary-value problem of dynamics. In other words, they are equivalent to dynamic differential form.Starting from unconventional Hamilton variational principle in phase space, SSFE-TSM is presented. In this method dynamic problem is changed from solving a series of second order ordinary differential equations to solving a series of linear algebraic equations by introducing momentum as another independent variable and applying time mesh. As a result computation is simplified and the computational efficiency is improved. Dynamic response analyses of rectangular FGMs plates with arbitrary variations of material properties, several boundary conditions and load conditions in which SSFE-TSM is implemented show that SSFE-TSM is a good numerical method with high computational accuracy, practicability and reliability. Meanwhile some dynamical features of FGMs plates are realized to some extend.