Nonlinear Mechanical Analysis For Functionally Graded And Fiber Metal Laminated Structures With Temperature Variation

Functionally graded beams, fiber metal laminated plates and shells are considered in this thesis. The problems of thermal postbuckling, nonlinear vibration and bending as well as nonlinear thermal transient dynamic responses are studied systematically including the effects of thermal environment, transverse shear deformation and geometrical nonlinearity. This thesis establishes a set of methods to solve the nonlinear structural problems in thermal environment, and enriches the methods and theories for structural nonlinear analysis.Expanding the displacement field as Laurent series expansion form, a higher-order shear deformation theory which can exactly characterize the stress boundary conditions on inner and outer surfaces and the geometrical shape is obtained. The nonlinear governing equations for thermal postbuckling of functionally graded tubes are established by using the generalized variational principle which are solved by a two-step perturbation method. To compare the results briefly, the exact solutions for Timoshenko beam and Euler beam are obtained. The effects of transverse shear deformation, temperature-dependent material properties, volume fraction and inner radius on the thermal postbuckling of functionally graded tubes are discussed.Based on previous higher-order shear deformation theory, the governing equations for nonlinear vibration and bending of functionally graded tubes are founded which will be solved by a two-step perturbation method. The effects of transverse shear deformation, temperature-dependent material properties and volume, inner radius and thermal environment on nonlinear vibration and bending of functionally graded tubes are discussed.Based on Euler beam model, the nonlinear governing equations for thermal shock of functionally graded beam resting on tensionless two parameter foundations are established. The thermal conduction equations and nonlinear governing equations are solved by the differential quadrature method, Newmark method and Newton-Raphson method. The effect of elastic foundation types, the foundation stiffness, length-to-thickness ration and the amplitude of thermal shock on nonlinear thermal transient dynamic responses of functionally graded beams are discussed.The interfacial shape functions, Heaviside step function as well as the interfacial relative slippage are introduced into the displacement field, and the thermal postbuckling governing euqaionts for fiber metal laminated plates with interfacial damage are established based on the weakly bonded interface theory. The whole problems are solved by finite difference method and iteration method comprehensively. The effects of initial deflection, interfacial damage, temperature distribution types as well as the width-to-thickness on fiber metal laminated plates are discussed.Based on previous higher-order shear deformation theory which can exactly describe the stress boundary conditions on surfaces and stress continuity conditions at interfaces, the nonlinear governing equations for thermal transient thermoelastic problems of fiber-metal laminated circular cylindrical shells with interfacial damage are established which are solved by adopting the differential quadrature method, Newmark method and iteration method. The effects of components on thermal conduction and temperature distribution, the effect of interfacial damage on deformation and the shear stress distribution of fiber metal circular cylindrical shells are investigated.