Nonlinear Static/Dynamic Behavior Analysis For Functionally Graded Material/Fiber Metal Laminated Beams With Damage

In this dissertation,the delaminated functionally graded beam/fiber metal laminated beams are the subjects of the investigating.Considering thermal effect,contact effect,geometrical nonlinearity and material nonlinearity,the thermal buckling,elasto-plastic postbuckling?elasto-plastic delamination growth,nonlinear dynamic,as well as delamination fatigue growth are systematically studied.The research results have important effect on the enrichment and development of fiber metal materials in theory and on its engineering application.The main results contain as follows.The thermal buckling problem of functionally graded beam with longitudinal crack is presented.The whole beam is divided into four sub-beams and each one is modeled as a Timoshenko beam.The buckling governing equation of each subbeam in thermal environment is established by using Hamilton Principle.Combining with the boundary conditions,the continuous conditions of the displacements and the forces,the buckling governing equations are solved by both the analytical and numerical methods.The buckling modes and critical buckling temperatures are obtained,and the effects of the functionally graded index,crack length,crack depth,and crack longitudinal location on the buckling characteristics of beams are discussed in numerical examples.The elasto-plastic postbuckling of fiber metal laminated beams with delamination and the energy release rate along the delamination front are discussed.Considering geometrical nonlinearity,thermal environment and geometrical initial imperfection,the incremental nonlinear equilibrium equations of delaminated fiber metal laminated beams are established,which are solved using the differential quadrature method and iterative method.Based on these,according to the J-integral theory,the elasto-plastic energy release rate is studied.The effects of some important parameters on the elasto-plastic postbuckling behavior and energy release rate of the aramid reinforced aluminum laminated beams are discussed in details.The nonlinear dynamic response problems of fiber-metal laminated beams with delamination are studied.Basing on the Timoshenko beam theory,and considering geometric nonlinearity,transverse shear deformation,temperature effect and contact effect,the nonlinear governing equations of motion for fiber-metal laminated beams under unsteady temperature field are established,which are solved by the differential quadrature method,Nermark method and iterative method.In numerical examples,the effects of delamination length,delamination depth,temperature field,geometric nonlinearity and transverse shear deformation on the nonlinear dynamic response of the glass reinforced aluminum laminated beam with delamination are discussed in details.The nonlinear dynamic response of fiber metal laminated beam with a single delamination subjected to a moving load in thermal environment is studied.Basing on Timoshenko beam theory,and introducing the Heaviside step function into the assumed displacement components,the new displacement field is established which is effective to the delaminated beam.Then,Considering the geometrical nonlinearity and the nonlinear contact effect between the two delamination regions,the nonlinear governing equations of motion for the delaminated FML beam is derived by the Hamilton principle,and solved by Galerkin method and Newmark method.The effects of different parameters such as contact effect,velocity of moving load,delamination length,delamination depth,and thermal effect on the nonlinear dynamic responses of the delaminated fiber metal laminated beam are studied.A nonlinear analysis model of delamination fatigue growth for fiber-metal laminated beams subjected to cyclic thermal load is presented.Considering thermal effect,transverse shear deformation and geometrical nonlinearity,the nonlinear governing equations of the delaminated fiber-metal laminated beams are deduced by applying Hamilton principle and solved by differential quadrature method and Newmark method.Besides,according to fracture dynamics and J integral theory,the energy release rate along the delamination is obtained.Then,according to the Paris law and the Arrhenius relationships,a working relation between delamination growth rate and amplitude of energy release rate concluding the thermal effect are established.Applying the new relationship,the delamination growth rate is arrived and using cyclic skip method,the delamination growth lengths along the delamination fronts under cycle thermal load are finally determined.In the numerical evaluation,the effects of temperature,delamination length and depth on the energy release rate and delamination growth length for the fiber-metal laminated beams are discussed.