Impact Response And Elastoplastic Thermal Buckling Of Functionally Graded Beams

Functionally graded materials(FGMs)are widely used in engineering due to they can effectively reduce the stress concentration inside strutures and have excellent thermal and crack resistance in extreme thermal environments.The study of mechanical behavior of FGM structures under external loads is a key issue that needs to be solved in the field of FGM applications,which has also become a hot research direction in solid mechanics.In this thesis,the functionally graded material beam is taken as the research object,and the transient response characteristics under the impact loads and the elastoplastic buckling problems under the thermal loads are studied respectively.The main contents are as follows:The dynamic response characteristics of a cantilever functionally graded material beam subjected to impact load are studied.Considering that the material properties change continuously along the thickness direction with the power function,the dynamical governing equations of the cantilever FGM beam under concentrated impact load is established based on the classical Euler theory.The free vibration characteristics of the cantilever FGM beam are studied,the natural frequencies and the principle mode are also obtained.Using the modal superposition and Duhamel integration method,the transient response of the inertial effect beam subjected to the concentrated impact load at the end is analytically studied.The exactly analytical solution of the maximum deflection with respected to time is solved and gives the numerical results of the impact within a short time are also presented.The results show that the dynamic displacements and natural frequencies of a cantilever functionally graded beam under impact load are between the corresponding results of uniform ceramic beam and metal beam.The transient displacements decrease,and the natural frequency increase with the increase of the volume fraction index of the material.As the slenderness ratio increases,the displacement of the dynamic response increases and the natural frequencies decrease.Based on the classical Euler beam theory,the elastoplastic buckling problem of FGM beams subjected to thermal load is investigated using the symplectic method in the Hamilton system.The linear hybrid enhanced elastoplastic models is used to simulate the elastoplastic material properties of FGM beams.The elastoplastic constitutive equations of functionally graded materials are established based on the TTO model.The canonical equation is established to transform the critical load and buckling mode of the FGM beam into symplectic eigenvalues and eigensolutions in the symplectic space.The complete buckling mode space and the critical thermal axial force are obtained by analytically.Meanwhile,the buckling temperature and elastoplsstic interface of structural deformation are obtained by inverse solution.The solution processes of the symplectic method for solving the elastoplastic thermal buckling problem of the FGM structure in the Hamilton system are established.The results show that the slenderness ratio of the FGM beam has a significant influence on the critical buckling temperature increase;The strength and the critical temperature of FGM beams are all decrease,with the increase of the index of the volume fraction of the materialThe research results in this thesis have positive significance for the study of impact mechanic and elastoplastic properties of FGM structures.It has theoretical guidance value for the practical engineering application and structural optimization design of functionally graded materials.