Elastoplastic Buckling Of Functionally Graded Beams

Functionally graded beams mainly adopt flexible design of their component parameters and mechanical properties to meet the appli cation needs of mechanical material properties and beam elements in various engineering problems.They have broad applications in aerospace,marine engineering,information engineering,micromechanics and other fields.In this thesis,the elastoplastic static stability characteristics of functionally graded beams under variable temperature field are studied based on the classical beam theory and the shear deformable beam theory,respectively.The main contents are as follows:(1)Based on the Euler-Bernoulli beam theory,considering the temperature dependent properties of each component material of the functionally graded beam,the elastoplastic thermal buckling characteristics of ceramic-metal functionally graded Euler-Bernoulli beams subjected to thermal load in the transversely non-uniform temperature field are studied by using the symplectic method in Hamilton system.The TTO model is used to simulate the elastoplastic material properties of functionally graded materials,and the elastoplastic constitutive equations are established with the linear hybrid hardening elastoplastic model.The canonical equations in Hamilton system can be obtained,and the critical thermal loads and buckling modes can be converted into symplectic eigenvalues and symplectic eigensolutions.Through the analytical method,the critical thermal loads of the functionally graded beam can be obtained,and the elastoplastic interfaces can be obtained by inverse solution method.The impacts of factors such as material parameters,geometric parameters and temperature differences on critical thermal loads and elastoplastic interfaces are discussed in an elastoplastic thermal buckling example of functionally graded beams.(2)Based on the first-order shear deformation theory,considering the temperature dependent properties of each component material of the functionally graded beam,the elastoplastic buckling characteristics of ceramic-metal functionally graded Timoshenko beams subjected to axial mechanical load in the variable temperature field are studied by using the symplectic method in Hamilton system.The TTO model is used to simulate the elastoplastic material properties of functionally graded materials,and the elastoplastic constitutive equations are established wi th the linear hybrid hardening elastoplastic model.The canonical equations in Hamilton system can be obtained,and the critical loads and buckling modes can be converted into symplectic eigenvalues and symplectic eigensolutions.Through the analytical method,the critical loads of the functionally graded beam can be obtained,and the elastoplastic interfaces can be obtained by inverse solution method.An elastoplastic buckling example of functionally graded beams is given,the impacts of factors such as material parameters,geometric parameters and temperature differences on critical loads and elastoplastic interfaces are discussed,and the conditions that need to consider the temperature dependent properties are given.In this thesis,the symplectic method in Hamilton system is used to solve the elastoplastic buckling problems of functionally graded beams in a more detailed and complete process,and the analyzed buckling modes can be used as initial defects in the subsequent post-buckling analysis of functionally graded beams.In addition,the critical buckling loads have certain value for engineering instability designs.At the same time,it also provides a theoretical reference for the optimal designs of functionally graded beams in actual engineering,so as to avoid the adverse material properties and usage of functionally graded beams in engineering.