Mechanical Property And Nonlinear Behavior Research On Gradient Foam Material

At present,all kinds of new functional materials are actively developed around the world.New materials are the focus of competition among countries,and also the key factor determining the national high-end manufacturing industry and national defense security.The research on new materials change rapidly at home and abroad,especially the research of functional materials,and gradient foam as a kind of functional materials has become one of the focuses of scholars.Therefore,gradient foam is taken as the research object.On the basis of deepening the literature research at home and abroad,the basic mechanical and physical quantities of gradient foam metal materials are mathematically characterized,and tests research for mechanical properties of uniform foam materials are carried.Which are including tensiling,impacting and bending test.The results of mechanical analysis of foam materials with different density are obtained by rational analysis.At the same time,the mathematical model of gradient foam metal beam and circular plate under mechanical load and thermal load is established by combining theoretical and numerical research.Considering mechanical and thermal load,the governing differential equations of beams and circular plates are derived by using the theory of axis elongation Euler beam and the classical theory of circular plates.The equilibrium equations under different boundary conditions are solved by shooting method,and a large number of numerical results are obtained.The engineering application of gradient foam materials provides data support and reference.The main research work of this paper are as follows:1.First,the basic mechanical relationship of gradient foams was analyzed,including the relationship between the size and shape of foams and the relative density.The relative density,porosity and foam gradient parameters of foam materials were used to characterize the mechanical physical quantities(elastic / shear modulus,yield strength,etc.).2.The mechanical properties of aluminum foam with different relative density under different conditions were studied experimentally.The tensile,impact and flexural properties of uniform foam materials are dependent on the test rate,temperature and relative density,and the dependence of relative density was obvious.3.For the gradient foamed beam structure,firstly,based on the theory of Euler beam with axis extension,the dynamic control equations of the free vibration of gradient foam beam near the thermal buckling were established with the transverse steady temperature field.Then,the solution of the control equations were decomposed into two parts: the static solution and the dynamic solution.Considering the transverse non-uniformity of the temperature field,the gradient foam material under the temperature load was studied.The free vibration of the beam structure near the nonlinear static equilibrium configuration was solved.Finally,the shooting method is used to solve the small amplitude free vibration near the static thermal elastic deformation and the static equilibrium configuration.The influence of temperature load and material porosity on the static equilibrium path and natural vibration frequency of the gradient foam beam was numerically studied.4.Based on the classical theory of circular plates,the governing equations for free vibration of circular plates with gradient foams near the thermal buckling before and after the thermal buckling were established.In senior high school entrance examination,the free vibration of a circular foamed circular plate with a gradient of temperature in the vicinity of a nonlinear static equilibrium configuration was studied.The numerical solution of the small amplitude vibration response near the static thermoelastic deformation and the static equilibrium configuration was obtained by using the shooting method.The effects of temperature load,material density gradient index and boundary conditions on the static equilibrium path and free vibration frequency of circular plates with gradient foams were quantitatively analyzed.5.Based on the classical theory of circular plates,a dynamic control equation for the free vibration of a gradient foam circular plate near the thermal buckling equilibrium configuration was established first,and then the solution of the governing equation was decomposed into two parts: the static solution and the dynamic solution.Considering the transverse non-uniformity of the temperature field,the circular structure of the gradient foam material under temperature load was studied in the nonline.Finally,the problem of small amplitude free vibration near the thermoelastic deformation and the static equilibrium configuration was solved by shooting method.The effects of different boundary conditions,thermal load and relative density gradient on critical buckling thermal load,buckling deformation and free vibration of gradient foamed circular plates were quantitatively analyzed.