Bending,Vibration And Buckling Analysis Of Porous Functionally Graded Plates

Functionally Graded Materials(FGM)are widely used in aerospace industry,nuclear industry,biomedicine,machinery and electronics industry due to its superior characteristics to traditional composite materials.Due to the limitations of the preparation process and technology,internal defects are generated during the preparation process of FGM.Pore defects in Porous Functionally Graded(PFG)materials make the structural stiffness somewhat lacking,but at the same time,they also have the advantages of high performance weight ratio and impact resistance,especially suitable for high-speed and high-temperature environments in aerospace and nuclear industry.Therefore,the research on PFG materials has practical significance.In recent years,with the development of Micro Electro Mechanical System(MEMS),the design and manufacturing of micro-nano intelligent components have received increasing attention.The mechanical properties of microstructures cannot be predicted within the framework of classical continuum theory,and the mechanical response different from macroscopic structures needs to take into account the scale effect of microstructures and nanostructures.Therefore,the analysis and discussion of micro and nanostructures have attracted research interest from scholars.This article investigates the static and dynamic responses of porous FG plates on elastic foundations,the free vibration of nano porous FG MEE plates in thermal environments,and the static and dynamic responses of porous FG plates on elastic foundations considering temperature dependence under thermal loads.The specific research content is as follows:1.This article summarizes the research background and progress of porous FG materials and FG-MEE materials,presents the influence curves of elastic modulus and density under two pore distribution modes,as well as the load modes of two elastic foundations.It also introduces the application of nonlocal theory under the framework of non-classical continuum theory.2.The influence of elastic foundation and porosity on the bending and vibration of FG plates was studied based on the four-variable shear theory.Considering three types of pore distributions,the modulus and density of the material was calculated using the effective physical property parameter formula.Then,the control differential equation was obtained using Hamilton’s principle.Finally,the calculation structure was validated,and the effects of porosity,gradient index,and foundation stiffness parameters on the deflection stress and natural frequency of porous FG plates were discussed.3.Based on Eringen’s non-local elasticity theory,the natural frequencies of nano porous FG-MEE plates were studied under different temperature rise environments.Using the Voigt mixed power law and symmetric cosine pore model,the Navier method was used to obtain the vibration frequency of the nano porous FG-MEE plate under temperature field.The model was validated by simplifying it to a regular FG material plate,and the effects of different temperature rise conditions,non local parameters,porosity,gradient index on the first three order dimensionless frequencies were considered.4.Considering the temperature dependent characteristics of materials and the cosine asymmetric pore model,the vibration and buckling characteristics of porous FG plates on elastic foundations under thermal loads were studied.The motion control differential equation of the structure was derived using Hamilton’s principle and its analytical solution was obtained.The accuracy of the model was verified through numerical examples,and the effects of different gradient index,temperature rise environment,edge thickness ratio,aspect ratio,porosity,and external mechanical loads on the natural frequency and critical buckling load of porous FG plates were calculated and discussed.