Analysis Of Functional Gradient Materials Circular Plate Buckling By Finite Element Method

The structure and properties of functionally graded materials are different from homogeneous materials because of their special fabrication process.In essence,the bright interface between materials can be eliminated and the stress concentration phenomenon at the interface can be relieved in functionally graded materials.As a result,functionally graded materials have good physical and mechanical properties.Since the functionally graded material plates have the characteristics of continuous change of components and properties in a certain direction,it is able to achieve different design and use requirements by adjusting the distribution of components.The application of functionally graded materials is more and more extensive.More scholars have paid attention to the study of the buckling behavior of functionally graded material plates in recent years.In this paper,based on physical neutral surface,we use the finite element method to study the buckling behavior of circular thin and medium thick plates of functionally graded materials based on classical plate theory and first-order shear deformation plate theory,respectively.The study mainly includes,1.Based on the classical plate theory and physical neutral surface,the buckling control equation of functionally graded circular plate under radial load is established on the basis of geometric relations,physical relations and equilibrium equations,using the principle of minimum potential energy.With the help of MATLAB,the critical load of the circular plate of functionally graded materials can be solved.The relationship between the critical load and the functional gradient index,diameter-thickness ratio and boundary conditions is analyzed.It is found that the larger the functional gradient index and the diameter-thickness ratio are,the larger the critical load of the circular plate.The stronger the support is,the more stable the circular plate is.2.Based on the first-order shear deformation plate theory and physical neutral surface,the buckling control equation of the circular plate of functionally graded material under radial load is established by applying the principle of minimum potential energy.MATLAB is used to calculate the critical load of the circular plate of functionally graded material.The relationship between the two theoretical solutions is discussed.It is found that the solution based on the first-order shear deformation plate is smaller than that on the classical plate theory due to the consideration of shear deformation.The influence of the boundary condition and the thickness-to-radius ratio on the relative error between the two theories is larger,and the influence of the functional gradient index is smaller.In this paper,the displacement field is established on the physical neutral surface,and the tensile-bending coupling term of the buckling control equation is eliminated,which is simple to calculate.It is complementary and instructive to the study of the buckling behavior of circular plates of functionally graded materials based on the physical neutral surface using the finite element method.