The Post-Buckling Analysis Of Beam And Plate With Various Elastic Modulus Materials In Tension And Compression

In traditional classical mechanics, such as elastic and material mechanics, they usually only involve isotropic materials that have nothing to do with Young’s modulus and the stress field. However, some materials are not so. About different tension and compression modulus problem, scholars at home and abroad carry out some researches, they successively put forward the concept, hypothesis, analytical and numerical solution of finite element method (FEM) of simple problems of this theory. Most of the approximation and exact solution only analyze the study object’s stress and deformation in the case of pure linear elasticity. With the progress of material science and industrial technology, new materials also emerge in endlessly, materials that show the characteristics of double modulus are also more and more. Stress formula of classical theory are not applicable, and they need to be analyzed and derived by mechanics. Combining with problem of different modulus, the post-buckling responses of beam under the condition of different constraints and simply supported circular plate was analyzed by this article.Firstly, this paper introduces the deduce process of rectangular plate. Based on elasticity theory of different modulus, nonlinear theory, dimensionless theory, the geometric equations of the structure, the physical relations and the force equilibrium differential equation and its boundary conditions are builded. The general research regularity is provided for the similar problem’s solve of other subsequent structure.Secondly, we analyze the post-buckling problem of beam maded of material with different tension and compression modulus. By considering material characteristics of different tension and compression modulus, setting up constitutive relation of beam with different modulus, and establishing corresponding equations according to the geometrical relationship of beam with large deflection and the differential equations of force system equilibrium and so on. Under different modulus ratio, relationships are derived between the neutral axis location and coordinate, and the axial force changed with angle, moreover, critical loads of the study object are found out. To study the effect of different modulus ratio, and changes of mechanics properties during the post-buckling process by considering different constraints. The difference between them can be concluded by comparing corresponding conclusions of classic mechanics with different modulus theory of beam’s post-buckling problem. Analyzing the influence on structure of tension and compression modulus; Analyzing the relationship between tension-compression modulus ratio and the corresponding physical parameters, establishing the corresponding charts, and analyzing its effect on the structure itself or engineering.Finally, Post-buckling problems of circular plate with different tension and compression modulus should be analyzed through charts. Corresponding modulus parameters are considered according to the mechanics characteristics of bimodulus circular plate. Physical parameters of post-buckling problem are studied by numerical analysis, and nonlinear relations between the paremeters and different modulus rates can be found, accuracy and effect of circular plate’s post-buckling can be concluded under the influence of bimodulus characteristics. When analyzing specific numerical problems, the corresponding unknown parameters’ values shoule be gained, then we can conclude the relationship between the corresponding physical parameters, analyze the influence to theory and practical engineering, find out the deficiencies and defects of classical theory to actual engineering and structure.