Mechanical Behavior Of Porous Metal Circular Plates With Nonlinear Constitutive Relation

In this paper,problems of nonlinear axisymmetric bending,buckling and post-buckling of circular plate of porous metal,with nonlinear constitutive relation under mechanical load are studied.Assuming that the elastic modulus of the material is a linear function of strain,numerical solutions of the problems of the circular porous metal materials plate are obtained by the shooting method.(1)The problem of nonlinear axisymmetric bending of circular plate of porous metal was studied by numerical method.The basic equation of bending problem of circular plate of porous metal under the action of transversely uniformly distributed load and nonlinear constitutive relation is derived by energy method,based on the classical plate theory and the nonlinear constitutive relation,two boundary conditions are given,peripheral fixed support and peripheral simple support.After dimensionless,the shooting method is used to solve the of bending problems of axisymmetric large deflection of circular plate of porous metal.According to the numerical results,the influences of the nonlinear parameters of the constitutive relation,boundary conditions and mechanical loads on the axisymmetric bending of circular plate and the position of the neutral layer,and the influences of the nonlinear parameters of the constitutive relation on the bending with different thickness-diameter ratios are analyzed.The results show that:Under the simply supported periphery and fixedly supported periphery,The circular plate of porous metal bears the action of transversely uniformly distributed load,When the constitutive nonlinear parameterE_P>0,the bending deformation resistance of the circular plate increases,whileE_P<0,the bending deformation resistance of the circular plate decreases.Under the same conditions,the influence of the constitutive nonlinear parameters on bending deformation is the peripheral fixed support is smaller than the peripheral simply supported.In the large deflection problem,under the two boundary conditions the bending deformation resistance of the circular plate increases with the increases ofE_P,The position of the neutral layer is further away from the geometric midplane as it increases.The position of the neutral layer is further away from the geometric middle surface as the increases ofE_P.The effect of thickness-diameter ratio on bending deformation is more obvious when the boundary of peripheral fixed support inE_P>0,but it is more obvious when the boundary of peripheral simple support inE_P<0.(2)The buckling and post-buckling problems of circular plate of porous metal under radial load are solved by numerical method under the conditions of simply supported peripheral sliding and movable peripheral clamping.Based on the equilibrium equation of axisymmetric post-buckling of circular plates with nonlinear constitutive relation,thebuckling and post-buckling problems of circular plates of porous metal under two boundaries are solved by shooting method.According to the numerical results,the effects of constitutive nonlinear parameters on critical load and post-buckling are analyzed.The results show that:The stronger of the boundary constraint,the greater of the critical load,and the critical load decreases with the increase of constitutive nonlinear parameters.The deformation increases with the increase of peripheral radial load,when the circular plates are subjected to post-buckling deformation,which is consistent with the results of classical theory.Constitutive nonlinear parameters affect the post-buckling deformation of circular plates,and the effect is greater when clamped with movable periphery than simply supported with sliding periphery.The smaller of the constitutive nonlinear parametersE_P,the greater of the buckling deformation resistance of the structure.