Investigation On Contact And Dynamic Behavior Of Functionally Gradient Plates And Shells Subjected To Low-velocity Impact

Based on Hertz contact model,the classical theory of plate and shell,Von-karman equations and corresponding numerical methods and related theory as the foundation,the concept of impact dynamic contact model about plate and shell structures under low-velocity that considering the deformation of structure is proposed.Application of this model were discussed for a functionally graded plate with ring stiffeners in the temperature field and its response under impact at low speed,the laminated plates with a functionally graded layer transition to of low speed impact's response of and function gradient shallow spherical shells and concave shells under low-velocity impact response,respectively.On the base of Hertz contact theory,von Karman equation and classical thin plate theory and the mixing rule,by using the Hamilton variation method,established the impact/mechanical contact loads in plane displacement motion control equations of the single layer plate.By considering the influence of structural deformation and geometrical nonlinearity,the nonlinear dynamic contact model of thin plate structure is established.At last,the problem is separated in space and time domain by using finite difference method and Newmark method.Using the numerical example,the model and the selection of related parameters in the calculation of requirements,impact velocity and impact in the process of the impact and physical size,thickness of plate,material in the process of impact parameters on the influence on the result of the dimensionless deflection and normal stress is analyzed.Consider the ring stiffener and the influence of the temperature field,by using dynamic Hertz contact model proposed by this paper,the functionally graded plates with ring stiffener under low-velocity impact on the dynamic response are studied.Applying Von-Karman equation and classical thin plate theory and equivalent reinforcement model and Hamilton variation method and mixing rule,infers the functionally graded circular plate with circular reinforced the nonlinear balance equation of motion,the control equation is sloved.by using the finite difference method and Newmark method.The influences of the ring stiffener,the geometric dimension of the plate and the impact kinetic energy on the impact process are discussed.A three-layer model with functionally gradient layer transition is built,where in the middle layer is a mixture of upper and lower layers,and its material ratio changes along the thickness.Using the dynamic Hertz contact model presented in this paper,the dynamic response of the laminated plate at low speed is studied.Based on the Von Karman equation,the classical thin plate theory,Hamilton variation method and laws of dynamic Hertz contact model and mixed with functional gradient transition layer of laminated plates under low-velocity impact at the mercy of the equation,and USES the numerical method to solve the equation.The function of a gradient shallow spherical shells and the symmetrical concave shells under low-velocity impact on the dynamic response are studied and dynamic Hertz contact model is used,applying Mori-Tanaka and Timoshenko-Mindlin hypothesis and Von Karman equation the governing equations is derived,using numerical methods the response results are obtained.In this paper,the response process of shallow spherical shell and symmetric concave shell under low-velocity impact is discussed.