Study On Dynamic Thermal Snap-through Behavior Of Thin Plate Based On VDQ Method

Thin plate structures have wide applications in fields such as ships,aerospace,bridge construction and machinery.Such structures are often accompanied by complex structures such as holes,cracks and so on,and are often used under complex working conditions such as high temperature and high pressure.Therefore,the study of the vibration characteristics of such structures has always been a hot issue for researchers.The Variational Differential Quadrature Method(VDQ method)is a numerical method for solving energy functional equations.Recently,researchers have combined this method with the finite element method to solve the thin plate vibration equation,but the computational complexity of the numerical scheme is high.In this paper,the VDQ method is combined with the meshless method to solve the vibration characteristics of thin plates with complex structures,and the computational complexity of the method is greatly reduced.The main work of this paper includes:(1)The differential operator and integral operator in VDQ method are improved.The differential operator in the VDQ method is constructed by using the differential reproducing kernel interpolation function and the radial basis interpolation function in the meshless method,so that the differential operator can be applied to the calculation of the partial derivatives of unstructured discrete points.For the integral operator in VDQ method,the Voronoi diagram is used to generate the background grid for the discrete points,and the stable node integral operator is obtained;(2)The mathematical model of complex thin plate is established and discretized.For three types of thin plate structures,such as single-layer plate,laminated plate and functionally graded material(FGM)plate,the energy conservation equation of thin plate under high-order shear deformation condition is constructed,and the discretization method of thin plate under complex boundary conditions such as circular hole,complex hole and crack is studied.When analyzing the influence of temperature field on thin plate,the heat conduction model is introduced in the process of thin plate modeling;(3)The vibration characteristics of complex thin plate are studied by numerical simulation.In the experiment,the forced vibration of thin plate under five kinds of shear deformation conditions is discussed,and the vibration characteristics of thin plate with T-shaped and tree-shaped cracks are analyzed.The results show that the modified VDQ method can be well combined with the meshless method,which is suitable for the numerical simulation of complex thin plate structure;(4)Numerical simulation experiments are carried out on the thermal vibration of thin plates under different temperature field conditions.In the experiment,four kinds of heat conduction conditions,such as surface thermal shock,surface continuous heating,local thermal shock and local continuous heating,are considered respectively.The results show that the vibration behavior of thin plate after heating is related to the size of thermal load,the adopted shear deformation theory and the structure of the plate itself.Compared with the plate with holes in the corner position,the plate with holes in the center position will be more stable after heating,and the vibration of FGM plate under surface load and local load is obviously different.The conclusions obtained in this paper extend the application scope of meshless method,improve the computational efficiency of meshless method,and provide mathematical theories and methods for the study of vibration characteristics of complex thin plate structures.