Thermal Elastic Stability Of Circular Plates Embedded In Infinite Elastic Plates

As a kind of structures or components commonly used in modern engineering,mechanical behaviors of circular plates under thermal loadings have become an important research direction in solid mechanics.This article studies the elastic stability problem of a circular plate which is embedded in an infinite plate in a variable temperature field.Under the uniform heating effect,the infinite elastic plate and the circular plate will expand.If the linear expansion coefficient of the circular plate is greater than that of the infinite elastic plate,the free expansion of the circular plate will be limited by the external infinite elastic plate to generate compressive stress in the circular plate.When the compressive stress of inner circular plate reaches the critical pressure value,the circular plate will undergo thermal buckling.The problems of critical buckling and post-buckling response of the circular plate which is embedded in an infinitely large elastic plate left in a uniformly variable temperature field under simply supported boundary conditions were studied by means of quantitative analysis.The effects due to the changes of physical parameters of the infinite external elastic plates on critical buckling temperature and over-buckling deformation of the circular elastic plate was discussed.The research includes the following aspects:1.Critical buckling of an inner circular plate embedded in an infinite elastic plate under uniform temperature fieldFirstly,based on the theory of plane elasticity,the plane stress solutions of infinite plates and circular plates of different materials under uniform change of temperature are obtained.On this basis,based on the classical thin plate theory bending theory,the critical temperature load of the axisymmetric buckling of the circular plate is obtained by analytical method and numerical target method respectively.The results show that the critical buckling temperature of the circular plate is greatly affected by the linear expansion coefficient and elastic modulus of the external infinite elastic plate.When the elastic modulus of the outer plate increases and the linear expansion coefficient decreases,the criticality buckling temperature of the internal circular plate will decrease;similarly,if the linear expansion coefficient of the circular plate is smaller than that of the infinite elastic plate,when the elastic modulus of the external infinite elastic plate increases and the linear expansion coefficient increases under the condition of cooling,the criticality buckling temperature of the internal circular plate will reduce.2.Thermal post-buckling of the circular embedded in an infinitely large elastic plate under uniform temperature change fieldWhen the temperature load exceeds the critical temperature of the circular plate,it will occur that the thermal post-buckling deformation is beyond the plane equilibrium state.Based on the large deflection theory of the thin plate,the governing differential equations of the thermal post-buckling of the axisymmetric circular plate are established.Under the in-plane elastic constraints and the laterally simply supported boundary conditions,the equilibrium configurations and equilibrium paths of the post-buckling of the circular plate are arrived at by solving nonlinear differential equations using shooting method.Through the numerical results,the influence of the physical property parameters of the external infinite elastic plate material on the buckling of the circular plate was quantitatively analyzed.The results show that if the linear expansion coefficient of the circular plate is larger than that of the outer plate,the post-bucking temperature of the inner circular plate decreases with the increase of the elastic modulus and the decrease of coefficient of the outer plate.After the thermal buckling,the displacement of the circular plate at the boundary increases linearly with the temperature load and the stresses in the circular plate increases linearly with the thickness.Similarly,if the linear expansion coefficient of the circular plate is smaller than that of the infinite elastic plate,the internal circular plate subjected to uniform cooling will also undergo buckling and post-buckling.The post-buckling temperature of the circular plate decreases with the increment of the elastic modulus and the linear expansion coefficient of the external infinite elastic plate.