Research On Bending Of Sandwich Plates Withhard Cores Based On Revised Hoff Theory

Sandwich plates with hard core is a kind of sandwich structure that core layer is taken into account in-plane stress components and bending stiffness.This kind of sandwich construction has fund a wide range of application in the field of industrial.This paper revises Hoff’s theory,taking into account in-plane stress components and bending stiffness of core layer when in-plane stress components of face sheet if considered.Firstly,this paper gives a solution to bending basic equations of sandwich plates with hard cores based on revised Hoff’s theory.In the process of solving,this paper still decouples the bending basic equations by introducing two new variables,then getting three new equations.This paper creatively introduces a new variable again,getting a fourth order differential equation.Solving the equation to get the expression of the introduced variable,so getting the linear relationship between the two variables in the decoupled bending basic equations.Then expressing one variable with another to plug into the first equation of the decoupled bending basic equations.Consequently,working out the expression of the deflection.In this way,this paper studies the bending of infinite sandwich plates,rectangular sandwich plates and circular sandwich plates under uniform loading,boundary conditions are mainly simply supported or clamped.Among which the bending of four edges simply supported rectangular sandwich plate under uniform loading is analyzed detailedly.Putting forward how to express the boundary conditions with the new variable and to work out the unknown constants,getting the expressions of deflection and internal force. Transforming coordinates,this paper also gets the bending basic equations and expression of internal force of circular sandwich plates.This paper also studies the bending of sandwich plates with hard cores for the different modulus in tension and compression materials,orthotropic and functionally graded materials,deriving the bending basic equations based on principle of minimum potential.This paper presents the finite element formulations for the bending of sandwich plates by using eight-node quadrilateral isoparametric element. Writing finite element’s programs to analyze the bending problem of sandwich plates to get the finite element result.Working out different results with the change in modulus and thickness of the core. Comparing which to analytical results to study the law.It’s find that analytical solutions are more and more close to finite element results with the increase of core layer modules. But changing the thickness,the analytical solutions and finite element results are always very close.When the core layer module is little, the analytical solution is close to Hoff theory’s solution,it’s show that analytical solutions are suit to sandwich plates with soft core.Conversely,the results vary widely,it’s show that Hoff theory’s solutions are not suit to sandwich plates with hard cores.