Laplace Transformation Solution Of Composite Material Orthogonal Hyperbolic Laminated Shell With Four Simply Supported

With the rapid development and application of composite materials and shell structure in recent years,the composite shell structure began to appear widely in practical engineering,in which the laminated orthogonal hyperbolic shell is widely used,therefore,the study of the mechanical properties of this engineering structure is very helpful to solve the aircraft’s design issues and security issues.In this paper,the basic equations of elastic plates and elastic materials,thermo elastic materials,piezoelectric materials and electromagnetism materials are given,and on the basis of the state space method,the homogeneous state equation of the four sided simply supported elastic plates and elastic materials,thermo elastic materials,piezo electric materials and electromagnetism materials are further deduced,by the Laplace transform and inverse transformation of these equations,the analytic solution of the homogeneous state equation is obtained.There is a process of inversing matrix in the inverse Laplace transformation,which is a matrix containing a single variable,the inverse of the matrix is obtained indirectly by means of the adjoint matrix,which avoids the problem that the inverse of the high order matrix could not be got directly.In the process of inversing the inverse matrix of Laplace transformation,taking the larger partial order of the formula to be obtained into account,as well as the Mathematica software used to solve the problem is too slow and the result is not very accurate,therefore,this thesis divides these fractions into the sum of fractions who’s fractional order is first order,so that the Laplace inverse transformation of each sub-fraction is easy to obtain,and this split is completely feasible in mathematics.This process simplifies the calculation,promotes the speed and ensures the correctness of the solution.By comparing with the results of the exact integral method,the feasibility and accuracy of the Laplace transform are proved.Laplace transform is not only simple,but also has high precision,which provides a new method for solving the homogeneous state equation of plate and shell.Finally,the given examples and parametric changes in the image can also provide a reference for other solutions.