Linear System Analysis Method For Transverse Stress Of Laminated Plates

The traditional displacement finite element method is widely used in the analysis of large engineering problems because of its high precision,small computer resource occupation and high calculation efficiency.But owing to the existence of differential operation of displacement results,the jump of stress results is discontinuous and the accuracy of stress results is not high.In the current general engineering laminated structure,transverse stress(out of plane stress)is discontinuous in the thickness direction,and the stress gradient is large,so the traditional displacement method cannot meet the accurate numerical results of the transverse stress.In order to obtain the ideal stress value by the displacement method,the model needs to be divided into a denser mesh in the thickness direction,and at the same time,the flattening technology is used to improve the stress to get a more optimized stress result.The mixed method is a multi-variable solution method,which can calculate displacement and stress at the same time,one of its advantages is the higher accuracy of the stress results.Because the mixed method solves the displacement and stress variables at the same time,it consumes a lot of resources.There are zero elements on the main diagonal of the coefficient matrix of the mixed method,which leads to the oscillation of the solution results and poor stability.To sum up,the content of this article is mainly studied in the following parts:(1)Based on the displacement method(minimum potential energy principle)and the modified Hellinger-Reissner(H-R)variational principle,a finite element linear system for transverse stress variables is established,the form of displacement variables in the system are incompatible.The main advantages include: The system equation provides support for the introduction of transverse stress boundary conditions.Therefore,the system equation about the transverse stress variable can ensure that the transverse stress component of the surface node is consistent with the given boundary value.Compared with the incompatible displacement finite element method,it can also provide high-precision numerical results inside the structure.On the other hand,the number of equations in this method is reduced by one-half compared to the mixed method or the symplectic finite element method.The occupied resources is the same as the displacement method,and only a quarter of the symplectic finite element method is required.(2)The numerical examples of laminated plates show that the results of the linear system method for transverse stress variables have good convergence,good agreement with the exact solution,and ensure the continuity of transverse stress at the interlayer interface.(3)Furthermore,combining the advantages of the linear system method of transverse stress,the linear system analysis method of local stress is proposed.The displacement results obtained by the displacement method are substituted into the mixed model of the local finite element to solve the stress.This method not only retains the advantages of high precision of the displacement results of the displacement method,but also inherits the advantages of high precision of stress results of the mixed method stress,and realizes local stress analysis and calculation of specific problems,the advanced and applicability of each method are fully realized,so the calculation efficiency is improved and the result precision is good,and the main diagonal of the coefficient matrix of the local finite element method has no zero element,so the result is stable.The numerical examples of local finite element further show that the displacement and stress results obtained by the linear system analysis method of transverse stress have the advantages of high accuracy and good stability.The work in this article has laid a solid foundation for the analysis of structural statics problems,and has a certain guiding role and research significance.