Multi-layer Symplectic Element And Its Application In Stress Analysis Of Laminated Plates

For composite laminates,how to accurately analyze the interlayer stress(especially the transverse shear stress)is of great significance in practical engineering applications.The research purpose of this paper is to propose a relatively simple and accurate finite element numerical method that can accurately analyze the transverse stresses between composite layers.The main work is as follows:Combining layerwise theory and symplectic finite element theory,based on the principle of minimum potential energy and the modified H-R variational principle,a multilayer symplectic formula is established.The main characteristics of multi-layer symplectic include: the diagonal of the element's coefficient matrix has no zero elements,so the corresponding finite element linear system equations have stable solutions;because the multilayer symplectic contains out-of-plane stress variables,it meets the layer The continuous requirements of transverse shear stress and normal stress;support for the introduction of stress boundary conditions of the structure.At the same time,there is no need to apply special post-processing techniques to calculate the out-of-plane stress results.Based on the multi-layer symplectic finite element model,several examples are analyzed.The numerical results are compared with the exact or analytical solutions.The results show that: on the boundary,the accuracy of multi-layer symplectic stress results is better than non-coordinated displacement elements;the finite element model can significantly improve the accuracy of numerical results after introducing out-of-plane stress boundary conditions;The transverse stress analysis results of common composite laminates show that the results of multi-layer symplectic elements are more accurate than those of noncoordinated displacement elements and hybrid stress elements.For different boundary conditions,multi-layer symplectic elements can give ideal stress results.The establishment of multi-layer symplectic element proposed an effective new method for stress analysis of composite laminates.