| The advantages of the incompatible displacement method are high accuracy of displacement results,simple formula,high calculation efficiency and low memory requirements.It has become one of the most widely used finite element methods in practical problems.The displacement method can obtain the node displacement with high accuracy,but the accuracy of the stress result is not as good as that of the displacement result because the derivative operation is needed to solve the stress.The existing stress recovery methods of displacement method often have some disadvantages,such as low accuracy of results,complex calculation process and insufficient consideration of stress boundary conditions.Some of them are only suitable for some specific problems.Based on the summary of the existing stress recovery methods,two alternative stress recovery methods are proposed.The stress at Gauss points in the element have high accuracy.In this paper,a stress recovery method different from extrapolation method is proposed for incompatible 4-node quadrilateral element and 8-node hexahedral element models.For the internal nodes,the Gauss points around the nodes can be used to construct a new isoparametric element,and then the stress of the nodes included in the new element can be calculated directly by interpolation.When calculating the stress of boundary nodes,the interior points which are collinear with the boundary nodes are selected,and the linear Lagrange interpolation method is used to calculate the stress.Numerical examples show that the stress results of this method meet the requirements of convergence,and the accuracy of this method is superior to the extrapolation method.In view of the fact that the current stress recovery method can not effectively introduce the stress boundary conditions,the mixed finite element method can only solve the whole model and its calculation requires large memory resources,this paper proposes a stress recovery method using generalized mixed element in local model.The local model is constructed by selecting the elements around the node whose stress is needed,and the incompatible generalized mixed element model is used to introduce the stress boundary conditions in the local model to construct the finite element linear system for solving the unknown stress in the local model.For the problem of composite structure,the modified generalized mixed variational principle is used to obtain the solution equation of out-plane stress,and then the local models are constructed according to different material layers,and the corresponding linear system of in-plane stress is established.The continuous results of in-plane stress in each layer of material can be obtained,and the discontinuity of in-plane stress at the interface of each material layer is ensured at the same time.Numerical examples show that this method can obtain more objective and accurate stress results.Compared with the mixed finite element method,this method greatly improves the computational efficiency. |
