In this paper, on the basis of the incremental Reissner variational principle.a nonlinear finite element analysis has been accomplished and a formulation of hybrid stress element has been presented for incompressible ...In this paper, on the basis of the incremental Reissner variational principle.a nonlinear finite element analysis has been accomplished and a formulation of hybrid stress element has been presented for incompressible Mooney rubber-like materials. The corrected terms of the non-equilibrium force and the incompressibility deviation are considered in the formulation. The computed values of numerical example agree very closely with the exact solution.展开更多
The paper presents a new method for classifying the stress modes in hybrid stress finite element in terms of natural stress modes in finite element and the rank analysis of matrix G in forming element It reveals the r...The paper presents a new method for classifying the stress modes in hybrid stress finite element in terms of natural stress modes in finite element and the rank analysis of matrix G in forming element It reveals the relation among the different assumed stress field, and gives the general method in forming stress field Comparing with the method of eigenvalue analysis, the new method is more efficient展开更多
Superconvergence and recovery type a posteriori error estimators are analyzed for Pian and Sumihara's 4-node hybrid stress quadrilateral finite element method for linear elasticity problems. Superconvergence of or...Superconvergence and recovery type a posteriori error estimators are analyzed for Pian and Sumihara's 4-node hybrid stress quadrilateral finite element method for linear elasticity problems. Superconvergence of order O(h^(1+min){α,1}) is established for both the displacement approximation in H^1-norm and the stress approximation in L^2-norm under a mesh assumption, where α > 0 is a parameter characterizing the distortion of meshes from parallelograms to quadrilaterals. Recovery type approximations for the displacement gradients and the stress tensor are constructed, and a posteriori error estimators based on the recovered quantities are shown to be asymptotically exact. Numerical experiments confirm the theoretical results.展开更多
The following is proved: 1) The linear independence of assumed stress modes is the necessary and sufficient condition for the nonsingular flexibility matrix; 2) The equivalent assumed stress modes lead to the identica...The following is proved: 1) The linear independence of assumed stress modes is the necessary and sufficient condition for the nonsingular flexibility matrix; 2) The equivalent assumed stress modes lead to the identical hybrid element. The Hilbert stress subspace of the assumed stress modes is established. So, it is easy to derive the equivalent orthogonal normal stress modes by Schmidt's method. Because of the resulting diagonal flexibility matrix, the identical hybrid element is free from the complex matrix inversion so that the hybrid efficiency, is improved greatly. The numerical examples show that the method is effective.展开更多
文摘In this paper, on the basis of the incremental Reissner variational principle.a nonlinear finite element analysis has been accomplished and a formulation of hybrid stress element has been presented for incompressible Mooney rubber-like materials. The corrected terms of the non-equilibrium force and the incompressibility deviation are considered in the formulation. The computed values of numerical example agree very closely with the exact solution.
文摘The paper presents a new method for classifying the stress modes in hybrid stress finite element in terms of natural stress modes in finite element and the rank analysis of matrix G in forming element It reveals the relation among the different assumed stress field, and gives the general method in forming stress field Comparing with the method of eigenvalue analysis, the new method is more efficient
基金supported by National Natural Science Foundation of China (Grant No. 11171239)Major Research Plan of National Natural Science Foundation of China (Grant No. 91430105)
文摘Superconvergence and recovery type a posteriori error estimators are analyzed for Pian and Sumihara's 4-node hybrid stress quadrilateral finite element method for linear elasticity problems. Superconvergence of order O(h^(1+min){α,1}) is established for both the displacement approximation in H^1-norm and the stress approximation in L^2-norm under a mesh assumption, where α > 0 is a parameter characterizing the distortion of meshes from parallelograms to quadrilaterals. Recovery type approximations for the displacement gradients and the stress tensor are constructed, and a posteriori error estimators based on the recovered quantities are shown to be asymptotically exact. Numerical experiments confirm the theoretical results.
文摘The following is proved: 1) The linear independence of assumed stress modes is the necessary and sufficient condition for the nonsingular flexibility matrix; 2) The equivalent assumed stress modes lead to the identical hybrid element. The Hilbert stress subspace of the assumed stress modes is established. So, it is easy to derive the equivalent orthogonal normal stress modes by Schmidt's method. Because of the resulting diagonal flexibility matrix, the identical hybrid element is free from the complex matrix inversion so that the hybrid efficiency, is improved greatly. The numerical examples show that the method is effective.
