Mathematics – Numerical Analysis
Scientific paper
2011-01-06
Mathematics
Numerical Analysis
Scientific paper
Assumed stress hybrid methods are known to improve the performance of standard displacement-based finite elements and are widely used in computational mechanics. The methods are based on the Hellinger-Reissner variational principle for the displacement and stress variables. This work analyzes two existing 4-node hybrid stress quadrilateral elements due to Pian and Sumihara [Int. J. Numer. Meth. Engng, 1984] and due to Xie and Zhou [Int. J. Numer. Meth. Engng, 2004], which behave robustly in numerical benchmark tests. For the finite elements, the isoparametric bilinear interpolation is used for the displacement approximation, while different piecewise-independent 5-parameter modes are employed for the stress approximation. We show that the two schemes are free from Poisson-locking, in the sense that the error bound in the a priori estimate is independent of the relevant Lame constant $\lambda$. We also establish the equivalence of the methods to two assumed enhanced strain schemes. Finally, we derive reliable and efficient residual-based a posteriori error estimators for the stress in $L^{2}$-norm and the displacement in $H^{1}$-norm, and verify the theoretical results by some numerical experiments.
Carstensen Carsten
Xie Xiaoping
Yu Guozhu
No associations
LandOfFree
Uniform convergence and a posteriori error estimation for assumed stress hybrid finite element methods does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Uniform convergence and a posteriori error estimation for assumed stress hybrid finite element methods, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Uniform convergence and a posteriori error estimation for assumed stress hybrid finite element methods will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-399472