TY - JOUR
T1 - Nonlinear versions of flexurally superconvergent elements
AU - Liu, Wing Kam
AU - Belytschko, Ted
AU - Chen, Jiun Shyan
N1 - Funding Information:
The support of the U.S. Army Research Office under Contract DAAG29-84-K-0057 and the support of the National Science Foundation for one of the authors (WKL) under Grant ECE-8420735a re gratefully acknowledged.
PY - 1988/12
Y1 - 1988/12
N2 - Flexurally superconvergent four-node elements, which can achieve engineering beam accuracy with a single layer of elements through the thickness of the beam, are generalized to nonlinear problems. The Hu-Washizu variational principal in terms of the first Piola-Kirchhoff stress tensor and the deformation gradient is used in conjunction with the γ-projection to develop an efficient form of this element. Example solutions show that while there is some degradation of the accuracy in the nonlinear range, the performance of these elements still permits very coarse meshes.
AB - Flexurally superconvergent four-node elements, which can achieve engineering beam accuracy with a single layer of elements through the thickness of the beam, are generalized to nonlinear problems. The Hu-Washizu variational principal in terms of the first Piola-Kirchhoff stress tensor and the deformation gradient is used in conjunction with the γ-projection to develop an efficient form of this element. Example solutions show that while there is some degradation of the accuracy in the nonlinear range, the performance of these elements still permits very coarse meshes.
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U2 - 10.1016/0045-7825(88)90034-5
DO - 10.1016/0045-7825(88)90034-5
M3 - Article
AN - SCOPUS:0024127677
SN - 0374-2830
VL - 71
SP - 241
EP - 258
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
IS - 3
ER -