20-Node Hexahedron Symplectic Elements for Stress Analysis of Composite Laminates

TONG Yao; YAO Yuzhe

doi:10.21656/1000-0887.400283

Volume 41 Issue 5

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TONG Yao, YAO Yuzhe. 20-Node Hexahedron Symplectic Elements for Stress Analysis of Composite Laminates[J]. Applied Mathematics and Mechanics, 2020, 41(5): 509-516. doi: 10.21656/1000-0887.400283

Citation:

TONG Yao, YAO Yuzhe. 20-Node Hexahedron Symplectic Elements for Stress Analysis of Composite Laminates[J]. Applied Mathematics and Mechanics, 2020, 41(5): 509-516. doi: 10.21656/1000-0887.400283

Citation:

TONG Yao, YAO Yuzhe. 20-Node Hexahedron Symplectic Elements for Stress Analysis of Composite Laminates[J]. Applied Mathematics and Mechanics, 2020, 41(5): 509-516. doi: 10.21656/1000-0887.400283

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20-Node Hexahedron Symplectic Elements for Stress Analysis of Composite Laminates

doi: 10.21656/1000-0887.400283

TONG Yao¹,
YAO Yuzhe²

¹Shanghai Aircraft Design & Research Institute,Shanghai 201206, P.R.China;²College of Aeronautical Engineering, Civil Aviation University of China, Tianjin 300300, P.R.China

Funds: The National Natural Science Foundation of China（11502286）

Received Date: 2019-09-20
Rev Recd Date: 2019-11-22
Publish Date: 2020-05-01

Abstract

Abstract

Usually, the accuracy of the stresses obtained with the conventional displacement finite element method is one-order lower than that of the displacements, and the out-of-plane stresses can hardly meet the continuity requirements. Then, combined with the minimum potential energy principle and the H-R variational principle, a 20-node hexahedral symplectic element involving displacement and out-of-plane stress variables was established. Incompatible displacement terms are needless in the element since the 2 kinds of variables are approximated with higher-order interpolation functions. Hence, the derivation process of the theory is very simple. Unlike in the partially mixed Hamiltonian element, the variables involved in the symplectic element are discretized in 3 coordinate directions without restriction of the element thickness and the structure geometry. Numerical examples show that, the 20-node symplectic elements exhibit stable convergence. Under the coarse mesh, the out-of-plane stresses obtained with the proposed element are closer to the exact solution than those by the incompatible 8-node symplectic element.
- composite material,
- out-of-plane stress,
- H-R variational principle,
- 20-node symplectic element,
- displacement method,
- mixed method

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References(17)

References

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