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.

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

##### doi: 10.21656/1000-0887.400283
Funds:  The National Natural Science Foundation of China（11502286）
• Rev Recd Date: 2019-11-22
• Publish Date: 2020-05-01
• 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.
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沈阳化工大学材料科学与工程学院 沈阳 110142