P-version hybrid analytical finite element method for plate bending problems |
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Authors: | Xiao-Ping Zheng Tian-Qi Ye and Qing-Hua Du |
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Institution: | (1) Tsinghua University, 100084 Beijing, P.R.China;(2) Northwestern Polytechnical University, 710072 Xi'an, P.R.China |
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Abstract: | Two sets of trial functions with different variables are constructed for the admissible space of the finite element analysis. The trial functions satisfy the equilibrium differential equation inside elements, while the deflections and rotations on the edges of the elements are approximated by the Peano hierarchical interpolation functions. Then, a generalized variational principle is applied to set up the p-version hybrid analytical finite element method for plate bending problems. The accuracy of finite element computation can be improved by increasing the order of the interpolation polynomials with fixed mesh. In the finite element formulation, to obtain the stiffness matrices and the load vectors, it is only necessary to perform quadrature over the edges of the elements. These matrices and vectors possess an embedding structure. The conformability between the elements can be controlled automatically.This work is supported by the Natural Science Foundation of China and the Aeronautical Science Foundation of China. |
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Keywords: | plate bending problems generalized variational principle p-version refinement biharmonic polynomial space finite element method |
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