轴对称弹性体扭转问题的完全光滑有限元法

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中图分类号：0343 文献标志码：A

Abstract： A fully smoothed finite element method to solve the torsion problem of axisymmetric elastic body is proposed.Due to axial symmetry of geometry and boundary conditions，computing the torsion problem of axisymmetric elastic body requires extracting one cross section for meshing and analysis.In order to address the problemof high sensitivity to mesh distortion，the edge-based smoothing domains are further constructed based on the triangular mesh and smoothing operations are performed on the strain in each smoothing domain. The smoothing strain technique is combined with the quasi-weak form of smoothed integral for treatment of the partial derivative and non-partial derivative of shape functions.Accordingly，allthe smoothed domain integrals can be simplified as boundary integrals of the smoothing domains and there is no need for the coordinate mapping and calculation of Jacobian matrix.Numerical examples demonstrate that the proposed method for the torsion problems of axisymmetric elastic body can produce accurate solutions even for irregular elements.

Keywords：axisymmetric elastic body;torsion; fullysmoothed technique; smoothing strain technique; irregular elements

Citation format： CEHN S S，DING L C，LI QH.A fulysmoothed finite element method for torsion problems of axisymmetric elastic body[J]. Journal ofEast China Jiaotong University，2025，42（5）： 121-126.

作为工程和科学计算的主要工具，有限元法已经得到了广泛的应用，但是仍面临着完备阶数低和网格畸变敏感等困难。（剩余6973字）