A hybrid fundamental-solution-based 8-node element for axisymmetric elasticity problems.

*(English)*Zbl 1464.74424Summary: A novel hybrid finite element approach using fundamental solutions in conjunction with the boundary integration is proposed for the analysis of axisymmetric elasticity problems. In the formulation two displacement fields are independently assumed within the element domain and at the element boundary, which combines the advantages of conventional finite and boundary element methods. The resulting system of algebraic equations is symmetric and positive definite, which reduces the spatial dimension of the problem by one. It offers great flexibility in generating the mesh with arbitrary higher-order elements. Firstly, the proposed approach is validated by the analytical solution of a thick-walled hollow cylinder. A good agreement is observed. Meantime, the optimal number and location of source points for fundamental solutions as well as sensitivity to mesh distortion are studied. Finally, two more numerical examples including a flange and a wheel are provided. Compared to ABAQUS, the proposed approach exhibits higher efficiency, better convergence rate and strong capability to capture geometric singularities.

##### MSC:

74S99 | Numerical and other methods in solid mechanics |

65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |

65N80 | Fundamental solutions, Green’s function methods, etc. for boundary value problems involving PDEs |

74B05 | Classical linear elasticity |

##### Keywords:

axisymmetric elasticity; fundamental solution; finite element method; hybrid functional; mesh distortion##### Software:

ABAQUS
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\textit{J. Zhou} et al., Eng. Anal. Bound. Elem. 101, 297--309 (2019; Zbl 1464.74424)

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