## Abstract

In this study we propose a meshfree scheme for the numerical solution of boundary value problems (BVP) for the nonhomogeneous Cauchy-Navier equations of elastodynamics. The method uses the classical approach where first a particular solution for the partial differential equation (PDE) is calculated and then the corresponding homogeneous BVP is solved for the homogeneous part of the total solution. In particular, we approximate each component of the source term of the nonho-mogeneous PDE by superposition of plane wave functions with different frequencies and directions of propagation. Using these expansions, a particular solution for the PDE is derived in the form of a linear combination of elastic P-And S-waves, at no extra computational cost. In the second step of the scheme, we solve the corresponding homogeneous BVP using the classical method of fundamental solutions (MFS), with shape functions given by the Kupradze tensor. The accuracy and the convergence of the proposed technique is illustrated for a Dirichlet BVP, posed in a 2D multiply connected domain, bounded by polygonal and parametric curves.

Original language | English |
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Title of host publication | Proceedings - 2021 3rd International Conference on Control Systems, Mathematical Modeling, Automation and Energy Efficiency, SUMMA 2021 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 149-154 |

Number of pages | 6 |

ISBN (Electronic) | 9781665439817 |

DOIs | |

Publication status | Published - 2021 |

Event | 3rd International Conference on Control Systems, Mathematical Modeling, Automation and Energy Efficiency, SUMMA 2021 - Lipetsk, Russian Federation Duration: 10 Nov 2021 → 12 Nov 2021 |

### Conference

Conference | 3rd International Conference on Control Systems, Mathematical Modeling, Automation and Energy Efficiency, SUMMA 2021 |
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Country/Territory | Russian Federation |

City | Lipetsk |

Period | 10/11/21 → 12/11/21 |

## Keywords

- Cauchy-Navier equations of elastodynamics
- meshfree method
- method of fundamental solutions
- nonhomogeneous PDE
- plane wave functions