This paper introduces a high-order finite volume method for solving solid dynamics problems on three-dimensional unstructured meshes. The method is based on truncated Taylor series constructed about each control volume face using the least squares method, extending the classical finite volume method to arbitrary interpolation orders. As verification tests, a static analytical example for small deformations, a hyperelastic cantilever beam with large deformations, and a cantilever beam subject to a dynamic load are analyzed. The results provide an optimal set of parameters for the interpolation method and allow a comparison with other classic schemes, yielding to improved results in terms of accuracy and computational cost. The final test consists in the simulation of a compressor reed valve in a dynamic scenario mimicking real-life conditions. Numerical results are compared against experimental data in terms of displacements and velocity; then, a comprehensive physical analysis of stresses, caused by bending and impact of the valve, is carried out. Overall, the method is demonstrated to be accurate and effective in handling shear locking, stress concentrations, and complex geometries and improves the effectiveness of the finite volume method for solving structural problems.

本文介绍了一种用于求解三维非结构化网格上的固体动力学问题的高阶有限体积方法。该方法基于使用最小二乘法关于每个控制体积面构造的泰勒级数，将经典有限体积方法扩展到任意插值阶数。作为验证试验，对小变形静力分析算例、大变形超弹性悬臂梁、动荷载悬臂梁进行了分析。结果为插值方法提供了一组最佳参数，并可以与其他经典方案进行比较，从而在准确性和计算成本方面产生改进的结果。最终测试包括在模拟现实生活条件的动态场景中模拟压缩机簧片阀。将数值结果与位移和速度方面的实验数据然后，对阀门弯曲和冲击引起的应力进行全面的物理分析。总体而言，该方法被证明在处理剪切锁定、应力集中和复杂几何形状方面准确有效，并提高了有限体积法解决结构问题的有效性。