基于轴对称光滑有限元的身管动力学仿真

Dynamic Simulation of Barrel Based on Axisymmetric Smoothed Finite Element Method

摘要

针对火炮身管数值仿真计算规模大的问题,发展了一种基于梯度光滑有限元理论的二维轴对称应变光滑单元。该方法基于三角形有限单元的边中心进行应变光滑运算,然后根据边中心的光滑应变插值构建出单元内线性应变场,与传统线性有限元相比可有效缓解单元应变不光滑现象,从而提高计算精度。基于该方法,构建了身管轴对称有限元模型,在考虑火药燃气时空变化载荷下开展了身管结构动力学仿真分析。结果表明:在内弹道过程中,最大变形和应力出现在身管坡膛处,其中主要产生径向变形,但是载荷沿轴向的空间分布变化导致存在一定的轴向变形,这是不能基于厚壁圆筒理论分析解释的。该方法通过引入应变光滑稳定技术来改善传统三角形单元在模态分析中的性能,在保持网格生成便利性的同时,获得了接近传统六面体单元方法的计算精度。研究结果可以为火炮身管设计提供更全面的理论支持。

Abstract

To address the issue of large-scale numerical simulation in artillery barrel analysis, a two-dimensional axisymmetric strain-smoothed element was developed based on the gradient-smoothed finite element method. This approach performs strain smoothing operations at the edge centroids of triangular finite elements and subsequently constructs a linearly varying strain field within the element by interpolating the smoothed strains from these edge centroids. Compared with conventional linear finite elements, this method effectively mitigates strain discontinuity across elements, thereby improving computational accuracy. Utilizing this method, an axisymmetric finite element model of the barrel was established, and structural dynamic simulations were conducted considering the spatiotemporal variations in propellant gas loading. The results demonstrate that during the interior ballistic process, the maximum deformation and stress occur at the forcing cone of barrel, where radial deformation dominates. However, the axial spatial distribution variation of the load induces non-negligible axial deformation, which cannot be captured by thick-walled cylinder theory. The method in this paper improves triangular elements in modal analysis by introducing strain smoothing stabilization techniques. While maintaining the convenience of mesh generation, it achieves computational accuracy close to that of the traditional hexahedral element method. This study provides more comprehensive theoretical support for the design of artillery barrel.

关键词

火炮身管 / 结构动力学 / 有限元 / 应变光滑 / 轴对称单元

Key words

barrel / structural dynamics / finite element method / strain smoothed / axisymmetric element

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