弹性壳结构静力与动力分析的光滑粒子法

本文通过采用移动最小二乘函数作为近似函数 和完全拉格朗日方程作为近似方程来改善光滑粒子法的稳定性和数值精度; 在此基础上, 提出了壳结构静力分析的光滑粒子法, 并完善了壳结构动力分析方法; 最后, 采用国际公认的壳结构的标准测试模型对静力和动力问题分别进行了验证, 所得结果与已有数据吻合良好, 证明了本文数值模型的有效性和可靠性, 为光滑粒子法进一步在裂纹、破碎等非线性壳结构中的应用提供参考.关键词：弹性壳静力与动力分析光滑粒子法完备性和稳定性

Static and dynamic analysis of elastic shell structures with smoothed particle method

Meshfree smoothed particle method has great advantages in dealing with nonlinear problems of solid structures However, due to the instability and poor accuracy, it has been limited to the application in solid mechanics for a long time; especially the study on shell structure with smoothed particle method is even rarely reported on account of expensive three-dimensional continuum modeling and the phenomenon of numerical fracture in the traditional method The moving least square function and total Lagrangian equations are introduced as an approximation function and approximation equations respectively to improve the stability and numerical accuracy of smoothed particle method; on this basis, the method of static analysis is proposed, and meanwhile the dynamic analysis method is also refined. Finally, the internationally recognized standard test models on static and dynamic problems are adopted to verify the above shell theory, and the results are in good agreement with the existing data, which proves the validity and reliability of the present numerical model. This paper aims to provide a reference for the further research of smoothed particle method on nonlinear shell structures, such as crack, crushing, etc.
Keywords：elastic shellstatic and dynamic analysissmoothed particle hydrodynamics (SPH)completeness and stability