浙江大学学报(工学版)  2019, Vol. 53 Issue (6): 1019-1030    DOI: 10.3785/j.issn.1008-973X.2019.06.001
 土木与建筑工程

1. 浙江大学 空间结构研究中心，浙江 杭州 310058
2. 广东省高等学校结构与风洞重点实验室，广东 汕头 515063
Nonlinear dynamic analysis of shells using finite particle method
Chao YANG1,2(),Yao-zhi LUO1,*(),Yan-feng ZHENG1
1. Space Structure Research Center of Zhejiang University, Hangzhou 310058, China
2. Key Laboratory of Structure and Wind Tunnel of Guangdong Higher Education Institutes, Shantou 515063, China
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Abstract:

A discrete particle model of thin shells with large displacement and large rotation analysis capability was constructed based on the principle of finite particle method and K-L classical thin shell theory, and the fundamental governing equations and formulas were derived. For the particle displacement and the deformation and internal force of the shell element, the two parts corresponding to the in-plane tension and the out-of-plane bending and twisting were split and superimposed, respectively. The pure deformation related with the membrane rigidity and bending rigidity was sequentially separated by using a physical modeling procedure involving fictitious motions. Then in the local deformation coordinate system, the internal forces and moments were solved, and the explicit time integral formula with variable step sizes for calculation of the out-of-plane rotation was established. The determinations of several key parameters were also given, including particle mass, time step and damping. Moreover, an stress correction algorithm for solving material nonlinearity was introduced to simulate the dynamic nonlinear behavior of a thin shell with large elastic-plastic strain. The efficiency and validity of the presented method and the self-developed program are verified by several benchmark examples of nonlinear shell dynamics.

Key words: shell structures    finite particle method    nonlinearity    dynamic    complicated behaviors of structures

 CLC: TU 33

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Chao YANG,Yao-zhi LUO,Yan-feng ZHENG. Nonlinear dynamic analysis of shells using finite particle method. Journal of ZheJiang University (Engineering Science), 2019, 53(6): 1019-1030.

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 图 1  薄壳离散质点群模型及任一质点的运动情况 图 2  质点转动计算的局部切平面坐标系 图 3  三节点薄壳元的空间运动描述 图 4  质点的质量截面转动惯量 图 5  扁球壳模型：几何、边界及材料性质 图 6  扁球壳的有限质点离散模型 图 7  扁球壳受突加均布荷载作用下的顶点竖向位移时程 表 1  扁球壳中心顶点处的竖向位移比较 图 8  受冲击作用柱面曲壳：几何、材料与载荷作用 图 9  受冲击后不同时刻的柱面壳形态 图 10  柱面曲壳的最终剖面形状与试验结果比较（t=1.0 ms） 图 11  柱面曲壳纵轴线上位于y=15.95 cm和y=23.93 cm两点的竖向位移时程曲线 图 12  薄壁方管受刚块撞击：几何尺寸、材料与约束条件 图 13  受撞击后薄壁方管的动力响应 图 14  受撞击后不同时刻的方管形态 图 15  t=13.4 ms时方管壁表面的等效塑性应变分布
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