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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     
采用有限质点法的薄壳动力非线性行为分析
杨超1,2(),罗尧治1,*(),郑延丰1
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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摘要:

基于有限质点法原理和K-L经典薄壳理论,构造具有大位移大转动分析能力的薄壳离散质点模型,推导表述基本控制方程与公式. 对于质点位移以及壳元的变形和内力,均按照面内拉压和面外弯扭两部分进行拆分与叠加,并通过物理方式的虚拟运动依次分离出与薄膜刚度和弯曲刚度相关的纯变形,进而在局部变形坐标系下求解面外变形相对应的质点内力和内力矩,建立质点切平面外转角的变步长显式时间积分式,并对质点质量、时间步长、阻尼等关键参数取值给出建议. 在此基础上引入材料非线性应力修正算法,实现对薄壳弹塑性大应变动力非线性行为的模拟,并通过典型算例验证方法及程序的有效性和正确性.

关键词: 薄壳结构有限质点法非线性动力结构复杂行为    
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
收稿日期: 2018-05-23 出版日期: 2019-05-22
CLC:  TU 33  
通讯作者: 罗尧治     E-mail: 04tmgcyc@zju.edu.cn;luoyz@zju.edu.cn
作者简介: 杨超(1986—),男,博士后,从事大跨度空间结构研究. orcid.org/0000-0003-1405-2592. E-mail: 04tmgcyc@zju.edu.cn
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引用本文:

杨超,罗尧治,郑延丰. 采用有限质点法的薄壳动力非线性行为分析[J]. 浙江大学学报(工学版), 2019, 53(6): 1019-1030.

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.

链接本文:

http://www.zjujournals.com/eng/CN/10.3785/j.issn.1008-973X.2019.06.001        http://www.zjujournals.com/eng/CN/Y2019/V53/I6/1019

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
计算方法 t=0.2 ms t=0.4 ms t=0.6 ms
弹性 塑性 弹性 塑性 弹性 塑性
Bathe等[23] ?1.183 6 ?1.473 2 ?2.032 0 ?1.572 3 1.160 8 ?0.916 9
BST/EBST(O?ate等[24]) ?1.270 0 ?1.351 3 ?2.324 1 ?1.508 8 1.104 9 ?0.624 8
TRIC(Argyris等[25]) ?1.234 4 ? ?2.301 2 ? 1.066 8 ?
本文(模型③) ?1.211 6 ?1.364 0 ?2.265 7 ?1.468 1 1.122 7 ?0.627 4
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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