﻿ 含模态缺陷的环向加肋圆柱壳极限强度分析
 舰船科学技术  2021, Vol. 43 Issue (3): 1-5    DOI: 10.3404/j.issn.1672-7649.2021.03.001 PDF

1. 上海海事大学 海洋科学与工程学院，上海 201306;
2. 上海海事大学 物流工程学院，上海 201306

Ultimate strength analysis of circumferential ribbed cylindrical shells with modal defects
XIONG Zhi-xin1, HUI Han-ju1, HUANG Zhi-quan2, ZHAN Yi-ting1
1. College of Ocean Science and Engineering, Shanghai Maritime University, Shanghai 201306, China;
2. College of Logistic Engineering, Shanghai Maritime University, Shanghai 201306, China
Abstract: In order to study the effect of initial defect on the ultimate strength of circumferential ribbed cylindrical shell modal defect is introduced as the initial geometric defect of cylindrical shell. Firstly, a finite element model consistent with the physical model was established, and the first 30 modes were classified into four categories according to the shape characteristics of the modes. It was found that the 23rd mode in the first category obtained the lowest ultimate strength, and the radius-thickness ratio, defect amplitude and sensitivity of different materials were analyzed for cylindrical shells with modal defects. The results show that the ultimate strength is approximately linear with different thickness radius ratio and defect amplitude. The modal order corresponding to the minimum ultimate strength of different materials is different, but the modal shape is the same.
Key words: ring- stiffened cylinder     ultimate strength     initial imperfection     mode
0 引　言

1 模态缺陷方法 1.1 计算模型

 图 1 圆柱壳受力情况与约束条件 Fig. 1 Force condition and constraint conditions of cylindrical shell
1.2 计算结果

 图 2 计算结果与实验值的比值 Fig. 2 Ratio of the result to the experimental value
2 模态缺陷的敏感性分析 2.1 缺陷幅值对临界屈曲荷载的影响

 图 3 缺陷幅值与临界屈曲荷载对应不同厚度的关系 Fig. 3 Relation between defect amplitude and critical buckling load corresponding to different thickness

2.2 厚度半径比对临界屈曲荷载的影响

 图 4 厚度半径比与临界屈曲荷载之间的关系 Fig. 4 Relation between thickness radius ratio and critical buckling load

 图 5 t/R值对应的临界屈曲压力差值ΔPcr Fig. 5 t/R value corresponding to the critical buckling pressure difference ΔPcr
2.3 材料特性对于模态缺陷的影响

3 结　语

1）通过计算发现，第23阶模态缺陷的极限强度低于第1阶模态缺陷的极限强度。从模态形状上，这两者均属于表1中的类别一。计算时，可以针对该类别的模态进行计算，从而降低了数值模拟的计算量。

2）对含初始几何缺陷的耐压圆柱壳，缺陷幅值与径厚比的影响趋势均为线性，缺陷幅值越小，径厚比越大所得到的耐压圆柱壳的极限强度越大。本文取缺陷幅值δ=6 mm与δ=20 mm为例，观察ΔPcr曲线发现径厚比会在一个区域中相对应地降低缺陷幅值对极限强度的敏感性。

3）选取的6种材料属性对模态形状的影响不大，不同材料属性得到最低极限强度的模态均不相同，但均属于表1中类别一的模态形状。对于常用的金属材料，最不利的模态出现在类别一中。

 [1] 万春华, 段世慧, 吴存利, 等. 初始几何缺陷对加筋结构后屈曲分析的影响[J]. 航空计算技, 2017, 47(1): 90-93. WAN CHUN-hua, DUAN Shi-hui, WU Cun-li, et al. Influence of initial geometrical imperfection on post-buckling analysis for stiffened structure[J]. Aeronautical Computer Technique, 2017, 47(1): 90-93. [2] 王林, 蒋理, 王仁华, 等. 初始缺陷对耐压圆柱壳塑性稳定性影响初探[J]. 江苏科技大学学报: 自然科版, 2007, 21(5): 1-3. WANG Lin, JIANG Li, WANG Ren-hua, et al. Original research on influence of initial deflection on plastic stability of ring-stiffened circular cylindrical shell[J]. Journal of Jiangsu University of Science and Technology: Natural Science Edition, 2007, 21(5): 1-3. [3] 乔丕忠, 王艳丽, 陆林军. 圆柱壳稳定性问题的研究进展[J]. 力学季刊, 2018, 39(2): 223-236. QIAO Pi-zhong, WANG Yan-li, LU Lin-jun. Advances in stability study of cylindrical shells[J]. Chinese Quarterly of Mechanics, 2018, 39(2): 223-236. [4] European Committee for Standardization. Strength and stability of shell structures: EN 1993-1-6[S]. EN Special Publication, 2007. [5] 沈世钊, 陈昕. 网壳结构稳定性[M]. 北京: 科学出版社, 1999. [6] 魏协宇, 陈冰冰, 郑浣琪, 等. 压力容器设计标准中外压圆筒初始几何偏差规定的讨论[J]. 压力容器, 2015, 32(3): 20-28. WEI Xie-yu, CHEN Bing-bing, ZHENG Huan-qi, et al. Discussion of regulations of initial geometric deviations on cylindrical shells under external pressure in pressure vessel design standard[J]. Pressure Vessel Technology, 2015, 32(3): 20-28. DOI:10.3969/j.issn.1001-4837.2015.03.003 [7] 万福腾, 陈志平, 焦鹏, 等. 含初始几何缺陷薄壁圆柱壳屈曲载荷的数值模拟方法研究[J]. 压力容器, 2017, 34(3): 1-9. WAN Fu-teng, CHEN Zhi-ping, JIAO Peng, et al. Research on buckling load numerical method of cylindrical shells with initial imperfection[J]. Pressure Vessel Technology, 2017, 34(3): 1-9. DOI:10.3969/j.issn.1001-4837.2017.03.001 [8] 罗珊, 王纬波. 基于模态缺陷的受压球壳屈曲特性研究[J]. 计算力学学报, 2019, 36(04): 498-504. LUO Shan, WANG Wei-bo. Research on buckling behavior of the spherical pressure hull considering initial imperfections[J]. Chinese Journal of Computational Mechanics, 2019, 36(04): 498-504. [9] 张建, 周通, 王纬波, 等. 模态缺陷条件下复合材料柱形壳屈曲特性[J]. 复合材料学报, 2017, 34(3): 588-596. ZHANG Jian, ZHOU Tong, WANG Wei-bo, et al. Buckling property of a composite cylindrical shell considering mode imperfections[J]. Acta Materiae Compositae Sinica, 2017, 34(3): 588-596. [10] 罗昱. 改进的一致缺陷模态法在单层网壳稳定分析中的应用研究[D]. 天津: 天津大学, 2007. LUO Yu. The application of the improved uniform defect mode method to the stability analysis of single reticulated shell[D]. Tianjin: Tianjin university, 2007. [11] CHO SR, MUTTAQIE T, DO QT, et al. Experimental investigations on the failure modes of ring-stiffened cylinders under external hydrostatic pressure[J]. International Journal of Naval Architecture and Ocean Engineering, 2017. [12] 潜水系统与潜水器入级规范[S]. 北京: 中国船级社, 2019. Classification specification for diving systems and submersibles[S]. Beijing: China Classification Society, 2019. [13] 雒高龙, 张淑茳, 任慧龙. 船用钢应力-应变关系的数学表达及其在计算加筋板屈曲应力中的应用[J]. 造船技术, 2006(3): 13-18. LUO Gao-long, ZHANG Shu-jiang, REN Hui-long. Mathematical expression of ship plate stress-strain relation and its use in calculating stiffened plate buckling[J]. Journal of Marine Technology, 2006(3): 13-18. DOI:10.3969/j.issn.1000-3878.2006.03.004 [14] 刘涛, 大深度潜水器结构分析与设计研究[D]. 无锡: 中国船舶科学研究中心, 2001. LIU Tao, Structural analysis and design of large depth submersible[D]. Wuxi: China ship science research center, 2001. [15] 姜旭胤, 刘涛, 张美荣, 等. 基于材料数据的耐压壳结构极限承载力弹塑性物理修正[J]. 船舶力学, 2013, 17(11): 1278-1291. JIANG Xu-yin, LIU Tao, ZHANG Mei-rong, et al. Plastic correction of pressure hull’s limit load considering material properties[J]. Journal of Ship Mechanics, 2013, 17(11): 1278-1291. DOI:10.3969/j.issn.1007-7294.2013.11.008