结构稳定可靠性初探
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摘要
目前，人们已普遍认识到许多工程结构系统具有不确定的因素。结构可靠度就是研究结构在各种随机因素作用下的安全问题。应用可靠性解决结构的强度、刚度、疲劳等在理论上和应用上都已取得巨大的成功，而结构稳定性的可靠性分析，至今仅对压杆的稳定性作过介绍。但在实际结构中一般是由稳定性决定了构件的承载力。因此，研究结构的稳定可靠性具有重要的应用价值。本文针对简单杆系结构的稳定可靠性，主要作了以下一些工作：
1．对于轴心压杆，通过平衡微分方程求得轴心受压构件的欧拉临界力并将它作为应力强度模型的强度，将压杆所受的荷载作为应力，用哈桑-林德法求解轴心压杆的可靠度。由于用埃特金迭代代替牛顿迭代，避免了迭代不收敛的可能性，提高了迭代的收敛速度。
2．压弯构件同时承受轴向压力和弯矩作用，且弯矩不是次要的。在本文中分别应用边缘纤维屈服准则和弹塑性失稳考虑了压弯构件的稳定可靠性。对于边缘纤维屈服准则，截面中的最大应力作为应力强度模型中的应力，材料的屈服极限作为强度。弹塑性失稳是非线性失稳，构件的极限荷载不能通过解析式导出。应用数值积分法计算极限荷载，通过蒙特卡罗法计算了构件的可靠度。
3．对于对称刚架系统，可取半边结构将刚架化为单个构件的可靠度问题。对于一般的刚架系统，将失稳作为一种失效模式，用分枝限界法，寻找主要失效模式，用窄带Ditlevsen法计算结构系统的可靠性指标(或失效概率)。由于稳定失效是一种脆性破坏，失效路径不再与失效顺序无关，考虑稳定问题后，失效模式数明显增多。算例表明，考虑后失效概率明显增大，失稳在杆系结构可靠性计算中不可忽略。
At present, it is generally recognized that almost all structural systems are indeterminate. Structural reliability is to study the safety question of structure under stochastic factor. Great progress has been made in theory and application by applying reliability theory to solve in intensity, stiff and fatigue of structure, but little in buckle reliability. The strength of actual structure is generally decided by stability. Therefore, it has significant application value to study stable reliability of structure. Stable reliability of spar and simple spar system has been studied in this article. Now the main conclusions gained are given as follows.
1. Euler critical force of axis pole can be gained by equilibrium differential equation. It can be regard as strength of the stress-strength modal and the load that the pole beared as stress. Applying Hasofer-Lind method has got the reliable index. Using Aitken substitute to Newton iteration can void the possibility of divergence and speed divergence.
2. The beam column is loaded by axis press and moment and the moment isn't subsidiary. Both margin yield criterion and elastic-plastic buckle are used to solve the stable reliability of beam column in this article. As for margin yield criterion, the maximum stress of section is regarded as stress of stress-strength modal and yield stress of the material as strength. The elastic-plastic buckle is nonlinear and the utmost load can't be got through analytic result. The reliable index has been gained by Monte-Carlo method.
3. The symmetrical rigid frame system can be separated into single component to calculate reliable index. For generally rigid frame, taking buckle into account, boundary branch method is used to looking for main failure modes. The reliability of rigid frame is evaluated by narrow band Ditlevsen method. Because buckle is brittle failure, failure route is related to failure sequence. The
failure mode is increased evidently when taking buckle failure into account. The sample indicates that failure probability is larger when thing buckle failure and buckle can't be ignored in calculating reliability.
1．对于轴心压杆，通过平衡微分方程求得轴心受压构件的欧拉临界力并将它作为应力强度模型的强度，将压杆所受的荷载作为应力，用哈桑-林德法求解轴心压杆的可靠度。由于用埃特金迭代代替牛顿迭代，避免了迭代不收敛的可能性，提高了迭代的收敛速度。
2．压弯构件同时承受轴向压力和弯矩作用，且弯矩不是次要的。在本文中分别应用边缘纤维屈服准则和弹塑性失稳考虑了压弯构件的稳定可靠性。对于边缘纤维屈服准则，截面中的最大应力作为应力强度模型中的应力，材料的屈服极限作为强度。弹塑性失稳是非线性失稳，构件的极限荷载不能通过解析式导出。应用数值积分法计算极限荷载，通过蒙特卡罗法计算了构件的可靠度。
3．对于对称刚架系统，可取半边结构将刚架化为单个构件的可靠度问题。对于一般的刚架系统，将失稳作为一种失效模式，用分枝限界法，寻找主要失效模式，用窄带Ditlevsen法计算结构系统的可靠性指标(或失效概率)。由于稳定失效是一种脆性破坏，失效路径不再与失效顺序无关，考虑稳定问题后，失效模式数明显增多。算例表明，考虑后失效概率明显增大，失稳在杆系结构可靠性计算中不可忽略。
At present, it is generally recognized that almost all structural systems are indeterminate. Structural reliability is to study the safety question of structure under stochastic factor. Great progress has been made in theory and application by applying reliability theory to solve in intensity, stiff and fatigue of structure, but little in buckle reliability. The strength of actual structure is generally decided by stability. Therefore, it has significant application value to study stable reliability of structure. Stable reliability of spar and simple spar system has been studied in this article. Now the main conclusions gained are given as follows.
1. Euler critical force of axis pole can be gained by equilibrium differential equation. It can be regard as strength of the stress-strength modal and the load that the pole beared as stress. Applying Hasofer-Lind method has got the reliable index. Using Aitken substitute to Newton iteration can void the possibility of divergence and speed divergence.
2. The beam column is loaded by axis press and moment and the moment isn't subsidiary. Both margin yield criterion and elastic-plastic buckle are used to solve the stable reliability of beam column in this article. As for margin yield criterion, the maximum stress of section is regarded as stress of stress-strength modal and yield stress of the material as strength. The elastic-plastic buckle is nonlinear and the utmost load can't be got through analytic result. The reliable index has been gained by Monte-Carlo method.
3. The symmetrical rigid frame system can be separated into single component to calculate reliable index. For generally rigid frame, taking buckle into account, boundary branch method is used to looking for main failure modes. The reliability of rigid frame is evaluated by narrow band Ditlevsen method. Because buckle is brittle failure, failure route is related to failure sequence. The
failure mode is increased evidently when taking buckle failure into account. The sample indicates that failure probability is larger when thing buckle failure and buckle can't be ignored in calculating reliability.
引文
[1] 胡云昌，郭振邦编著．结构系统可靠性分析原理及应用．天津：天津大学出版社，1992
[2] 李杰．随机结构系统—分析与建模．北京：科学出版社，1996
[3] 杨绿峰，高兑现，李桂青．随机结构在随机激励下的二阶摄动随机势能泛函及其应用．应用力学学报．1999，16(4)
[4] 秦权．随机有限元及其进展Ⅱ：可靠度随机有限元和随机有限元的应用．工程力学．1995，12(1)
[5] 李龙元．结构稳定性分析的基本原理及讨论．上海大学学报．1990(3)：189-195
[6] 吕震宙，冯元生．结构刚度可靠性分析方法．航空学报．1994，15(8)：910-916
[7] GB50153-92，工程结构可靠度设计统一标准[S]．北京：中国计划出版社，1992
[8] GBJ68-84，建筑结构设计统一标准[S]．北京：中国建筑工业出版社，1984
[9] GB50158-92，港口工程结构可靠度设计统一标准[S]．北京：中国计划出版社，1992
[10] 赵国藩，贡金鑫，赵尚传．我国土木工程结构可靠性研究的一些进展[J]．大连理工大学学报．2000，40(3)：253-258
[11] 邵文蛟编著．不完整结构的可靠性分析．北京：国防工业出版社，1997
[12] 吴世伟．结构可靠度分析．北京：交通出版社，1988
[13] 赵国藩，曹居易，张宽权．工程结构可靠度．北京：水利电力出版社，1984
[14] 刘宁．可靠度随机有限元法及其工程应用．北京：中国水利水电出版社，2001
[15] Timoshenko, S. P. and Gere, J. M., Theory of elastic stability. 2nd, Ed., McGraw-Hill, 1961. 中译本：弹性稳定理论．科学出版社．1965
[16] 唐家祥，王仕统，裴若娟．结构稳定理论．北京：中国铁道出版社，1989
[17] 何水清，王善编著．结构可靠性分析与设计．北京：国防工业出版社，1993
[18] 盖京波，王善．轴心压杆的稳定可靠性计算．哈尔滨工程大学学报．2002(4)：91-93
[19] 陈骥编著．钢结构稳定理论与设计．北京：科学出版社．2001
[20] 徐雪玲，王善编著．结构可靠性原理导论．北京：中国船舶工业总公司可靠性中心，1996
[21] Hasofer A H, Lind N C. Exact and invariant Second Moment Format, Journal of the Engineering Mechanics Division, ASCE, 1974, Vol.100:111-121
[22] 索夫特-克里斯坦森P，贝可M J．结构可靠性理论及其应用．范水士，陈慰如，李学伟译．北京：科学出版社，1988
[23] 李庆杨，王能超，易大义．数值分析．武汉：华中科技大学出版社，1986
[24] 吕烈武，沈世钊，沈祖炎等．钢结构构件稳定理论．北京：中国建筑工业出版社，1983
[25] 唐家祥，王仕统，裴若娟．结构稳定理论．北京：中国铁道出版社，1989
[26] 郑伟国，沈祖炎．结构稳定分析的改进数值积分法．同济大学学报，1990，18(3)：396-405
[27] 董聪．系统可靠性理论与工程．博士后研究工作报告，1995
[28] 陈虬，刘先斌．随机有限元法及其工程应用．成都：西南交通大学出版社，1993
[29] 印朝富．空间梁系结构极限荷载有限元解法[J]．河海大学学报，1998，26(4)：29-34
[30] W. F. Chen and T. Aisuta. Theory of beam-column. Vo1.1,1977
[31] 安伟光编著．结构系统可靠性和基于可靠性的优化设计．北京：国防工业出版社，1997
[32] 余建星，郭振邦，徐慧，黄衍顺．船舶与海洋结构物可靠性原理．天津：天津大学出版社，2001
[33] 刘刚，郑云龙．非线性刚架系统可靠性分析．工程力学增刊，1999：738-743页
[34] 龙驭球，包世华．结构力学教程．高等教育出版社，1987
[35] 赵超燮．结构矩阵分析原理．人民教育出版社，1982
[36] Murotsu Y, Okada H, Yonezawa M, et al., Automatic Generation of Stochastically Dominant Modes of Structural Failure in Frame Structure, Struct. Safety, 1984,2:17-25
[37] Ditlevsen O, Narrow Reliability Bounds for Structural Systems, J. Struct. Mech., 1979, 7(4): 453-472
[2] 李杰．随机结构系统—分析与建模．北京：科学出版社，1996
[3] 杨绿峰，高兑现，李桂青．随机结构在随机激励下的二阶摄动随机势能泛函及其应用．应用力学学报．1999，16(4)
[4] 秦权．随机有限元及其进展Ⅱ：可靠度随机有限元和随机有限元的应用．工程力学．1995，12(1)
[5] 李龙元．结构稳定性分析的基本原理及讨论．上海大学学报．1990(3)：189-195
[6] 吕震宙，冯元生．结构刚度可靠性分析方法．航空学报．1994，15(8)：910-916
[7] GB50153-92，工程结构可靠度设计统一标准[S]．北京：中国计划出版社，1992
[8] GBJ68-84，建筑结构设计统一标准[S]．北京：中国建筑工业出版社，1984
[9] GB50158-92，港口工程结构可靠度设计统一标准[S]．北京：中国计划出版社，1992
[10] 赵国藩，贡金鑫，赵尚传．我国土木工程结构可靠性研究的一些进展[J]．大连理工大学学报．2000，40(3)：253-258
[11] 邵文蛟编著．不完整结构的可靠性分析．北京：国防工业出版社，1997
[12] 吴世伟．结构可靠度分析．北京：交通出版社，1988
[13] 赵国藩，曹居易，张宽权．工程结构可靠度．北京：水利电力出版社，1984
[14] 刘宁．可靠度随机有限元法及其工程应用．北京：中国水利水电出版社，2001
[15] Timoshenko, S. P. and Gere, J. M., Theory of elastic stability. 2nd, Ed., McGraw-Hill, 1961. 中译本：弹性稳定理论．科学出版社．1965
[16] 唐家祥，王仕统，裴若娟．结构稳定理论．北京：中国铁道出版社，1989
[17] 何水清，王善编著．结构可靠性分析与设计．北京：国防工业出版社，1993
[18] 盖京波，王善．轴心压杆的稳定可靠性计算．哈尔滨工程大学学报．2002(4)：91-93
[19] 陈骥编著．钢结构稳定理论与设计．北京：科学出版社．2001
[20] 徐雪玲，王善编著．结构可靠性原理导论．北京：中国船舶工业总公司可靠性中心，1996
[21] Hasofer A H, Lind N C. Exact and invariant Second Moment Format, Journal of the Engineering Mechanics Division, ASCE, 1974, Vol.100:111-121
[22] 索夫特-克里斯坦森P，贝可M J．结构可靠性理论及其应用．范水士，陈慰如，李学伟译．北京：科学出版社，1988
[23] 李庆杨，王能超，易大义．数值分析．武汉：华中科技大学出版社，1986
[24] 吕烈武，沈世钊，沈祖炎等．钢结构构件稳定理论．北京：中国建筑工业出版社，1983
[25] 唐家祥，王仕统，裴若娟．结构稳定理论．北京：中国铁道出版社，1989
[26] 郑伟国，沈祖炎．结构稳定分析的改进数值积分法．同济大学学报，1990，18(3)：396-405
[27] 董聪．系统可靠性理论与工程．博士后研究工作报告，1995
[28] 陈虬，刘先斌．随机有限元法及其工程应用．成都：西南交通大学出版社，1993
[29] 印朝富．空间梁系结构极限荷载有限元解法[J]．河海大学学报，1998，26(4)：29-34
[30] W. F. Chen and T. Aisuta. Theory of beam-column. Vo1.1,1977
[31] 安伟光编著．结构系统可靠性和基于可靠性的优化设计．北京：国防工业出版社，1997
[32] 余建星，郭振邦，徐慧，黄衍顺．船舶与海洋结构物可靠性原理．天津：天津大学出版社，2001
[33] 刘刚，郑云龙．非线性刚架系统可靠性分析．工程力学增刊，1999：738-743页
[34] 龙驭球，包世华．结构力学教程．高等教育出版社，1987
[35] 赵超燮．结构矩阵分析原理．人民教育出版社，1982
[36] Murotsu Y, Okada H, Yonezawa M, et al., Automatic Generation of Stochastically Dominant Modes of Structural Failure in Frame Structure, Struct. Safety, 1984,2:17-25
[37] Ditlevsen O, Narrow Reliability Bounds for Structural Systems, J. Struct. Mech., 1979, 7(4): 453-472