大跨度空间网格结构的可靠度、敏感性及失效过程研究
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摘要
近来,工程结构的可靠度与敏感性分析得到了前所未有的关注。近年来,尤其在2008年北京奥运会的推动下,国内兴建了大量的大跨度空间结构,同时空间钢结构的事故又接连发生,其可靠度与安全性亟待深入探讨与研究。目前,对大跨度空间结构的可靠度与敏感性研究刚刚起步,国内外可供参考的文献很少,尚没有系统地对空间结构进行可靠度与敏感性研究。
地震等自然灾害一直困扰着人类,近几十年来,全球多次发生大地震,造成了大量严重的工程破坏和惨重的生命财产损失。大跨度空间结构作为城市标志性建筑(如国家体育馆鸟巢、国家游泳馆水立方等)和灾后的主要应急避难场所(如2011年日本海域9.0级地震中的新泻体育馆、2008年汶川8.0级大地震中的绵阳九州体育馆和2005年美国路易斯安那州新奥尔良市遭受“卡特里娜”飓风袭击中的“超级穹顶”体育馆等)其安全性及抗震性能一直是国内外学术界及工程界共同关注的重要课题。该类结构是人群集合或配置重要设施的场所,一旦发生倒塌,后果不堪设想,因此对空间结构进行可靠度、动力失效及破坏机理的研究意义重大。
基于此,系统地研究了空间结构的可靠度和敏感性,并对双层网壳结构在静力极限荷载和三维地震动作用下的破坏过程及失效机理进行深入探讨,主要研究内容如下：
(1)在大跨度空间网格结构的非线性有限元可靠度分析当中,经常会遇到两个问题：特定材料模型会导致不连续的梯度,继而计算不能正常收敛；试算点离失效域过远,导致计算难收敛于正确结果。针对以上两个问题,将光滑的双线性材料模型和Bouc-Wen材料模型引入到空间结构的可靠度计算中解决了第一个问题；除了将改进的HL-RF法、梯度投影法、序列二次规划法,又首次将Polak-He算法引入至空间结构的可靠度计算中解决了第二个问题,且对四种算法的效率、精度和稳定性进行了详细阐述,建议将影响其收敛和计算效率的参数取值在一定范围之内,为空间结构的可靠度分析提供了参考。
(2)研究了初始缺陷大小对空间网架结构可靠度的影响规律,将七种厚度不同的网架结构作为研究对象,考虑了六种大小不同的初始几何缺陷,将网架结构的最低阶屈曲模态作为初始缺陷分布模态,详细分析了初始缺陷的大小对网架结构变形能力可靠度的影响规律；为全面考察各阈值下网架结构的可靠度,对七种厚度的空问网架结构进行了参数化可靠度分析；选取了随机变量间六种大小不同的相关系数,考察了其值对网架可靠度影响规律。
(3)敏感性分析是工程结构可靠度分析一个重要方面,其结果可提供失效概率对随机变量的重要性排序。应用直接微分法对空间结构进行敏感性分析,将简单桁架、双层柱面网壳和平板网架作为数值算例,将α、γ、δ和η作为四种重要性度量指标,重点研究了功能函数对各随机变量、及其均值和标准差的敏感性及相关性。对空间网架结构进行了敏感性,将杆件的横截面面积、弹性模量、屈服强度、应变硬化率和外载荷等作为随机变量,应用FORM法对结构进行可靠度与敏感性计算。通常在工程结构的可靠度计算中,将节点坐标作为不变量来处理,这样就会造成一定的误差,因此对空间网架结构进行计算时,考察了节点坐标的变异性对空间结构的可靠性及敏感性的影响。对于大型复杂的空间结构而言,可靠度与敏感性计算量大,为减少计算量,引入了随机变量缩减法,大大提高了计算效率,为大跨度空间结构的可靠度与敏感性计算提供了方便。
(4)一次可靠度方法具有高效、精度较高等优点而被广泛采用,但当功能函数在设计点附近曲率较大时,在迭代过程中有时会在设计点附近左右摆动致使不收敛；当可靠度指标较大时,数值收敛速度慢。基于此,首次将近年来提出的功能度量法引入到大跨度空间结构的非线性有限元可靠度计算中。与可靠指标法不同的是,在功能度量法中,约束函数评估被处理为搜索具有规定的目标可靠指标的最小功能目标问题。为验证PMA在空间结构可靠度中的高效性与稳定性,分别采用可靠度指标法和功能度量法对四种矢跨比的双层柱面网壳和双层凯威特型球面网壳进行可靠度与敏感性计算,计算表明,功能度量法在空间结构的可靠度计算中具有更高的效率和更好的数值稳定性。
(5)为考察不同类型及不同部位随机变量对空间结构可靠度及敏感性的影响,分别对四种矢跨比的双层柱面网壳和四种矢跨比的双层球面网壳进行可靠度与敏感性分析,根据随机变量类型和杆件在网壳中的分布状况,分别将荷载、横截面面积、弹性模量和屈服强度作为一个和多个随机变量,从而研究功能函数对各类型及各部位随机变量的敏感程度；考察了不同类型的功能函数对随机变量的敏感性程度及功能函数间的相关性；研究了随机变量对失效概率的敏感性随不同矢跨比的变化规律；考察了随机变量服从不同概率分布时对空间结构可靠度、敏感性和相关性的影响。
(6)系统地研究了双层球面网壳结构在静力极限荷载及三维地震动作用下的破坏过程及失效机理。以四种不同矢跨比的双层球面作为研究对象,将网壳结构的变形能力、屈服杆件数、总应变能、总弹性应变能、总塑性应变能、总弹性应变和总塑性应变等作为考察指标,深入研究了双层球面网壳结构在静动力载荷作用下的破坏过程,给出了各矢跨比网壳杆件失效的先后次序,研究了各矢跨比网壳结构失效机理异同之处,计算结果可为双层球面网壳结构的设计提供借鉴与参考。
Reliability and sensitivity analysis of engineering structures are paid much attention nowadays. A great number of large-span space structures have been erected in succession, especially with the host of the 2008 Beijing Olympics Games. However, engineering accidents of space steel structures occurred simultaneously. The research on reliability and sensitivity of space structures just started at home and abroad, and even no systematical investigations on them, hence only few of literatures can be referred.
Humankind always suffers from natural disasters, e.g., earthquake. Especially, earthquakes occurred time and again all over the world in recent years, which caused plenty of engineering destruction and loss of life and property. As the symbols of city (e.g., Beijing National Stadium, known as the Bird's Nest, Beijing National Aquatics Center, known as the Water Cube) and emergency shelters (e.g., Niigata Gymnasium in 2011 catastrophic Ms 9.0 earthquake, Mianyang Jiuzhou Stadium in 2008 Wenchuan Ms 8.0 earthquake and New Orleans's Louisiana Superdome in Hurricane Katrina) after disaster's attack, the safety and seismic performance of large-span space structures got much attention in scholar and engineering fields at all times. This kind of structures, accommodating lots of people and important facilities, once destroyed, catastrophic accident will be occurred. Therefore, it is meaningful to research on reliability, dynamic failure and destruction mechanism of space structures.
Based on above issues, reliability and sensitivity analysis of large-span space structures have been systematically carried out. Failure process and failure mechanism of double-layer reticular dome under static critical loads and three-dimensional earthquake motions have been intensively studied. The main contents in this thesis are concluded as follows:
(1) Two issues are sometimes come forth when carry out nonlinear FE reliability analysis of large-span space frame structures, one is that certain material models may cause gradient discontinuity, which will lead to failure of the search algorithm to converge; the other is that the search algorithmes may generate trial points too far in the failure domain, which causes difficulties to obtain reasonable results. To settle the above two issues, the former issue is addressed by introducing smoothed bi-liner material model and Bouc-Wen material model, while the latter one is settled by introducing advanced searching algorithms, i.e. improved HL-RF Algorithm, the Gradient Projection Method (GPM), Sequential Quadratic Programming (SQP) and Polak-He algorithm. Furthermore, efficiency, accuracy and robustness are of the above four searching algorithms are elaborately illustrated and extensively compared, and gives some advices on how to choose the value of parameters that influence the computation efficiency and robustness of these algorithms, which can offer some valuable guidance to reliability evaluation in space structures.
(2) Effect of initial imperfection on reliability of space grid structures is extensively investigated. Seven trusses with different thicknesses and six different magnitudes of initial imperfection are taken into considerations, respectively. Layout of initial imperfection is chosen from the lowest order buckling mode of truss structures. Subsequently, initial imperfection's influence on reliability of grid structures is systematically researched; to comprehensively investigate reliability of truss under different thresholds, parametric reliability evaluations are carried out for these trusses; in order to research the effect of correlation coefficients of random variables on reliability of truss structures, six correlation coefficients are selected.
(3) Sensitivity analysis is an important aspect in reliability evaluation of engineering structures because its results can rank the random variables based on their relative importance. Different Difference Method (DDM) is adopted in the sensitivity analysis. Three numerical examples (e.g., a simple truss, a double-layer cylindrical reticular shell and a plane truss structure) are demonstrated, Four parameters (α,γ,δandη) are taken as importance measures to identify the sensitivities of random variables, their means and standard deviations. Cross-sectional area, Young's modulus, yielding strength, strain hardening rate and loads etc. are taken as random variables in space truss, and reliability and sensitivity are evaluated by FORM. Nodal coordinates are usually treated as invariants in reliability analysis, which will cause significant error in some cases. Thus, the variations of nodal coordinates are considered into reliability and sensitivity analysis of space grid truss structures. For large and complicated structures, much time and effort have to be paid to carry out reliability and sensitivity analysis. Hence, random variable reduction technique is introduced to reduce computation effort, and it facilitates the reliability and sensitivity analysis in space structures.
(4) First-order Reliability Method (FORM) is widely applied for its better efficiency and accuracy, however, it will oscillates around the design point and fails to converge in iteration process when the curvature is too large; large reliability index will impedes to converge. To settle the above issues, Performance Measure Approach (PMA) is firstly introduced into nonlinear FE reliability evaluation in space structures. Compared with Reliability Index Approach (RIA), constraint function can be treated as the problem that searching prescribed minimum performance target point in PMA. To verify the efficiency and robustness of PMA, reliability and sensitivity of four cylindrical reticulated shells with different rise-to-span ratios and four spherical reticulated shells with different rise-to-span ratios are evaluated by RIA and PMA, respectively. Numerical results indicate that PMA has better efficiency and robustness in reliability and sensitivity analysis of space structures.
(5) To identify the influences of different types and parts of random variables on reliability and sensitivity of space structures, four cylindrical reticulated shells with different rise-to-span ratios and four spherical reticulated shells with different rise-to-span ratios are selected. Based on the type and location of random variables, vertical loads, cross-sectional area of members, Young's modulus and yielding strength are treated as one or more random variables, respectively, to identify the sensitivity of these variables; several performance functions are selected to identify the effect of random variables on them and research their correlations; variation rules of sensitivity of all random variables are investigated with the change of rise-to-span ratio; the effect of different probabilistic distribution types of random variables on reliability, sensitivity and correlation is also extensively researched.
(6) Failure process and destruction mechanism of double-layer spherical reticulated shell under statically critical loads and three-dimensional earthquake motion are systematically investigated. Four double-layer spherical latticed domes with different rise-to-span ratios are selected, and deformation capability, number of yielding members, total strain energy, total elastic strain energy, total plastic strain energy, total elastic strain and total plastic strain of reticular domes are elaborately investigated. Failure processes of these domes under statically critical loads and dynamic excitations are captured, furthermore, failure sequence of members is illustrated in detail. Finally, similarities and differences of failure mechanism of four reticulated shells are developed. Numerical results can give some reasonable suggestions and advices for the design of double-layer spherical reticular shell.
地震等自然灾害一直困扰着人类,近几十年来,全球多次发生大地震,造成了大量严重的工程破坏和惨重的生命财产损失。大跨度空间结构作为城市标志性建筑(如国家体育馆鸟巢、国家游泳馆水立方等)和灾后的主要应急避难场所(如2011年日本海域9.0级地震中的新泻体育馆、2008年汶川8.0级大地震中的绵阳九州体育馆和2005年美国路易斯安那州新奥尔良市遭受“卡特里娜”飓风袭击中的“超级穹顶”体育馆等)其安全性及抗震性能一直是国内外学术界及工程界共同关注的重要课题。该类结构是人群集合或配置重要设施的场所,一旦发生倒塌,后果不堪设想,因此对空间结构进行可靠度、动力失效及破坏机理的研究意义重大。
基于此,系统地研究了空间结构的可靠度和敏感性,并对双层网壳结构在静力极限荷载和三维地震动作用下的破坏过程及失效机理进行深入探讨,主要研究内容如下：
(1)在大跨度空间网格结构的非线性有限元可靠度分析当中,经常会遇到两个问题：特定材料模型会导致不连续的梯度,继而计算不能正常收敛；试算点离失效域过远,导致计算难收敛于正确结果。针对以上两个问题,将光滑的双线性材料模型和Bouc-Wen材料模型引入到空间结构的可靠度计算中解决了第一个问题；除了将改进的HL-RF法、梯度投影法、序列二次规划法,又首次将Polak-He算法引入至空间结构的可靠度计算中解决了第二个问题,且对四种算法的效率、精度和稳定性进行了详细阐述,建议将影响其收敛和计算效率的参数取值在一定范围之内,为空间结构的可靠度分析提供了参考。
(2)研究了初始缺陷大小对空间网架结构可靠度的影响规律,将七种厚度不同的网架结构作为研究对象,考虑了六种大小不同的初始几何缺陷,将网架结构的最低阶屈曲模态作为初始缺陷分布模态,详细分析了初始缺陷的大小对网架结构变形能力可靠度的影响规律；为全面考察各阈值下网架结构的可靠度,对七种厚度的空问网架结构进行了参数化可靠度分析；选取了随机变量间六种大小不同的相关系数,考察了其值对网架可靠度影响规律。
(3)敏感性分析是工程结构可靠度分析一个重要方面,其结果可提供失效概率对随机变量的重要性排序。应用直接微分法对空间结构进行敏感性分析,将简单桁架、双层柱面网壳和平板网架作为数值算例,将α、γ、δ和η作为四种重要性度量指标,重点研究了功能函数对各随机变量、及其均值和标准差的敏感性及相关性。对空间网架结构进行了敏感性,将杆件的横截面面积、弹性模量、屈服强度、应变硬化率和外载荷等作为随机变量,应用FORM法对结构进行可靠度与敏感性计算。通常在工程结构的可靠度计算中,将节点坐标作为不变量来处理,这样就会造成一定的误差,因此对空间网架结构进行计算时,考察了节点坐标的变异性对空间结构的可靠性及敏感性的影响。对于大型复杂的空间结构而言,可靠度与敏感性计算量大,为减少计算量,引入了随机变量缩减法,大大提高了计算效率,为大跨度空间结构的可靠度与敏感性计算提供了方便。
(4)一次可靠度方法具有高效、精度较高等优点而被广泛采用,但当功能函数在设计点附近曲率较大时,在迭代过程中有时会在设计点附近左右摆动致使不收敛；当可靠度指标较大时,数值收敛速度慢。基于此,首次将近年来提出的功能度量法引入到大跨度空间结构的非线性有限元可靠度计算中。与可靠指标法不同的是,在功能度量法中,约束函数评估被处理为搜索具有规定的目标可靠指标的最小功能目标问题。为验证PMA在空间结构可靠度中的高效性与稳定性,分别采用可靠度指标法和功能度量法对四种矢跨比的双层柱面网壳和双层凯威特型球面网壳进行可靠度与敏感性计算,计算表明,功能度量法在空间结构的可靠度计算中具有更高的效率和更好的数值稳定性。
(5)为考察不同类型及不同部位随机变量对空间结构可靠度及敏感性的影响,分别对四种矢跨比的双层柱面网壳和四种矢跨比的双层球面网壳进行可靠度与敏感性分析,根据随机变量类型和杆件在网壳中的分布状况,分别将荷载、横截面面积、弹性模量和屈服强度作为一个和多个随机变量,从而研究功能函数对各类型及各部位随机变量的敏感程度；考察了不同类型的功能函数对随机变量的敏感性程度及功能函数间的相关性；研究了随机变量对失效概率的敏感性随不同矢跨比的变化规律；考察了随机变量服从不同概率分布时对空间结构可靠度、敏感性和相关性的影响。
(6)系统地研究了双层球面网壳结构在静力极限荷载及三维地震动作用下的破坏过程及失效机理。以四种不同矢跨比的双层球面作为研究对象,将网壳结构的变形能力、屈服杆件数、总应变能、总弹性应变能、总塑性应变能、总弹性应变和总塑性应变等作为考察指标,深入研究了双层球面网壳结构在静动力载荷作用下的破坏过程,给出了各矢跨比网壳杆件失效的先后次序,研究了各矢跨比网壳结构失效机理异同之处,计算结果可为双层球面网壳结构的设计提供借鉴与参考。
Reliability and sensitivity analysis of engineering structures are paid much attention nowadays. A great number of large-span space structures have been erected in succession, especially with the host of the 2008 Beijing Olympics Games. However, engineering accidents of space steel structures occurred simultaneously. The research on reliability and sensitivity of space structures just started at home and abroad, and even no systematical investigations on them, hence only few of literatures can be referred.
Humankind always suffers from natural disasters, e.g., earthquake. Especially, earthquakes occurred time and again all over the world in recent years, which caused plenty of engineering destruction and loss of life and property. As the symbols of city (e.g., Beijing National Stadium, known as the Bird's Nest, Beijing National Aquatics Center, known as the Water Cube) and emergency shelters (e.g., Niigata Gymnasium in 2011 catastrophic Ms 9.0 earthquake, Mianyang Jiuzhou Stadium in 2008 Wenchuan Ms 8.0 earthquake and New Orleans's Louisiana Superdome in Hurricane Katrina) after disaster's attack, the safety and seismic performance of large-span space structures got much attention in scholar and engineering fields at all times. This kind of structures, accommodating lots of people and important facilities, once destroyed, catastrophic accident will be occurred. Therefore, it is meaningful to research on reliability, dynamic failure and destruction mechanism of space structures.
Based on above issues, reliability and sensitivity analysis of large-span space structures have been systematically carried out. Failure process and failure mechanism of double-layer reticular dome under static critical loads and three-dimensional earthquake motions have been intensively studied. The main contents in this thesis are concluded as follows:
(1) Two issues are sometimes come forth when carry out nonlinear FE reliability analysis of large-span space frame structures, one is that certain material models may cause gradient discontinuity, which will lead to failure of the search algorithm to converge; the other is that the search algorithmes may generate trial points too far in the failure domain, which causes difficulties to obtain reasonable results. To settle the above two issues, the former issue is addressed by introducing smoothed bi-liner material model and Bouc-Wen material model, while the latter one is settled by introducing advanced searching algorithms, i.e. improved HL-RF Algorithm, the Gradient Projection Method (GPM), Sequential Quadratic Programming (SQP) and Polak-He algorithm. Furthermore, efficiency, accuracy and robustness are of the above four searching algorithms are elaborately illustrated and extensively compared, and gives some advices on how to choose the value of parameters that influence the computation efficiency and robustness of these algorithms, which can offer some valuable guidance to reliability evaluation in space structures.
(2) Effect of initial imperfection on reliability of space grid structures is extensively investigated. Seven trusses with different thicknesses and six different magnitudes of initial imperfection are taken into considerations, respectively. Layout of initial imperfection is chosen from the lowest order buckling mode of truss structures. Subsequently, initial imperfection's influence on reliability of grid structures is systematically researched; to comprehensively investigate reliability of truss under different thresholds, parametric reliability evaluations are carried out for these trusses; in order to research the effect of correlation coefficients of random variables on reliability of truss structures, six correlation coefficients are selected.
(3) Sensitivity analysis is an important aspect in reliability evaluation of engineering structures because its results can rank the random variables based on their relative importance. Different Difference Method (DDM) is adopted in the sensitivity analysis. Three numerical examples (e.g., a simple truss, a double-layer cylindrical reticular shell and a plane truss structure) are demonstrated, Four parameters (α,γ,δandη) are taken as importance measures to identify the sensitivities of random variables, their means and standard deviations. Cross-sectional area, Young's modulus, yielding strength, strain hardening rate and loads etc. are taken as random variables in space truss, and reliability and sensitivity are evaluated by FORM. Nodal coordinates are usually treated as invariants in reliability analysis, which will cause significant error in some cases. Thus, the variations of nodal coordinates are considered into reliability and sensitivity analysis of space grid truss structures. For large and complicated structures, much time and effort have to be paid to carry out reliability and sensitivity analysis. Hence, random variable reduction technique is introduced to reduce computation effort, and it facilitates the reliability and sensitivity analysis in space structures.
(4) First-order Reliability Method (FORM) is widely applied for its better efficiency and accuracy, however, it will oscillates around the design point and fails to converge in iteration process when the curvature is too large; large reliability index will impedes to converge. To settle the above issues, Performance Measure Approach (PMA) is firstly introduced into nonlinear FE reliability evaluation in space structures. Compared with Reliability Index Approach (RIA), constraint function can be treated as the problem that searching prescribed minimum performance target point in PMA. To verify the efficiency and robustness of PMA, reliability and sensitivity of four cylindrical reticulated shells with different rise-to-span ratios and four spherical reticulated shells with different rise-to-span ratios are evaluated by RIA and PMA, respectively. Numerical results indicate that PMA has better efficiency and robustness in reliability and sensitivity analysis of space structures.
(5) To identify the influences of different types and parts of random variables on reliability and sensitivity of space structures, four cylindrical reticulated shells with different rise-to-span ratios and four spherical reticulated shells with different rise-to-span ratios are selected. Based on the type and location of random variables, vertical loads, cross-sectional area of members, Young's modulus and yielding strength are treated as one or more random variables, respectively, to identify the sensitivity of these variables; several performance functions are selected to identify the effect of random variables on them and research their correlations; variation rules of sensitivity of all random variables are investigated with the change of rise-to-span ratio; the effect of different probabilistic distribution types of random variables on reliability, sensitivity and correlation is also extensively researched.
(6) Failure process and destruction mechanism of double-layer spherical reticulated shell under statically critical loads and three-dimensional earthquake motion are systematically investigated. Four double-layer spherical latticed domes with different rise-to-span ratios are selected, and deformation capability, number of yielding members, total strain energy, total elastic strain energy, total plastic strain energy, total elastic strain and total plastic strain of reticular domes are elaborately investigated. Failure processes of these domes under statically critical loads and dynamic excitations are captured, furthermore, failure sequence of members is illustrated in detail. Finally, similarities and differences of failure mechanism of four reticulated shells are developed. Numerical results can give some reasonable suggestions and advices for the design of double-layer spherical reticular shell.
引文
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