【作者】 余波；

【导师】 杨绿峰；

【作者基本信息】 广西大学 ， 结构工程， 2011， 博士

【摘要】 结构的极限承载能力和地震延性需求是反映工程结构强度和延性的两个重要指标,也是结构安全性和适用性评估以及结构抗震设计的重要参数。本论文基于极限分析理论和广义屈服准则,研究建立了复杂结构极限承载能力分析的弹性模量缩减法；结合随机有限元、极限分析和点可靠度理论,研究建立了复杂结构体系可靠度分析的影响系数法和随机弹性模量缩减法；对经典的单轴Bouc-Wen模型进行改进,分别建立了单、双向地震激励和平扭耦联作用下非弹性体系非线性地震动力响应分析的新型Bouc-Wen模型,结合69条强震记录定量地分析了p-Δ效应、捏拢效应、强度退化、刚度退化等因素对非弹性体系的地震延性需求和Park-Ang地震损伤指标的概率统计特征的影响,并建立了地震延性需求的经验概率分布模型和预测方程。上述研究成果对于工程结构的安全性、适用性评估以及抗震可靠度分析具有重要的理论意义和工程应用价值。本论文的主要研究工作有：(1)基于极限分析理论和广义屈服准则,定义了单元承载比、承载比均匀度、基准承载比等参数的物理意义和计算表达式,并以单元承载比作为控制参数,结合应变能平衡原理研究建立了复杂结构极限承载能力分析的弹性模量缩减法。算例分析表明,该方法的计算精度高、收敛速度快、且适用于由多种材料和多种单元类型构成的复杂结构的极限承载能力分析。(2)基于常应变法、圆弧法、应变能守恒和应变能平衡等不同原理研究建立了确定弹性模量缩减因子的四种策略,并结合空间桁架、刚架以及板壳结构对四种策略的计算精度和效率进行讨论,发现基于应变能平衡原理的弹性模量缩减法具有较高的计算效率和计算精度,为弹性模量缩减因子的确定提供了明确的物理意义和科学依据。(3)针对极限分析的解析法、数学规划法以及传统弹性模量调整法中“比例加载”这一限定,对所建立的弹性模量缩减法作进一步改进,研究提出了一种适用于非比例加载条件下结构极限承载能力分析的新方法。算例分析表明,该方法的计算精度高、收敛速度快、且适用于恒荷载和活荷载共同作用下的复杂工程结构的极限承载能力分析。(4)考虑P-Δ效应、捏拢效应、强度退化、刚度退化以及应变硬化等因素对非弹性体系地震动力响应的影响,研究建立了单向地震激励作用下非弹性单自由度体系非线性地震动力响应分析的新型单轴Bouc-Wen模型,并结合69条强震记录定量地分析了P-A效应和捏拢效应对非弹性单自由度体系的地震延性需求和Park-Ang地震损伤指标的概率统计特征的影响,进而建立了地震延性需求的经验概率分布模型和预测方程。(5)提出采用规一化位移作为控制参数,以圆形屈服而来描述双向规一化恢复力之间的耦合效应,研究建立了双向地震激励下非弹性体系非线性地震动力响应分析的新型双轴Bouc-Wen模型,结合69条强震记录定量地分析了双向地震激励和P-A效应对地震延性需求和Park-Ang损伤指标的概率统计特征的影响,并建立了地震延性需求和累积滞回耗能的近似公式。(6)提出采用圆形屈服面来描述双向规一化抗侧恢复力之间的耦合效应,采用锥体或球体屈服而来描述双向抗侧恢复力和扭矩之问的耦合效应,研究建立了平而不规则结构非弹性地震动力响应分析的平扭耦联Bouc-Wen模型,结合69条强震记录定量地分析了结构的规一化屈服强度、非耦联平动自振周期、规一化刚度偏心距、非耦联扭转平动频率比、屈服后刚度比等参数对平面不规则结构非弹性平扭耦联效应的概率统计特征的影响。(7)结合极限分析的弹性模量调整策略和点可靠度理论,研究建立了结构体系可靠度分析的影响系数法。该方法利用确定性有限元分析建立外荷载和单元内力之间的关系,以单元可靠指标作为控制参数定义结构的可靠指标均匀度和基准可靠指标,通过系统地调整各单元的弹性模量以模拟结构的可靠指标重分布和失效状态转移,通过一系列线弹性有限元迭代分析确定结构的最终失效模式和体系可靠度。计算结果显示,该方法的计算精度高、收敛速度快,且有效克服了传统体系可靠度分析中失效状态演化过程模拟复杂、主要失效模式难以识别两大难点。(8)结合随机有限元、极限分析和点可靠度理论,研究建立了空间变异结构体系可靠度分析的随机弹性模量缩减法。该方法考虑结构参数和外荷载的空间变异性,利用数值积分法确定随机场局部平均间的协方差矩阵,采用摄动随机有限元法确定结构的随机响应量和各控制单元的可靠指标,进而以单元可靠指标作为控制参数,结合弹性模量调整策略和随机有限元迭代分析模拟结构的可靠指标重分布和失效状态转移,最终确定结构的整体失效模式和体系可靠度。由于该方法避免通过虚拟塑性铰、虚加外荷载来模拟结构的失效演化历程和破坏模式,所以结构的单元刚度矩阵和荷载列阵计算公式始终保持不变,因此具有计算精度高、收敛速度快、且可以有效考虑结构参数和外荷载的空间变异性等特点。更多还原

【Abstract】 Ultimate bearing capacity and seismic ductility demand are two important indices representing strength and ductility performance of engineering structures, which are also key parameters for safety and applicability evaluation as well as structural seismic design. In this study, the Elastic Modulus Reduction Method (EMRM) was proposed to evaluate ultimate bearing capacity of complex structures based on the generalized yield criterion and limit analysis theory. Two novel methods including the Influence Coefficient Method (ICM) and Stochastic Elastic Modulus Reduction Method (SEMRM) were developed for system reliability analysis of large complicated structures based on theories of stochastic finite flement, limit analysis and component reliability. Furthermore, three new Bouc-Wen models for nonlinear seismic dynamic analysis of inelastic systems under unidirectional-, bidirectional-, and lateral-torsional coupling excitations were developed by improving the traditional uniaxial model. The influences of P-△and pinching effects as well as strength and stiffness degradations on probabilistic characteristics of seismic ductility demand and Park-Ang damage index of inelastic system were also quantitatively investigated using 69 earthquake records. The probability distribution type and prediction equation of seismic ductility demand for inelastic system with strength and stiffness degradations as well as P-△and pinching effects were also developed. This study provides significative foundation of theory research and guidance of engineering application in safety and applicability evaluation as well as seismic reliability analysis. The main contents of this thesis are as follows:(1) The element bearing ratio (EBR), degree of uniformity of EBRs, and the reference EBR were defined based on the generalized yield criterion and limit analysis theory. By adopting the EBR as a governing parameter, the Elastic Modulus Reduction Method (EMRM) was developed based on the Strain Energy Equilibrium Principle (SEEP). Numerical examples show that the EMRM is accurate and efficient for limit analysis of complex structures constructed with multi-material and with complicated configuration.(2) Four strategies including the Fixed Strain Method (FSM), the Circular Arc Method (CAM), the Strain Energy Conservation Law (SECL), and the Strain Energy Equilibrium Principle (SEEP) were proposed to determine the elastic modulus reduction factor. The applications and limitations of above four strategies in limit analysis of spatial frame and truss as well as thin plate and shell structures were investigated. Numerical results show that flexibility and accuracy of the SEEP is most satisfied, which provides a rational way to determine the elastic modulus reduction factor.(3) A novel method to calculate ultimate bearing capacity of frame structure under combined action of initial constant and proportional loads was developed by modifying the proposed Elastic Modulus Reduction Method (EMRM), which eliminates the assumption of proportional loading existed in various analytical and mathematical programming methods as well as traditional elastic modulus adjustment procedures for limit analysis. Numerical results show that the method is accurate and efficient to evaluate ultimate bearing capacity of frame structure under both dead and live loads.(4) A new uniaxial Bouc-Wen model for nonlinear seismic dynamic response analysis of inelastic single-degree-of-freedom (SDOF) system under unidirectional ground motion excitation was developed considering P-A effect, pinching effect, strength and stiffness degradations, and strain hardening. The influences of P-A and pinching effects on probabilistic characteristics of seismic ductility demand and Park-Ang seismic damage index of inelastic SDOF system were quantitatively investigated using 69 earthquake records. The probability distribution type and prediction equation of seismic ductility demand for inelastic SDOF system with P-A and pinching effects were also developed.(5) Adopting the normalized displacement as governing parameter, a new biaxial Bouc-Wen model for nonlinear seismic dynamic analysis of inelastic two-degree-of-freedom (2DOF) system under bidirectional ground motion excitations was developed using circular yield surface to describe coupling effect of biaxial normalized restoring forces. The influences of bidirectional excitation and P-A effect on statistical characteristics of seismic ductility demand and Park-Ang seismic damage index of inelastic 2DOF system were discussed using 69 earthquake records. Approximate prediction equations for seismic ductility demand and cumulative dissipated energy of inelastic 2DOF system under bidirectional excitation and with P-△effect were also developed.(6) By adopting the circular yield surface to describe the coupling effect between biaxial normalized lateral restoring forces and the pyramidal or spheriform yield surface to describe the coupling effect of normalized biaxial lateral restoring forces and torsion, a new lateral-torsional coupling Bouc-Wen model for nonlinear seismic dynamic analysis of planar asymmetric structure under bidirectional ground motion excitations was developed. The influences of the normalized yield strength, uncoupled translational frequency ratio, normalized stiffness eccentricity, uncoupled lateral-to-torsional frequency ratio, and post-yield stiffness to initial stiffness ratio on statistical characteristics of seismic ductility demand and Park-Ang seismic damage index of planar asymmetric structure were also investigated using 69 earthquake records.(7) The Influence Coefficient Method (ICM) was proposed to evaluate system reliability of frame structure by combining elastic modulus adjustment procedure and component reliability theory. The relationship between internal forces and external loads was determined by determinate linear elastic finite element analysis and the element reliability index was adopted as governing parameter to define the degree of uniformity of reliability indices and reference reliability index. A new procedure for elastic modulus adjustment was proposed to simulate redistribution of element reliability indices and transition of failure modes. The failure probability of complex structural system can be achieved based on iterative linear elastic finite element analyses. Numerical results show that the ICM is accurate and efficient for system reliability analysis of large complicated structures, and overcomes difficulties for simulation of failure transition and identification of dominant failure modes in traditional methods.(8) The Stochastic Elastic Modulus Reduction Method (SEMRM) for system reliability analysis of spatial variance frame was proposed based on theories of random field, limit analysis and component reliability. The structural parameters and external loads were modeled as random fields to account for their spatial variations and the covariance matrix of local averages of random fields was calculated using the numerical integration method. The stochastic response and reliability index of each element were achieved by the Perturbation Stochastic Finite Element Method (PSFEM). By adopting the element reliability index as governing parameter, a new strategy for elastic modulus adjustment in system reliability analysis was developed. The collapse mechanism and system reliability index of stochastic frame can be determined through iterative stochastic finite element analyses. Comparing with traditional failure mode approaches, the SEMRM is accurate and efficient, which also avoids modification of element stiffness matrix and artificial loading to simulate failure mode transition and accounts for spatial variations of both structural parameters and external loads rationally.更多还原