基于风险的球柱组合壳结构性能分析
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摘要
船舶与海洋工程结构物在建造、运输与安装、运行以及拆除等阶段，都将承受各种各样的突发性、偶然性因素的影响，使得结构系统面临着被破坏的风险。现有的确定性结构设计方法和基于可靠性的结构设计方法，对建造工艺和使用环境诸多等因素考虑并不十分完善，因此需要研究基于风险的结构性能分析。对作为单壳体潜艇耐压船体的球柱组合壳结构，由于具有超长舱和大分舱的特点，球壳和柱壳之间的相互作用影响了组合壳的结构性能规律。因此本文在球柱组合壳结构的力学性能、系统可靠性及优化、基于风险的结构设计三个方面，采用理论分析与模型试验相结合的方法开展了研究，主要内容如下：
（1）考虑组合壳连接处的变形协调条件，建立了球柱组合壳结构的力学模型，通过解析方法分析了结构参数的变化对组合壳强度的影响，阐明了组合壳结构的性能规律。并采用简化边界模型分析了组合壳结构的边缘效应问题。对于球柱组合壳结构的稳定性，忽略连接处的转角协调，构建了满足位移协调的组合壳结构位移函数，将球柱组合壳结构的总势能分为外力功、薄膜应变能和弯曲应变能，推导了球柱组合壳结构整体稳定性的计算公式。
（2）为了验证球柱组合壳结构理论分析的结果，设计了不同参数的3个球柱组合壳结构模型。进行静水压力试验，通过实测应变分析了模型在试验载荷下的应力分布规律以及结构参数的影响，并与理论分析的结果进行比较，验证了结构参数对边缘效应的影响规律。
（3）通过分析球柱组合壳结构的不确定因素，确定了失效模式、结构参数随机变量分布和统计特征，建立了失效模式的可靠性模型。通过二维联合概率密度函数，推导了两个相关失效模式的联合失效概率计算公式，进而给出考虑失效模式相关性的球柱组合壳串联结构系统失效的全概率公式，并采用蒙特卡罗模拟验证了系统可靠度计算的正确性。采用多岛遗传算法对组合结构进行了基于可靠性的优化设计。
（4）通过分析耐压结构计算载荷的安全系数问题，首次提出了下潜超深风险的概念。综合考虑社会、环境、个人、经济对下潜超深风险的要求，制定了“成本—效益”的结构设计准则。通过极值分布函数计算了下潜超深风险的发生概率，对不同的下潜超深选取99%的可靠度进行了球柱组合壳的可靠性优化设计，给出了每种方案的安全成本（结构重量）。依据结构的设计准则结合分析安全成本与发生概率，做出适当的结构设计决策并构建了一个基于风险的结构设计基本框架。
Ship and ocean engineering structures suffer from a variety of sudden and accidentalfactors in the stage of construction, transportation, installation, operation and demolition,which makes the structure system face the risk of damage. Due to comprehensivelyconsideration on structural safety, it is needed to study on the risk-based structuralperformance analysis. As the pressure hull structure of mono-shell submarine, sphere-cylindercombined shells have the characteristics of super-long cabin and large subdivision. Theinteractions between cylindrical shell and spherical shell will influence the structureperformance of combined shell.
Aiming at the above problems and using a combination of theoretical analysis andmodel test, this paper has carried out some researches, which include three aspects: thestructural mechanical performance of combined shell, structural system reliability, andrisk-based structure design. The main contents are as follows:
(1) Considering the deformation coordination conditions at the joint of combined shell,structural mechanics model of sphere-cylinder combined shell is established. The influence ofstructural parameters to sphere-cylinder combined shell strength is analyzed. The law ofcombined shell structure performance is summarized. The edge effect is analyzed usingsimplified boundary model. For the structural stability of sphere-cylinder combined shell, thestructure displacement function which meeting the displacement coordination is established.The stability calculation formula of sphere-cylinder combined shell is deduced, while the totalpotential energy is divided into external work, thin film strain energy and bending strainenergy.
(2) In order to validate the theory analysis results, three test models which have differentparameters were designed. The rule of stress distribution and the effects of structureparameters are analyzed by the measured strain of models. The edge effects of sphere-cylindercombined shells are verified through comparing with the results of theory analysis and modeltest.
(3) The failure mode and distribution and statistics characteristic of random variable ofsphere-cylinder combined shells are determined through the analysis of uncertainty factors, and the reliability models are established. Joint failure probability calculation formula of tworelated failure modes is derived through2d joint probability density function and the fullprobability formula of tandem structure system of sphere-cylinder combined shells whichconsidering the correlation among failure modes is given. And then the correctness of systemreliability calculation is verified through Monte Carlo simulation. The reliability-basedoptimization design is carried out through multi-island genetic algorithm.
(4) The concept of risk beyond the submerged depth is firstly put forward. The“cost-benefit” criteria of structure design is formulated through overall considering therequirements of society, environment, person and economy to risk beyond the submergeddepth. Through the extreme distribution function, the probability of risk beyond thesubmerged depth is described. Selecting the reliability of99%, the sphere-cylinder combinedshells are designed based on the reliability optimization under different submerged depth andthe structure security costs (structure weight) of each scheme are given. According to theprinciples of structure design, safety cost and occurrence probability of risk, the properdecisions is made. Finally, a framework of risk-based structure design is constructed.
（1）考虑组合壳连接处的变形协调条件，建立了球柱组合壳结构的力学模型，通过解析方法分析了结构参数的变化对组合壳强度的影响，阐明了组合壳结构的性能规律。并采用简化边界模型分析了组合壳结构的边缘效应问题。对于球柱组合壳结构的稳定性，忽略连接处的转角协调，构建了满足位移协调的组合壳结构位移函数，将球柱组合壳结构的总势能分为外力功、薄膜应变能和弯曲应变能，推导了球柱组合壳结构整体稳定性的计算公式。
（2）为了验证球柱组合壳结构理论分析的结果，设计了不同参数的3个球柱组合壳结构模型。进行静水压力试验，通过实测应变分析了模型在试验载荷下的应力分布规律以及结构参数的影响，并与理论分析的结果进行比较，验证了结构参数对边缘效应的影响规律。
（3）通过分析球柱组合壳结构的不确定因素，确定了失效模式、结构参数随机变量分布和统计特征，建立了失效模式的可靠性模型。通过二维联合概率密度函数，推导了两个相关失效模式的联合失效概率计算公式，进而给出考虑失效模式相关性的球柱组合壳串联结构系统失效的全概率公式，并采用蒙特卡罗模拟验证了系统可靠度计算的正确性。采用多岛遗传算法对组合结构进行了基于可靠性的优化设计。
（4）通过分析耐压结构计算载荷的安全系数问题，首次提出了下潜超深风险的概念。综合考虑社会、环境、个人、经济对下潜超深风险的要求，制定了“成本—效益”的结构设计准则。通过极值分布函数计算了下潜超深风险的发生概率，对不同的下潜超深选取99%的可靠度进行了球柱组合壳的可靠性优化设计，给出了每种方案的安全成本（结构重量）。依据结构的设计准则结合分析安全成本与发生概率，做出适当的结构设计决策并构建了一个基于风险的结构设计基本框架。
Ship and ocean engineering structures suffer from a variety of sudden and accidentalfactors in the stage of construction, transportation, installation, operation and demolition,which makes the structure system face the risk of damage. Due to comprehensivelyconsideration on structural safety, it is needed to study on the risk-based structuralperformance analysis. As the pressure hull structure of mono-shell submarine, sphere-cylindercombined shells have the characteristics of super-long cabin and large subdivision. Theinteractions between cylindrical shell and spherical shell will influence the structureperformance of combined shell.
Aiming at the above problems and using a combination of theoretical analysis andmodel test, this paper has carried out some researches, which include three aspects: thestructural mechanical performance of combined shell, structural system reliability, andrisk-based structure design. The main contents are as follows:
(1) Considering the deformation coordination conditions at the joint of combined shell,structural mechanics model of sphere-cylinder combined shell is established. The influence ofstructural parameters to sphere-cylinder combined shell strength is analyzed. The law ofcombined shell structure performance is summarized. The edge effect is analyzed usingsimplified boundary model. For the structural stability of sphere-cylinder combined shell, thestructure displacement function which meeting the displacement coordination is established.The stability calculation formula of sphere-cylinder combined shell is deduced, while the totalpotential energy is divided into external work, thin film strain energy and bending strainenergy.
(2) In order to validate the theory analysis results, three test models which have differentparameters were designed. The rule of stress distribution and the effects of structureparameters are analyzed by the measured strain of models. The edge effects of sphere-cylindercombined shells are verified through comparing with the results of theory analysis and modeltest.
(3) The failure mode and distribution and statistics characteristic of random variable ofsphere-cylinder combined shells are determined through the analysis of uncertainty factors, and the reliability models are established. Joint failure probability calculation formula of tworelated failure modes is derived through2d joint probability density function and the fullprobability formula of tandem structure system of sphere-cylinder combined shells whichconsidering the correlation among failure modes is given. And then the correctness of systemreliability calculation is verified through Monte Carlo simulation. The reliability-basedoptimization design is carried out through multi-island genetic algorithm.
(4) The concept of risk beyond the submerged depth is firstly put forward. The“cost-benefit” criteria of structure design is formulated through overall considering therequirements of society, environment, person and economy to risk beyond the submergeddepth. Through the extreme distribution function, the probability of risk beyond thesubmerged depth is described. Selecting the reliability of99%, the sphere-cylinder combinedshells are designed based on the reliability optimization under different submerged depth andthe structure security costs (structure weight) of each scheme are given. According to theprinciples of structure design, safety cost and occurrence probability of risk, the properdecisions is made. Finally, a framework of risk-based structure design is constructed.
引文
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