可靠性算法与超空泡航行体结构屈曲可靠性研究
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摘要
目前对水下超空泡航行体的结构问题研究较少,对其结构进行可靠性分析的研究则更少。与传统速度较低的水下航行体主要受全面静水压力有所不同,高速运行下的超空泡航行体所受前端空化器阻力与尾部发动机推力都非常大,而要满足流体动力学要求和完全被空泡包裹,航行体结构一般设计成细长体,因而在非常大的轴向压力与环向压力(在一定深度下航行时由通气超空泡内压力产生)作用下会发生屈曲问题,若考虑到超空泡流动参数和结构参数的不确定性,有必要对超空泡航行体结构进行可靠性分析。文中对超空泡航行体结构进行了屈曲的概率与非概率可靠性分析,主要研究内容如下：
1、讨论了改进的一次二阶矩法迭代不收敛问题,并针对有限步长迭代法存在的不足,引入黄金分割法对步长进行一维搜索,构造了一个评价函数,提出了改进的有限步长迭代法,并与另一修正迭代算法的迭代结果比较显示其具有较好的迭代收敛性。
2、针对结构强度集合与应力集合发生干涉与不发生干涉两种情况下,超椭球凸集合可靠性指标功能函数比值定义与体积比值定义两种指标各自存在的不足,将两指标相结合提出超椭球凸集合可靠性综合指标的概念,并提出采用改进的有限步长迭代法与Monte-Carlo法相结合计算超椭球凸集合可靠性综合指标。针对多维非线性安全余量方程体积比值定义的指标难于计算的问题,引入Monte-Carlo法计算超椭球凸集合可靠度,并通过算例验证了其计算的正确性、可行性与简便性。
3、与超椭球凸集合类似,同样提出了非概率区间可靠性综合指标的概念,并提出采用改进的混沌优化算法与Monte-Carlo法相结合计算非概率区间可靠性综合指标。基于Skew-Tent映射给出了四个改进的混沌优化算法ST-Geczb、ST-Powell、BST-Geczb及BST-Powell,并与相应文献的搜索结果比较显示ST-Powell与BST-Powell的全局寻优率较好。比较了区间集合,及由其确定的内外接超椭球凸集合这三种不确定信息描述形式下非概率区间(超椭球凸集合)可靠性综合指标的大小及变化趋势。
4、采用伽辽金法计算超空泡射弹变截面梁的临界屈曲载荷,推导了结构屈曲安全余量隐式方程对各随机变量的偏导矩阵,结合有限步长迭代法给出射弹变截面梁的屈曲概率可靠性指标的求解算法。将BST-Geczb混沌优化方法与Monte-Carlo法相结合,给出射弹结构屈曲非概率区间可靠性综合指标的计算方法。并结合工程算例分析了射弹底部直径与空化器直径之比与发射初速的均值对结构屈曲概率可靠性指标、非概率区间可靠性综合指标的影响,并给出了屈曲安全余量的上下界与非概率区间可靠性综合指标随各区间变量不确定程度的变化曲线。
5、采用半解析有限元求解环肋圆柱薄壳舱段的临界屈曲载荷,给出了屈曲安全余量隐式方程对各随机变量的敏度表达式,并将随机有限元与有限步长迭代法相结合给出环肋圆柱薄壳舱段的屈曲概率可靠性指标的求解算法。当前屈曲应力由半解析有限元得出时,推导了单元几何刚阵对各不确定变量的偏导矩阵,并对环肋圆柱薄壳舱段的屈曲载荷区间进行了分析。将BST-Geczb混沌优化方法与Monte-Carlo法相结合,给出环肋圆柱薄壳舱段屈曲非概率区间可靠性综合指标的计算方法。结合工程算例对自然超空泡鱼雷圆柱薄壳舱段进行了结构屈曲概率可靠性分析,并对通气超空泡鱼雷环肋圆柱薄壳舱段进行了屈曲概率与非概率可靠性分析。
The researches are less on structure problems of supercavitating vehicles, especially the researches about structural reliability analysis of supercavitating vechiles are few. Compared to traditional underwater vehicles which mainly suffer around hydrostatic pressure due to low velocity, it is different that super- cavitating vechiles which suffer high cavitator drag and engine thrust due to high velocity. To satisfy hydrodynamics requirements and be entirely enveloped by supercavity, generally it has to be designed as slender configuration. However, the high longitudinal force and circumferential pressure caused by ventilated cavity when operation depth is large, may cause structure buckling of supercavitating vehicles. When the uncertainty of supercavitating flow and structural own parameters is considered, it is necessary to perform structural reliability analysis of supercavitating vehicle. Structural buckling probability and non-probability reliability analysis of supercavitating vehicle is performed in this paper and the main contents are as follows:
1. Iterative non-convergence problem of modified first-order second- moment method is discussed. To promote the robustness of limit step iteration method, golden section method and a new merit function are introduced into limit step iteration method for one-dimension step search and modified limit step iteration method is presented. Compared to the iterative results of another modified iteration method, modified limit step iteration method shows better convergence.
2. In view of the insufficiency of both performance function ratio index and volume ratio index of super-ellipsoid convex sets under two conditions that stress sets and strength sets interfere or don't interfere with each other, super-ellipsoid convex sets reliability comprehensive index is presented by combining two above ratio definition index. Super-ellipsoid convex sets reliability comprehensive index is calculated by combined method of modified limit step iteration method and Monte-Carlo method. In view of difficulty to calculate the volume ratio definition index when limit state equation is multi-dimensional nonlinear equation, Monte-Carlo method is introduced to calculate super-ellipsoid convex sets reliability degree. The validity, feasibility and simpleness of calculation by Monte-Carlo method are proved by numerical example.
3. As same as super-ellipsoid convex sets, non-probabilistic interval reliability comprehensive index is also presented and it is calculated by combined method of modified chaotic optimization method and Monte-Carlo method. Based on Skew-Tent mapping formula, four modified chaotic optimization methods such as ST-Geczb, ST-Powell, BST-Geczb and BST-Powell are presented. Compared to the search results of relative literature, modified chaotic optimization methods such as ST-Powell and BST-Powell show better global search optimization rate. The values and variety trends of non-probabilistic interval and super-ellipsoid convex sets reliability comprehensive index are compared under three uncertainty information described types such as interval sets, internal and external connect super-ellipsoid convex sets which are determined by interval sets.
4. Critical buckling load of supercavitating projectile, which is simplified as variable cross-section beam, is calculated by Galerkin method. The partial matrixs of buckling safety margin implicit equation to each random variables are deduced, and structural buckling probabilistic reliability index of variable cross-section beam is calculated by combining with limit step iteration method. Structural buckling non-probabilistic interval reliability comprehensive index of super- cavitating projectile is calculated by combined method of modified chaotic optimization method BST-Geczb and Monte-Carlo method. Through the analysis of engineering numeric results, it is presented that the influence of the ratio which is defined as base diameter to the cavitation diameter and the mean value of initial launch velocity to buckling probabilistic reliability index and non-probabilistic interval reliability comprehensive index. Also it is presented that variation curves of the lower and upper bounds of buckling safety margin and non-probabilistic interval reliability comprehensive index with the variation of uncertainty degree of each interval variables.
5. Critical buckling load of thin cylindrical shell compartment with stiffened rings is calculated by semi-analytical finite element method. The sensitivity expressions of buckling safety margin implicit equation to each random variables are presented, and structural buckling probabilistic reliability index of thin cylindrical shell compartment with stiffened rings is calculated by hybrid method of stochastic finite element and limit step length iteration method. The partial matrixs of element geometric matrix to each uncertainty variables are deduced when pre-buckling stress is calculated by semi-analytical finite element method, and the buckling load interval of thin cylindrical shell compartment with stiffened rings is analysed. Structural buckling non-probabilistic interval reliability comprehensive index of thin cylindrical shell with stiffened rings is calculated by combined method of modified chaotic optimization method BST-Geczb and Monte-Carlo method. Through the engineering numeric examples, it is analysed that structural buckling probabilistic reliability of thin cylindrical shell compartment of natural supercavitating torpedo, and structural buckling probabilistic and non-probabilistic reliability of thin cylindrical shell compartment with stiffened rings of ventilated supercavitating torpedo.
1、讨论了改进的一次二阶矩法迭代不收敛问题,并针对有限步长迭代法存在的不足,引入黄金分割法对步长进行一维搜索,构造了一个评价函数,提出了改进的有限步长迭代法,并与另一修正迭代算法的迭代结果比较显示其具有较好的迭代收敛性。
2、针对结构强度集合与应力集合发生干涉与不发生干涉两种情况下,超椭球凸集合可靠性指标功能函数比值定义与体积比值定义两种指标各自存在的不足,将两指标相结合提出超椭球凸集合可靠性综合指标的概念,并提出采用改进的有限步长迭代法与Monte-Carlo法相结合计算超椭球凸集合可靠性综合指标。针对多维非线性安全余量方程体积比值定义的指标难于计算的问题,引入Monte-Carlo法计算超椭球凸集合可靠度,并通过算例验证了其计算的正确性、可行性与简便性。
3、与超椭球凸集合类似,同样提出了非概率区间可靠性综合指标的概念,并提出采用改进的混沌优化算法与Monte-Carlo法相结合计算非概率区间可靠性综合指标。基于Skew-Tent映射给出了四个改进的混沌优化算法ST-Geczb、ST-Powell、BST-Geczb及BST-Powell,并与相应文献的搜索结果比较显示ST-Powell与BST-Powell的全局寻优率较好。比较了区间集合,及由其确定的内外接超椭球凸集合这三种不确定信息描述形式下非概率区间(超椭球凸集合)可靠性综合指标的大小及变化趋势。
4、采用伽辽金法计算超空泡射弹变截面梁的临界屈曲载荷,推导了结构屈曲安全余量隐式方程对各随机变量的偏导矩阵,结合有限步长迭代法给出射弹变截面梁的屈曲概率可靠性指标的求解算法。将BST-Geczb混沌优化方法与Monte-Carlo法相结合,给出射弹结构屈曲非概率区间可靠性综合指标的计算方法。并结合工程算例分析了射弹底部直径与空化器直径之比与发射初速的均值对结构屈曲概率可靠性指标、非概率区间可靠性综合指标的影响,并给出了屈曲安全余量的上下界与非概率区间可靠性综合指标随各区间变量不确定程度的变化曲线。
5、采用半解析有限元求解环肋圆柱薄壳舱段的临界屈曲载荷,给出了屈曲安全余量隐式方程对各随机变量的敏度表达式,并将随机有限元与有限步长迭代法相结合给出环肋圆柱薄壳舱段的屈曲概率可靠性指标的求解算法。当前屈曲应力由半解析有限元得出时,推导了单元几何刚阵对各不确定变量的偏导矩阵,并对环肋圆柱薄壳舱段的屈曲载荷区间进行了分析。将BST-Geczb混沌优化方法与Monte-Carlo法相结合,给出环肋圆柱薄壳舱段屈曲非概率区间可靠性综合指标的计算方法。结合工程算例对自然超空泡鱼雷圆柱薄壳舱段进行了结构屈曲概率可靠性分析,并对通气超空泡鱼雷环肋圆柱薄壳舱段进行了屈曲概率与非概率可靠性分析。
The researches are less on structure problems of supercavitating vehicles, especially the researches about structural reliability analysis of supercavitating vechiles are few. Compared to traditional underwater vehicles which mainly suffer around hydrostatic pressure due to low velocity, it is different that super- cavitating vechiles which suffer high cavitator drag and engine thrust due to high velocity. To satisfy hydrodynamics requirements and be entirely enveloped by supercavity, generally it has to be designed as slender configuration. However, the high longitudinal force and circumferential pressure caused by ventilated cavity when operation depth is large, may cause structure buckling of supercavitating vehicles. When the uncertainty of supercavitating flow and structural own parameters is considered, it is necessary to perform structural reliability analysis of supercavitating vehicle. Structural buckling probability and non-probability reliability analysis of supercavitating vehicle is performed in this paper and the main contents are as follows:
1. Iterative non-convergence problem of modified first-order second- moment method is discussed. To promote the robustness of limit step iteration method, golden section method and a new merit function are introduced into limit step iteration method for one-dimension step search and modified limit step iteration method is presented. Compared to the iterative results of another modified iteration method, modified limit step iteration method shows better convergence.
2. In view of the insufficiency of both performance function ratio index and volume ratio index of super-ellipsoid convex sets under two conditions that stress sets and strength sets interfere or don't interfere with each other, super-ellipsoid convex sets reliability comprehensive index is presented by combining two above ratio definition index. Super-ellipsoid convex sets reliability comprehensive index is calculated by combined method of modified limit step iteration method and Monte-Carlo method. In view of difficulty to calculate the volume ratio definition index when limit state equation is multi-dimensional nonlinear equation, Monte-Carlo method is introduced to calculate super-ellipsoid convex sets reliability degree. The validity, feasibility and simpleness of calculation by Monte-Carlo method are proved by numerical example.
3. As same as super-ellipsoid convex sets, non-probabilistic interval reliability comprehensive index is also presented and it is calculated by combined method of modified chaotic optimization method and Monte-Carlo method. Based on Skew-Tent mapping formula, four modified chaotic optimization methods such as ST-Geczb, ST-Powell, BST-Geczb and BST-Powell are presented. Compared to the search results of relative literature, modified chaotic optimization methods such as ST-Powell and BST-Powell show better global search optimization rate. The values and variety trends of non-probabilistic interval and super-ellipsoid convex sets reliability comprehensive index are compared under three uncertainty information described types such as interval sets, internal and external connect super-ellipsoid convex sets which are determined by interval sets.
4. Critical buckling load of supercavitating projectile, which is simplified as variable cross-section beam, is calculated by Galerkin method. The partial matrixs of buckling safety margin implicit equation to each random variables are deduced, and structural buckling probabilistic reliability index of variable cross-section beam is calculated by combining with limit step iteration method. Structural buckling non-probabilistic interval reliability comprehensive index of super- cavitating projectile is calculated by combined method of modified chaotic optimization method BST-Geczb and Monte-Carlo method. Through the analysis of engineering numeric results, it is presented that the influence of the ratio which is defined as base diameter to the cavitation diameter and the mean value of initial launch velocity to buckling probabilistic reliability index and non-probabilistic interval reliability comprehensive index. Also it is presented that variation curves of the lower and upper bounds of buckling safety margin and non-probabilistic interval reliability comprehensive index with the variation of uncertainty degree of each interval variables.
5. Critical buckling load of thin cylindrical shell compartment with stiffened rings is calculated by semi-analytical finite element method. The sensitivity expressions of buckling safety margin implicit equation to each random variables are presented, and structural buckling probabilistic reliability index of thin cylindrical shell compartment with stiffened rings is calculated by hybrid method of stochastic finite element and limit step length iteration method. The partial matrixs of element geometric matrix to each uncertainty variables are deduced when pre-buckling stress is calculated by semi-analytical finite element method, and the buckling load interval of thin cylindrical shell compartment with stiffened rings is analysed. Structural buckling non-probabilistic interval reliability comprehensive index of thin cylindrical shell with stiffened rings is calculated by combined method of modified chaotic optimization method BST-Geczb and Monte-Carlo method. Through the engineering numeric examples, it is analysed that structural buckling probabilistic reliability of thin cylindrical shell compartment of natural supercavitating torpedo, and structural buckling probabilistic and non-probabilistic reliability of thin cylindrical shell compartment with stiffened rings of ventilated supercavitating torpedo.
引文
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