环肋圆环壳强度与变形分析
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摘要
水下运载器可在深海探测、水下试验研究、水下作业与控制、水下综合保障等方面发挥重大的作用。运载器的结构是关系到运载器能否承受深海高压及保证运载器总体性能的首要关键技术。鉴于传统圆柱形耐压壳的诸多缺点以及圆环壳在工程中的广泛应用,开展作为主体结构的圆环壳的结构特性研究具有重大的工程意义。
圆环壳运用于水下工程时需要设置一系列环形肋骨以提高壳体的稳定性。尽管肋骨提高了壳体的稳定性,但有时对壳体强度是不利的,因此环肋圆环壳的强度问题亟待解决。但是目前对圆环壳的研究多集中在不含加强肋骨型材的纯圆环壳,对环肋圆环壳研究较少。本论文首次开展环肋圆环壳与环肋圆柱壳结构强度性能的比较分析工作,从理论上和数值方法上分别进行变参数下的结构特性分析,论文的研究工作主要包含以下几个方面:
(1)运用弹性薄壳理论,对静水压力作用下圆环壳的变形及应力特性进行了参数化研究。研究了主应力随位置参数φ及相对弯曲半径R a的变化规律,从而揭示了圆环壳即使在薄膜受力状态下也存在着弯矩的结构特性及理论求解的难点所在。
(2)考虑肋骨型材对壳体弯曲变形的影响,根据静水压力作用下环肋圆环壳载荷及结构对称性的特点,首次提出了环肋圆环壳的一种简化力学模型,即将环肋圆环壳在均布压力作用下的变形简化为两端刚性固定在弹性支座上的弹性基础曲梁的复杂弯曲来研究。
(3)首次基于弹性曲梁和薄壳理论,运用简化等效原则求解了环肋圆环壳结构关键截面处应力与变形的理论表达式,从而给出了一种静水压力作用下环肋圆环壳强度与变形的分析计算方法。
(4)本文通过运用有限元求解方法验证了环肋圆环壳的简化理论解,比较结果表明本文所给理论解与有限元数值解结果一致,符合工程误差精度要求,从而验证了简化理论解的正确性及其求解的合理性。
(5)运用本文给出的理论解,首次对环肋圆环壳及其等效环肋圆柱壳的结构强度特征参数进行了比较分析,并给出了环肋圆环壳典型关键点位置上的应力随其结构参数的变化规律。
Underwater vehicles can play an important role in the areas such as deep-sea exploration, underwater experimental study, underwater operation and control, underwater comprehensive supply, etc. The hull of an underwater vehicle is the all-important and decisive technology that relates to the capability to resist deep-sea water pressure and the overall performance. In view of the disadvantages of the cylindrical pressure hulls and the widespread application of the circular toroidal shell structures in engineering, it is of great engineering significance to research on the structural characteristics of the circular toroidal shells that act as major structures.
Used in underwater engineering, a series of annular ribs need to be set to enhance the stability of the circular toroidal shell structures. While advantageous to the stability, the ribs may be disadvantageous to the strength of the circular toroidal shell structures sometimes. Therefore the strength of the rib-stiffened circular toroidal shell structures is a problem urgently waiting to be solved. But at present most of researchers are focusing on the circular toroidal shells without ribs, while few of them are turning to the rib-stiffened circular toroidal shells. In this thesis, contrastive analysis of the structural strength performance between the rib-stiffened circular toroidal shells and the rib-stiffened circular cylindrical shells are carried out and and the variation attribute of the structural characteristics of the rib-stiffened circular toroidal shells with the structural parameters is analyzed by theoretical and numerical methods respectively. The research contents of this thesis are as following:
(1) The deformation and the stress characteristics of the circular toroidal shells are analyzed by the theory of elastic thin shells. The variation law of the principal stress with the location parametersφand the relative bending radius R a is studied, and thus the difficulties in solving theoretically and the structural characteristic are revealed that moments exist even though the circular toroidal shells are at membrane stress condition.
(2) In accordance with the characteristic that the load and the deformation of the rib-stiffened circular toroidal shells is symmetrical in the cross-section where rib exists under hydrostatic pressure, a simplified mechanical model is firstly developed in this thesis, which considers the influence of ribs on the bending of the shells. In this model, the deformation of the rib-stiffened circular toroidal shells can be simplified to the complex bending of the elastic foundation curved beams, both ends of which are clamped rigidly on the elastic supports.
(3) Based on the theory of elastic curved beams and thin shells, the theoretical expression of the displacement and the stress in the key sections of the rib-stiffened circular toroidal shells is firstly deduced, applied the principle of simplification and equivalent. Consequently, the analytical and calculation method on the strength and the deformation of the rib-stiffened circular toroidal shells is presented here.
(4) The finite element method (FEM) is used to confirm the theoretical solution of the rib-stiffened circular toroidal shells proposed in this thesis. Comparative results of the two methods show good agreement and meet the accuracy requirement in engineering, which demonstrate the correctness of the theoretical solution and the rationality of the theoretical method.
(5) Contrastive analysis of the characteristic parameters of the structural strength is carried out for the first time between the rib-stiffened circular toroidal shells and its equivalent rib-stiffened circular cylindrical shells using the theoretical solution proposed in this thesis and the variation attribute of the stress at the typical locations in the rib-stiffened circular toroidal shells with the structural parameters is investigated.
圆环壳运用于水下工程时需要设置一系列环形肋骨以提高壳体的稳定性。尽管肋骨提高了壳体的稳定性,但有时对壳体强度是不利的,因此环肋圆环壳的强度问题亟待解决。但是目前对圆环壳的研究多集中在不含加强肋骨型材的纯圆环壳,对环肋圆环壳研究较少。本论文首次开展环肋圆环壳与环肋圆柱壳结构强度性能的比较分析工作,从理论上和数值方法上分别进行变参数下的结构特性分析,论文的研究工作主要包含以下几个方面:
(1)运用弹性薄壳理论,对静水压力作用下圆环壳的变形及应力特性进行了参数化研究。研究了主应力随位置参数φ及相对弯曲半径R a的变化规律,从而揭示了圆环壳即使在薄膜受力状态下也存在着弯矩的结构特性及理论求解的难点所在。
(2)考虑肋骨型材对壳体弯曲变形的影响,根据静水压力作用下环肋圆环壳载荷及结构对称性的特点,首次提出了环肋圆环壳的一种简化力学模型,即将环肋圆环壳在均布压力作用下的变形简化为两端刚性固定在弹性支座上的弹性基础曲梁的复杂弯曲来研究。
(3)首次基于弹性曲梁和薄壳理论,运用简化等效原则求解了环肋圆环壳结构关键截面处应力与变形的理论表达式,从而给出了一种静水压力作用下环肋圆环壳强度与变形的分析计算方法。
(4)本文通过运用有限元求解方法验证了环肋圆环壳的简化理论解,比较结果表明本文所给理论解与有限元数值解结果一致,符合工程误差精度要求,从而验证了简化理论解的正确性及其求解的合理性。
(5)运用本文给出的理论解,首次对环肋圆环壳及其等效环肋圆柱壳的结构强度特征参数进行了比较分析,并给出了环肋圆环壳典型关键点位置上的应力随其结构参数的变化规律。
Underwater vehicles can play an important role in the areas such as deep-sea exploration, underwater experimental study, underwater operation and control, underwater comprehensive supply, etc. The hull of an underwater vehicle is the all-important and decisive technology that relates to the capability to resist deep-sea water pressure and the overall performance. In view of the disadvantages of the cylindrical pressure hulls and the widespread application of the circular toroidal shell structures in engineering, it is of great engineering significance to research on the structural characteristics of the circular toroidal shells that act as major structures.
Used in underwater engineering, a series of annular ribs need to be set to enhance the stability of the circular toroidal shell structures. While advantageous to the stability, the ribs may be disadvantageous to the strength of the circular toroidal shell structures sometimes. Therefore the strength of the rib-stiffened circular toroidal shell structures is a problem urgently waiting to be solved. But at present most of researchers are focusing on the circular toroidal shells without ribs, while few of them are turning to the rib-stiffened circular toroidal shells. In this thesis, contrastive analysis of the structural strength performance between the rib-stiffened circular toroidal shells and the rib-stiffened circular cylindrical shells are carried out and and the variation attribute of the structural characteristics of the rib-stiffened circular toroidal shells with the structural parameters is analyzed by theoretical and numerical methods respectively. The research contents of this thesis are as following:
(1) The deformation and the stress characteristics of the circular toroidal shells are analyzed by the theory of elastic thin shells. The variation law of the principal stress with the location parametersφand the relative bending radius R a is studied, and thus the difficulties in solving theoretically and the structural characteristic are revealed that moments exist even though the circular toroidal shells are at membrane stress condition.
(2) In accordance with the characteristic that the load and the deformation of the rib-stiffened circular toroidal shells is symmetrical in the cross-section where rib exists under hydrostatic pressure, a simplified mechanical model is firstly developed in this thesis, which considers the influence of ribs on the bending of the shells. In this model, the deformation of the rib-stiffened circular toroidal shells can be simplified to the complex bending of the elastic foundation curved beams, both ends of which are clamped rigidly on the elastic supports.
(3) Based on the theory of elastic curved beams and thin shells, the theoretical expression of the displacement and the stress in the key sections of the rib-stiffened circular toroidal shells is firstly deduced, applied the principle of simplification and equivalent. Consequently, the analytical and calculation method on the strength and the deformation of the rib-stiffened circular toroidal shells is presented here.
(4) The finite element method (FEM) is used to confirm the theoretical solution of the rib-stiffened circular toroidal shells proposed in this thesis. Comparative results of the two methods show good agreement and meet the accuracy requirement in engineering, which demonstrate the correctness of the theoretical solution and the rationality of the theoretical method.
(5) Contrastive analysis of the characteristic parameters of the structural strength is carried out for the first time between the rib-stiffened circular toroidal shells and its equivalent rib-stiffened circular cylindrical shells using the theoretical solution proposed in this thesis and the variation attribute of the stress at the typical locations in the rib-stiffened circular toroidal shells with the structural parameters is investigated.
引文
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[2]谢祚水,王自立,吴剑国.潜艇结构分析[M].武汉:华中科技大学出版社, 2004.
[3] ROSS C T F. A conceptual design of an underwater missile launcher[J]. Ocean engineering, 2005, (32): 85-99.
[4] ROSS C T F. A conceptual design of an underwater vehicle[J]. Ocean Engineering, 2006, (3): 2087-2104.
[5]张维,任文敏,孙博华.环壳的研究现状及趋势[A].第五届空间结构学术交流会论文集[C].兰州:兰州大学出版社, 1990: 1-5.
[6]赵鸿宾,吴振辉,沈祖培.圆环壳在承受轴对称载荷时的复变量方程和渐近解[J].清华大学学报, 1981, 21(2): 54-59.
[7] T?LKE. Ingenieur Archiev, 1938, 282(9): 21-25.
[8] CLARK R A. On the Theory of Thin-Walled Toroidal Shells[J]. Math and Physics, 1950 (29): 146-178.
[9]诺沃日洛夫.北京石油学院材料力学教研组译.薄壳理论[M].北京:科学出版社, 1959.
[10]钱伟长.应用数学与力学论文集[C].南京:江苏科学技术出版社,1980:78-85.
[11] WISSLER H. Festigkeitberechung Von Ringschalen, Promationarbeit, Zurich, 1916.
[12] ZHANG WEI. Der spannungszustand in kreisringschaleund ahnlichen Schalen mit Scheitelkreisringen unterdrehsymmetrischer Beelastung. Berlin: Arbeit zur Erlangung des Grades eines Doctor-Ingenieurs der Technichen Hochschule, 1944.
[13]钱伟长,郑思梁.轴对称圆环壳的一般解[J].应用数学和力学, 1980, 1(3): 287-299.
[14]钱伟长,郑思梁.轴对称圆环壳的复变量方程和轴对称环壳的一般解[J].清华大学学报, 1979, 19(1): 27-47.
[15]吴振辉,赵鸿宾,沈祖培.轴对称圆环壳复变量方程的逼近——渐近解法[J].力学学报, 1986, 18(2): 32-36.
[16]赵鸿宾,沈祖培,吴振辉.计算结构力学有及其应用[M].北京:科学出版社, 1981.
[17]董明德. Novozhilov环壳方程的新解[J].应用数学与力学, 1985, 6(5): 48-57.
[18]王慎行,关于轴对称薄圆环壳方程级数解的收敛性[J].力学学报, 1985, 17(3):287-292.
[19]王慎行.轴对称薄圆环壳方程级数解收敛性的研究[J].力学学报, 1988, 20(6): 563-569.
[20] TUMARKIN S A. Asymptotic solutions of a linear non-homogeneous second order differential equation with a transition point and its application to the computation of toroidal shells and proreller blades [J]. Appl Math Mech, 1959, 23: 1549-1565.
[21] NOVOZHILOV V V. Theory of thin shells[M]. Leningrad: National Union Press of shipbuilding industry, 1951.
[22] STEELE C R. Los Angeles:Stanford University, 1959.
[23]夏子辉.承受任意载荷的薄壁圆环壳和弯管的一般解[D].北京:清华大学, 1984.
[24] XIA ZIHUI, ZHANG WEI. Int J Press, Vessel and Piping, 1986, 26: 129-144.
[25]陈山林.圆环壳在一般载荷下的轴对称问题[J].应用数学和力学, 1986, 7(5): 425-434.
[26]张若京,张维.承受非对称载荷圆环壳的完全渐近解[J].中国科学, 1995, 25(6):614-619.
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