非轴对称载荷下电磁轨道炮炮管的力学分析
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摘要
电磁轨道炮是一种全新概念的武器，在国防军事、航空航天、交通运输、工业生产和科学研究等领域都具有不可估量的应用前景，世界军事科技强国都从战略高度予以重视并不断加大力度开展研究。然而，目前电磁轨道炮的组成过重，体积过大，其原因之一是构件的强度、刚度计算方面研究的内容比较浅显，距离实际应用的要求相差很远。过去20多年的许多电磁轨道炮虽然也进行了结构设计，考虑了材料的受力环境，但严格说对材料的力学行为研究很不够。目前，关于电磁炮力学问题的研究主要集中在电枢自身的受力分析以及电枢与轨道的相互作用方面，而关于炮管自身力学分析的研究则较为少见。
电磁轨道炮圆柱形炮管实际是一个在两种非轴对称同步移动载荷作用下的有限长圆柱壳体。两种非轴对称同步移动载荷作用是指移动的非轴对称集中载荷，以及同步移动且作用范围随移动位置增加的均布载荷的共同作用。鉴于目前电磁炮炮管的实际构造尚未定型，为使研究成果能够适用于炮管的多种规格，将其简化为有限长圆柱薄壳或有限长圆柱厚壳，划分标准可以依据壳体厚度与中面半径的比值确定。本文针对电磁轨道炮圆柱形炮管在两种非轴对称同步移动载荷作用下的受力状态，以简支边界条件为例，首先开展了静力分析的理论研究，并以静力分析的研究成果为基础和对照基准，进行了动力响应的理论研究。
将电磁轨道炮圆柱形炮管简化为两种非轴对称载荷作用下的有限长圆柱薄壳，给出其在静力载荷作用下的变形与应力的基本方程；在给定两端约束条件下，应用Galerkin法，求得应力与位移的解析解，并通过具体算例与ANSYS数值解进行对比分析，验证薄壳静力解析解的正确性。
以非轴对称载荷作用下有限长圆柱薄壳的静力理论分析为基础，采用Dirac函数与Heaviside函数表示两种非轴对称同步移动载荷的作用，考虑壳体惯性力作用后建立动力学微分方程组。在给定边界条件及初始条件后，应用Galerkin法、Laplace变换及其逆变换，求得应力与位移的动态响应的解析解。通过具体算例与ANSYS数值解进行分析对比，验证薄壳动力响应解析解的可靠性。
将电磁轨道炮圆柱形炮管简化为有限长圆柱厚壳，假定材质各向同性且为线弹性，非轴对称载荷为作用在壳体内表面的径向线载荷与集中载荷，径向剪切应变沿厚度方向二次分布，径向正应变沿厚度方向一次分布，采用Dirac函数与Heaviside函数描述非轴对称载荷，基于最小势能原理推导静力平衡微分方程，应用Galerkin法，求得应力与位移的静力解析解。通过具体算例与ANSYS数值解进行对比分析，验证厚壳静力解析解的正确性。
以非轴对称有限长圆柱厚壳的静力理论分析为基础，采用Dirac函数与Heaviside函数表示两种非轴对称同步移动载荷的作用，考虑壳体惯性力作用后建立动力学微分方程组。在给定边界条件及初始条件后，应用Galerkin法和和Runge-Kutta-Fehlberg法，求得应力与位移的动态响应的解析解。通过具体算例与ANSYS数值解进行分析对比，验证厚壳动力响应解析解的可靠性。
本文推导的两种非轴对称同步移动载荷作用下的有限长圆柱薄壳及厚壳的静力分析和动力响应，相对以往的研究成果将更加接近于工程实际，可作为电磁轨道炮炮管结构设计的基础，同时又可供研究圆柱壳体在非轴对称工况下的静力、动力分析时参考。
Railgun is an entirely new concept of weapons, which has an immeasurableapplication prospects in the defense and military, aerospace, transportation, industrialproduction and scientific research field. Worldwide military technological powerscontinue to strengthen their efforts to carry out the research from a strategic perspective.The current composition of the electromagnetic railgun is too heavy and bulky. One of thereasons is the components’ strength and stiffness calculations are relatively plain and veryfar away from the actual application requirements. Although many railguns constructedduring the past20years have their structural design and consideration of mechanicalenvironment, they have no enough study of mechanical behavior of materials. Currently,railgun's mechanical research is focused on armature's machanical characteristics andtrack's interaction, and barrel's mechanical research is rarely conducted.
Railgun's cylindrical barrel is actually a length-limited cylindrical shell loaded bynon-axisymmetric loads, which consist of a moving concentrated load and a uniformlydistributed load with synchronously increasing its range of action. The barrel can be alength-limited cylindrical thin shell or thick shell, according to its actual structure. Basedon mechanical state of the cylindrical barrel of railguns, the static characteristcs anddynamic response of a length-limited cylindrical shell under non-axisymmetric loads areresearched through mechanical and mathematical tools in this paper.
Railgun’s cylindrical barrel is simplified as a length-limited thin cylindrical shellunder non-axisymmetric line load and concentrated loads. Based on fundamentalequations of the above problem, load function and displacement function are presented,and displacement and stress analytic solutions are obtained by Galerkin Method in thispaper. The analytical solutions are verified by comparing them with ANSYS numericalsolutions of an example problem.
Dynamic response of a length-limited cylindrical thin shell under non-axisymmetricloads is researched. Dynamic differential equations with symmetrical forms are derived,and the two moving loads are expressed by the Dirac function and the Heaviside function. Based on the assumed displacement functions, the analytical dynamic solutions to thedisplacement and stress of the cylindrical shell are obtained by means of the Galerkinmethod and Laplace transformation. The algorithm is verified through the comparativeanalysis of the analytical solutions and the ANSYS numerical solutions for a specificexample.
Railgun’s cylindrical barrel is simplified as a length-limited thick cylindrical shellunder non-axisymmetric line load and concentrated loads. Based on the assumption ofradial shear strains with quadratic distribution and radial normal strains with lineardistribution through the radial coordinate, displacement expressions containing theunknowns are established. The equilibrium differential equations containing7unkownsare derived according to the minimum potential energy principle. After the selection ofdouble triangle functions and application of the Galerkin Method, analytical solutions ofstress and displacement of thick shells are obtained. This method is verified by acomparative analysis of the analytical solutions with ANSYS numerical results.
Dynamic response of a length-limited cylindrical thick shell under non-axisymmetricloads is researched. Based on the assumption of radial shear strains with quadraticdistribution and radial normal strains with linear distribution through the radial coordinate,displacement expressions satisfying boundary conditions are established. After applicationof the Galerkin Method and the Modified Runge–Kutta–Fehlberg Mehtod, dynamicresponse of thick shells is obtained. This method is verified by a comparative analysis ofthe theoretical solutions with ANSYS numerical results from an example.
The static characteristics and dynamic responses of the length-limited thin shell andthe thick shell under non-axisymmetric uniform load and concentrated loads are derived inthis paper. They can serve as the foundation of railgun barrel's structural design, and as areference for static and dynamic analysis of cylindrical shells under non-axisymmetricloads.
电磁轨道炮圆柱形炮管实际是一个在两种非轴对称同步移动载荷作用下的有限长圆柱壳体。两种非轴对称同步移动载荷作用是指移动的非轴对称集中载荷，以及同步移动且作用范围随移动位置增加的均布载荷的共同作用。鉴于目前电磁炮炮管的实际构造尚未定型，为使研究成果能够适用于炮管的多种规格，将其简化为有限长圆柱薄壳或有限长圆柱厚壳，划分标准可以依据壳体厚度与中面半径的比值确定。本文针对电磁轨道炮圆柱形炮管在两种非轴对称同步移动载荷作用下的受力状态，以简支边界条件为例，首先开展了静力分析的理论研究，并以静力分析的研究成果为基础和对照基准，进行了动力响应的理论研究。
将电磁轨道炮圆柱形炮管简化为两种非轴对称载荷作用下的有限长圆柱薄壳，给出其在静力载荷作用下的变形与应力的基本方程；在给定两端约束条件下，应用Galerkin法，求得应力与位移的解析解，并通过具体算例与ANSYS数值解进行对比分析，验证薄壳静力解析解的正确性。
以非轴对称载荷作用下有限长圆柱薄壳的静力理论分析为基础，采用Dirac函数与Heaviside函数表示两种非轴对称同步移动载荷的作用，考虑壳体惯性力作用后建立动力学微分方程组。在给定边界条件及初始条件后，应用Galerkin法、Laplace变换及其逆变换，求得应力与位移的动态响应的解析解。通过具体算例与ANSYS数值解进行分析对比，验证薄壳动力响应解析解的可靠性。
将电磁轨道炮圆柱形炮管简化为有限长圆柱厚壳，假定材质各向同性且为线弹性，非轴对称载荷为作用在壳体内表面的径向线载荷与集中载荷，径向剪切应变沿厚度方向二次分布，径向正应变沿厚度方向一次分布，采用Dirac函数与Heaviside函数描述非轴对称载荷，基于最小势能原理推导静力平衡微分方程，应用Galerkin法，求得应力与位移的静力解析解。通过具体算例与ANSYS数值解进行对比分析，验证厚壳静力解析解的正确性。
以非轴对称有限长圆柱厚壳的静力理论分析为基础，采用Dirac函数与Heaviside函数表示两种非轴对称同步移动载荷的作用，考虑壳体惯性力作用后建立动力学微分方程组。在给定边界条件及初始条件后，应用Galerkin法和和Runge-Kutta-Fehlberg法，求得应力与位移的动态响应的解析解。通过具体算例与ANSYS数值解进行分析对比，验证厚壳动力响应解析解的可靠性。
本文推导的两种非轴对称同步移动载荷作用下的有限长圆柱薄壳及厚壳的静力分析和动力响应，相对以往的研究成果将更加接近于工程实际，可作为电磁轨道炮炮管结构设计的基础，同时又可供研究圆柱壳体在非轴对称工况下的静力、动力分析时参考。
Railgun is an entirely new concept of weapons, which has an immeasurableapplication prospects in the defense and military, aerospace, transportation, industrialproduction and scientific research field. Worldwide military technological powerscontinue to strengthen their efforts to carry out the research from a strategic perspective.The current composition of the electromagnetic railgun is too heavy and bulky. One of thereasons is the components’ strength and stiffness calculations are relatively plain and veryfar away from the actual application requirements. Although many railguns constructedduring the past20years have their structural design and consideration of mechanicalenvironment, they have no enough study of mechanical behavior of materials. Currently,railgun's mechanical research is focused on armature's machanical characteristics andtrack's interaction, and barrel's mechanical research is rarely conducted.
Railgun's cylindrical barrel is actually a length-limited cylindrical shell loaded bynon-axisymmetric loads, which consist of a moving concentrated load and a uniformlydistributed load with synchronously increasing its range of action. The barrel can be alength-limited cylindrical thin shell or thick shell, according to its actual structure. Basedon mechanical state of the cylindrical barrel of railguns, the static characteristcs anddynamic response of a length-limited cylindrical shell under non-axisymmetric loads areresearched through mechanical and mathematical tools in this paper.
Railgun’s cylindrical barrel is simplified as a length-limited thin cylindrical shellunder non-axisymmetric line load and concentrated loads. Based on fundamentalequations of the above problem, load function and displacement function are presented,and displacement and stress analytic solutions are obtained by Galerkin Method in thispaper. The analytical solutions are verified by comparing them with ANSYS numericalsolutions of an example problem.
Dynamic response of a length-limited cylindrical thin shell under non-axisymmetricloads is researched. Dynamic differential equations with symmetrical forms are derived,and the two moving loads are expressed by the Dirac function and the Heaviside function. Based on the assumed displacement functions, the analytical dynamic solutions to thedisplacement and stress of the cylindrical shell are obtained by means of the Galerkinmethod and Laplace transformation. The algorithm is verified through the comparativeanalysis of the analytical solutions and the ANSYS numerical solutions for a specificexample.
Railgun’s cylindrical barrel is simplified as a length-limited thick cylindrical shellunder non-axisymmetric line load and concentrated loads. Based on the assumption ofradial shear strains with quadratic distribution and radial normal strains with lineardistribution through the radial coordinate, displacement expressions containing theunknowns are established. The equilibrium differential equations containing7unkownsare derived according to the minimum potential energy principle. After the selection ofdouble triangle functions and application of the Galerkin Method, analytical solutions ofstress and displacement of thick shells are obtained. This method is verified by acomparative analysis of the analytical solutions with ANSYS numerical results.
Dynamic response of a length-limited cylindrical thick shell under non-axisymmetricloads is researched. Based on the assumption of radial shear strains with quadraticdistribution and radial normal strains with linear distribution through the radial coordinate,displacement expressions satisfying boundary conditions are established. After applicationof the Galerkin Method and the Modified Runge–Kutta–Fehlberg Mehtod, dynamicresponse of thick shells is obtained. This method is verified by a comparative analysis ofthe theoretical solutions with ANSYS numerical results from an example.
The static characteristics and dynamic responses of the length-limited thin shell andthe thick shell under non-axisymmetric uniform load and concentrated loads are derived inthis paper. They can serve as the foundation of railgun barrel's structural design, and as areference for static and dynamic analysis of cylindrical shells under non-axisymmetricloads.
引文
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