复合材料的多层、夹层和加筋圆柱曲板的稳定和振动

本文在文献〔1,2〕的基础上,考虑了沿壳体厚度方向的剪切变形,探讨周边简支的纤维增强复合材料的正交各向异性的多层、夹层和加筋矩形圆柱曲板(与圆柱壳),在轴压、侧压和剪切(扭矩)作用下的临界载荷和横向振动固有频率的计算问题。在编成计算程序后,用一些算例将用文献〔1〕中的扁壳方程(Donnell壳体理论) 和文献〔3〕中的非扁壳方程(Love的壳体一阶近似理论) 算得的结果作了比较;将轴压下轴对称失稳和非轴对称失稳的临界载荷作了比较;将在轴压和侧压作用下失稳时外加筋曲板和内加筋曲板的临界载荷作了比较;将有薄膜力N_x~0和N_y~0同时和分别作用时与没有薄膜力作用时的横向振动固有频率作了比较;将按壳体的剪切变形理论和经典理论算得的临界载荷作了比较;将铺层情况对临界载荷的影响作了比较。     

复合材料襟翼壁板屈曲失稳行为的栅线投影实验研究

本文利用栅线投影测量方法研究了蜂窝夹层板、工字型及T型加筋板三种不同结构形式复合材料襟翼壁板在压缩载荷下的屈曲失稳行为,得到了不同形式结构件屈曲的全场离面位移分布规律,分析了各自的屈曲失稳模式.研究结果表明,栅线投影测量方法在大尺度复合材料结构失稳变形测试中具有可行性;在相同面板尺寸条件下,工字型加筋复合材料襟翼壁板屈曲临界载荷最大,承载能力最强.本文结果可为飞机复合材料结构设计提供实验依据.     

环向加筋圆柱壳在横向冲击波作用下的动力响应

用一个均匀的单层壳作为“参考”结构,把环筋当作“外载”考虑其效应.利用“残余势”法处理流体和壳体之间耦合效应,导出了无限长、环筋等距分布圆柱壳体在计及中面有伸长和无伸长时,所有模式下的动响应表达式.方程式通过不同程度简化,能得到前人的一些结果.本文计算了两组壳体参数,绘出了相应的曲线,并比较了不同方法的结果.     

具有复合正交异性铺层和偏心加筋的圆柱壳体的屈曲问题

本文导出了具有正交异性复合铺层和偏心加筋的圆柱壳体在轴压、横向压力或它们的任意组合作用下的屈曲问题的近似解,文中提出的方法使壳中不同铺层及偏心加筋引起的弯曲与拉伸间的耦合研究成为可能。以前的研究方法表明由于忽略了弯一拉耦合效应,所予测的屈曲结果是不完全正确的。     

加筋土强度的理论研究及试验验证

将加筋材料对土体强度提高的贡献等效成一种附加围压, 通过莫尔圆法, 求得小主应力增量, 并认为土体在破坏时处于极限平衡状态, 得到了黏聚力和内摩擦角同时变化时的加筋土强度表达式, 对该式作了详细讨论, 用该式计算了6 例典型加筋土在轴对称荷载下的大主应力, 结果表明计算所得大主应力值与三轴试验值比较吻合.     

均匀外压圆柱薄壳弹性稳定性的实验研究

本文提供十个精车圆柱薄壳在全面外压作用下弹性稳定性的实验研究结果.着重于描述壳体的失稳过程,基于实验现象,讨论了结构稳定性特征和弹性失稳概念. 实验给出“前波”现象的大致规律,并确认,应用渐近线准则,可以不破坏而又精确地确定临界载荷. 实验发现了“飘移”,“吃波”,“反跳”以及“超临界压力”等现象.O7试件在临界压力下稳压半小时,观察到应变飘移,波形相继长大以至最终崩溃的“慢放”全过程. 理论计算和实验结果的比较表明,对于精加工的中等长度壳体而言,较小的初挠度对临界压力并无显著影响.     

含预置损伤复合材料加筋板的单轴压缩屈曲分析

通过试验和有限元方法分析了单轴压缩下加筋板的失效模式.研究了三种预置损伤位置及四种损伤尺寸的复合材料T型加筋板的线性及非线性屈曲行为,比较了损伤对临界屈曲载荷和最大失效载荷的影响.研究结果表明:损伤位置在桁条间蒙皮时,损伤的尺寸对其临界屈曲载荷和最大失效载荷影响较小;损伤位置在桁条区蒙皮时,加筋板的临界屈曲载荷随损伤尺寸的增加而明显降低,最大降低50%;损伤位置在桁条边凸缘处蒙皮时,加筋板最大失效载荷所受影响随损伤尺寸的增加而明显降低,最大降低25%.从而得到了复合材料加筋板临界屈曲载荷比和最大失效载荷比与损伤位置及尺寸的关系图.     

圆锥形薄壳在轴向压力作用下的稳定性

文献[1—3]对圆锥形薄壳在轴向压力作用下的轴对称失稳情况引出了可按相当圆柱壳计算的概念,它们都假定壳体沿其母线方向受压,但在实际上一般不易发生这种情况。文献[4,5]简略报导了进行圆锥壳受均匀外压作用下或弯曲和轴向压力混合作用下的实验结果。实验均按实际上常见的壳体沿轴向受压方向加载,但其工作似欠完整可靠。     

含初始缺陷复合材料格栅加筋圆柱壳的鲁棒优化设计

针对复合材料格栅加筋圆柱壳具有多约束、连续变量和非连续变量混合的特性,基于复合材料中厚圆柱壳体的非线性稳定性理论,考虑优化目标和约束鲁棒性,采用混合遗传算法,提出了一种非完善复合材料格栅加筋圆柱壳的鲁棒优化设计方法.应用正交设计理论确定主要的鲁棒优化设计变量,简化了运算过程,从而提高了优化分析效率;同时又采用五点差分格式代替梯度运算,解决了在优化计算过程中不可求导的问题.通过典型算例表明,鲁棒优化设计所得到的优化分析结果与传统确定性优化方法相比差别较大,此外壳体的初始缺陷亦将对优化结果产生很大的影响.     

局部径向载荷作用下外压薄壁圆筒稳定性分析

为简化真空塔器外挂件支撑区局部失稳分析,提炼出局部径向载荷作用下外压薄壁圆筒稳定性计算模型. 以易拉罐为薄壁圆筒试件,对不同外压下试件的局部径向临界载荷进行了测试. 利用有限元法对各实验模型进行了特征值屈曲分析,结果与实验数据能较好地吻合. 采用正交设计及参数化计算,得到了各结构参数及外压下的局部径向临界载荷经验公式. 实例计算表明,所得经验公式稍有保守,可用于真空塔器外挂件支撑件区的局部稳定性分析.     

A new displacement-type stability equation and general stability analysis of laminated composite circular conical shells with triangular grid stiffeners

In this paper,based on the theory of Donnell-type shallow shell,a new displacement-type stability equations is first developed for laminated composite circular conical shellswith triangular grid stiffeners by using the variational calculus and generalized smeared-stiffener theory.The most general bending stretching couplings,the effect of eccentricity ofstiffeners are considered.Then,for general stability of composite triangular grid stiffenedconical shells without twist coupling terms,the approximate formulas are obtained forcritical external pressure by using Galerkin‘s procedure.Numerical examples for a certainC/E composite conical shells with inside triangular grid stiffeners are calculated and theresults are in good agreement with the experimental data.Finally,the influence of someparameters on critical external pressure is studied.The stability equations developed andthe formulas for critical external pressure obtained in this paper should be very useful in theastronautical engineering design.     

A Donnell type theory for finite deflection of stiffened thin conical shells composed of composite materials

A Donnell type theory is developed for finite deflection of closely stiffened truncatedlaminated composite conical shells under arbitrary loads by using the variational calculusand smeared-stiffener theory.The most general bending-stretching coupling and the effectof eccentricity of stiffeners are considered.The equilibrium equations,boundary conditionsand the equation of compatibility are derived.The new equations.of the mixed-type ofstiffened laminated composite conical shells are obtained in terms of the transversedeflection and stress function.The simplified equations are also given for some commonlyencountered cases.     

Stability of laminated composite circular conical shells under external pressure

In this paper,based on the mixed-type theory developed by the same authors.atheoretical analysis is presented for the stability of laminated composite circular conicalshells under external pressure.The formulas for critical external pressure are obtained byusing the potential energy variation principle.Very good agreement is shown between thetheoretical prediction of critical external pressure and the experimental data.Finally,theinfluence of some parameters on critical external pressure is discussed numerically.Themixed-type theory developed by the same authors and the results obtained in this paperare very useful in aerospace engineering design.     

Free vibrations of rotating composite conical shells with stringer and ring stiffeners

In this paper, an analytical solution for the free vibration of rotating composite conical shells with axial stiffeners (stringers) and circumferential stiffener (rings), is presented using an energy-based approach. Ritz method is applied while stiffeners are treated as discrete elements. The conical shells are stiffened with uniform interval and it is assumed that the stiffeners have the same material and geometric properties. The study includes the effects of the coriolis and centrifugal accelerations, and the initial hoop tension. The results obtained include the relationship between frequency parameter and circumferential wave number as well as rotating speed at various angles. Influences of geometric properties on the frequency parameter are also discussed. In order to validate the present analysis, it is compared with other published works for a non-stiffened conical shell; other comparison is made in the special case where the angle of the stiffened conical shell goes to zero, i.e., stiffened cylindrical shell. Good agreement is observed and a new range of results is presented for rotating stiffened conical shells which can be used as a benchmark to approximate solutions.     

碳纳米管增强复合材料圆锥薄壳非线性自由振动

考虑碳纳米管复合材料作为功能梯度材料的不均匀性,基于连续介质理论以及哈密尔顿变分原理,建立了功能梯度碳纳米管增强复合材料开口圆锥薄壳结构的非线性运动偏微分控制方程,然后利用Galerkin法,将非线性偏微分控制方程转化为常微分控制方程,进而采用谐波平衡法求解了开口圆锥壳的非线性自由振动问题,并探讨了圆锥薄壳几何参数、碳纳米管参数对结构非线性自由振动的影响．数值研究表明结构的无量纲非线性自由振动频率与线性自由振动频率的比值随圆锥薄壳长厚比的增大而变小、并随圆锥角的增大而变大．     

Buckling analysis of functionally graded material (FGM) sandwich truncated conical shells reinforced by FGM stiffeners filled inside by elastic foundations

An analytical solution for buckling of an eccentrically stiffened sandwich truncated conical shell is investigated. The shell consists of two functionally graded material (FGM) coating layers and a core layer which are metal or ceramic subjected to an axial compressive load and an external uniform pressure. Shells are reinforced by stringers and rings, in which the material properties of shells and stiffeners are graded in the thickness direction following a general sigmoid law distribution. Two models of coated shell-stiffener arrangements are investigated. The change of the spacing between stringers in the meridional direction is taken into account. A couple set of three-variable-coefficient partial differential equations in terms of displacement components are solved by the Galerkin method. A closed-form expression for determining the buckling load is obtained. The numerical examples are presented and compared with previous works.     

Mechanical and thermal postbuckling of FGM thick circular cylindrical shells reinforced by FGM stiffener system using higher-order shear deformation theory

The postbuckling of the eccentrically stiffened circular cylindrical shells made of functionally graded materials(FGMs),subjected to the axial compressive load and external uniform pressure and filled inside by the elastic foundations in the thermal environments,is investigated with an analytical method.The shells are reinforced by FGM stringers and rings.The thermal elements of the shells and stiffeners in the fundamental equations are considered.The equilibrium and nonlinear stability equations in terms of the displacement components for the stiffened shells are derived with the third-order shear deformation theory and Leckhniskii smeared stiffener technique.The closed-form expressions for determining the buckling load and postbuckling load-deflection curves are obtained with the Galerkin method.The effects of the stiffeners,the foundations,the material and dimensional parameters,and the pre-existent axial compressive and thermal load are considered.     

旋转壳的数值传递函数方法

应用数值传递函数方法建立一种用于分析旋转壳静力、动力响应的截锥壳单元,在本方法中,单元的位移在环向展开为Fourier级数的形式,应用薄壳理论可以得到解耦的微分方程,通过Laplace变换可以将方程转化为频域内的常微分方程,将其表示为状态空间形式后,可以应用数值传递函数方法求解,对复杂的系统可以应用与有限元类似的方法,划分多个单元组合求解,文中给出了几种旋转壳的动力、静力问题的数值算例,并与其它方法进行了比较,表明本文方法具有精度高,计算方便等特点。     

Thermal buckling and free vibration of FG truncated conical shells with stringer and ring stiffeners using differential quadrature method

In this paper, thermal buckling and free vibration of orthogonally stiffened functionally graded truncated conical shells in thermal environment is investigated. Conical shell has been stiffened by rings and stringers, and the influences of the stiffeners are evaluated by the aid of smearing method. The material properties of the structure are assumed to be changed continuously in the thickness direction. First, the initial thermal stresses are obtained accurately by solving the thermoelastic equilibrium equations. Then, by taking into account the initial thermal stresses, equations of motion as well as boundary conditions are obtained, applying the Hamilton’s principle and the first-order shear deformation theory. The natural frequencies of the system have been achieved, solving these governing equations with considering Differential Quadrature Method (DQM). In addition to Eigen frequency analysis, the critical buckling-temperature of the conical shell has been computed. Moreover, the effects of geometrical parameters, number of stiffeners, thermal environment and various boundary conditions on natural frequency of the system have been investigated. Finally, in order to validate the present work, the results are compared with those of other researches available in literature.     

Exact shell solutions for conical springs

In this article, the equations of equilibrium of conical disk springs of thin and moderate thickness are obtained through the variational principles for thin-walled and thick-walled conical shells. The closed form analytical solutions based on the common deformation hypotheses for the equations of thin- and thick-walled truncated conical shells were achieved. The results of calculations of reaction forces, based on analytical formulae, were compared with the results of finite element analysis, demonstrating the good accuracy of the derived formulae. The theory is extended to incorporate the anisotropy of the material. The problem for optimal anisotropy is solved. The minimal stiffness of the spring is achieved, if the upmost modulus of the orthotropic material is in the meridional direction. Analogously, the highest stiffness is attained, if the maximal elastic modulus circumferentially oriented. Engineering applications of the current theory potentially include Bellville springs and slotted disk springs with moderate flatness for automotive and industrial applications.