Minimization of the weight of ribbed cylindrical shells made of a viscoelastic composite

The minimization of the weight of ribbed viscoelastic composite cylindrical shells under a long-term external pressure is considered. The shells are strengthened with six inner stiffening rings with identical geometric parameters and a square cross section. It is assumed that the shell material obeys the linear law of hereditary creep and the displacements across the shell wall are distributed according to the Timoshenko hypothesis. The shell must withstand an external pressure of –0.5 MPa without the loss of stability for an unlimited time. The parameters of optimization are the intensity of reinforcement and thickness of its covering and the height and width of the stiffening rings. It is found that the weight of an optimum ribbed shell is 24% lower than that of an optimum cylindrical shell without ribs.     

Thermoelastoplastic deformation of complexly reinforced shells

The problem on the elastoplastic deformation of reinforced shells of variable thickness under thermal and force loadings is formulated. A qualitative analysis of the problem is carried out and its linearization is indicated. Calculations of isotropic and metal composite cylindrical shells have shown that the load-carrying capacity of shell structures under elastoplastic deformations is several times (sometimes by an order of magnitude) higher than under purely elastic ones; the heating of shells with certain patterns of reinforcement sharply reduces their resistance to elastic deformations, but only slightly affects their resistance to elastoplastic ones; not always does the reinforcement in the directions of principal stresses and strains provide the greatest load-carrying capacity of a shell; there are reinforcement schemes that ensure practically the same resistance of shells at different types of their fastening. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 42, No. 6, pp. 707–728, November–December, 2006.     

Nonlinear buckling behavior of 3D-braided composite cylindrical shells subjected to internal pressure loads in thermal environments

The nonlinear buckling behavior of a 3D-braided composite cylindrical shell of finite length subjected to internal pressure in thermal environments is considered. According to a new micromacromechanical model, a 3D-braided composite may be treated as a cell system where the geometry of each cell strongly depends on its position in the cross section of the cylindrical shell. The material properties of the epoxy matrix are expressed as linear functions of temperature. The governing equations are based on Reddy’s higher-order shear deformation theory of shells with a von Karman–Donnell-type kinematic nonlinearity and include thermal effects. The singular perturbation technique is employed to determine the buckling pressure and the postbuckling equilibrium paths of the shell.     

Sound insulation of composite cylindrical shells

We study problems involving the acoustic insulation of cylindrical shells of finite length made of a composite material. The motion of the medium (a gas) is described by the usual wave equation of acoustic approximation, and the equations of the applied theory of composite shells are used to describe the vibrations of the shell. To determine the levels of sound suppression the finite-element method is applied for both the medium and the shell. Translated fromMatematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 41, No. 1, 1998, pp. 47–50.     

Buckling and the initial postbuckling behavior of cylindrical shells made of composites with one plane of symmetry

A method for calculating the buckling stability of layered cylindrical shells made of composite materials with one plane of symmetry of mechanical characteristics is worked out. As a special case, shells made of fibrous materials by winding in directions not coinciding with coordinate axes are considered. An analysis of stability of shells under an axial compression, external pressure, and torsion is carried out. It is shown that, at a great number of layers and appropriate reinforcing angles, the shells can be considered orthotropic. The solution to the problem of the initial postbuckling behavior of shells made of composites with one plane of symmetry is also obtained. It is found that shells of this type can be less sensitive to geometrical imperfections. This fact is important from the practical point of view. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 43, No. 2, pp. 213–236, March–April, 2007.     

Postbuckling of a shear-deformable anisotropic laminated cylindrical shell under external pressure in thermal environments

A postbuckling analysis is presented for a shear-deformable anisotropic laminated cylindrical shell of finite length subjected to external pressure in thermal environments. The material properties are expressed as linear functions of temperature. The governing equations are based on Reddy’s higher-order shear-deformation shell theory with the von Karman-Donnell-type kinematic nonlinearity. The nonlinear prebuckling deformations and initial geometric imperfections of the shell are both taken into account. The boundary-layer theory of shell buckling, which includes the effects of nonlinear prebuckling deformations, large deflections in the postbuckling region, and the initial geometric imperfections of the shell, is extended to the case of shear-deformable anisotropic laminated cylindrical shells under lateral or hydrostatic pressure in thermal environments. The singular perturbation technique is employed to determine the interactive buckling loads and postbuckling equilibrium paths. The results obtained show that the variation in temperature, layer setting, and the geometric parameters of such shells have a significant influence on their buckling load and postbuckling behavior. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 43, No. 6, pp. 789–822, November–December, 2007.     

Heat conduction of shells reinforced by fibers with constant and variable cross sections

We propose a model for heat conduction of a spatially reinforced medium and present its generalization to the case of a polyreinforced layer. We consider the heat-conduction equations for fibrous shells and construct a procedure for reduction of a three-dimensional problem of heat conduction to a two-dimensional one. Analytic solutions of a stationary problem of heat conduction are found for thin conic shells of revolution for various structures of reinforcement, and a graphical comparison of the corresponding results is performed. We study one of the approaches to rational reinforcement of thin shells, according to which the thermal “transparency” of a shell in the transverse direction is taken as a criterion of rational design. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev. Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 41, No. 2, pp. 132–150, April–June, 1998.     

湿热环境中复合材料层合圆柱薄壳屈曲和后屈曲

在宏-细观力学模型框架下,讨论湿热环境对复合材料层合圆柱薄壳在轴向压缩作用下屈曲和后屈曲行为的影响。基于细观力学模型复合材料性能与湿度和温度变化有关。壳体控制方程基于经典层合壳理论,并包括湿热效应。壳体屈曲的边界层理论被推广用于湿热环境的情况,相应的奇异摄动法用于确定层合圆柱薄壳的屈曲荷载和后屈曲平衡路径。分析中同时计及壳体非线性前屈曲变形和初始几何缺陷的影响。数值算例给出完善和非完善正交铺设层合圆柱薄壳在不同湿热环境中的后屈曲行为。讨论了温度和湿度,纤维体积比率,壳体几何参数,铺层数,铺层方式和初始几何缺陷等各种参数变化的影响。     

湿热环境中复合材料层合圆柱薄壳的屈曲和后屈曲

在宏-细观力学模型框架下,讨论湿热环境对复合材料层合圆柱薄壳在轴向压缩作用下屈曲和后屈曲行为的影响.基于细观力学模型复合材料性能与湿度和温度变化有关.壳体控制方程基于经典层合壳理论,并包括湿热效应.壳体屈曲的边界层理论被推广用于湿热环境的情况,相应的奇异摄动法用于确定层合圆柱薄壳的屈曲荷载和后屈曲平衡路径.分析中同时计及壳体非线性前屈曲变形和初始几何缺陷的影响.数值算例给出完善和非完善正交铺设层合圆柱薄壳在不同湿热环境中的后屈曲行为.讨论了温度和湿度,纤维体积比率,壳体几何参数,铺层数,铺层方式和初始几何缺陷等各种参数变化的影响.     

The numerical analysis of an orthotropic cylindrical shell

This paper is devoted to an orthotropic cylindricall simply supported shell subjected to external pressure. This analysis is focused on determining geometrical shape of shell. Main subject of investigation is to maximize the stability of the shell. Mathematical model of double layer shell was implemented. Numerical solution was obtained for particular class of shells by using the finite element code ABAQUS. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Yield condition for circular cylindrical shells made of a fiber-reinforced composite

A yield condition is obtained for circular cylindrical shells made of a definite class of fiber-reinforced composite material whose components possess plastic properties. It is shown that, in the plane of generalized stresses — the axial bending moment and the circumferential force (when the axial force is absent) — the yield curve consists of two linear and four curvilinear sections. By approximating the curvilinear sections, we get a piecewise linear yield condition described by a hexagon in the plane indicated. The nonlinear equations and the corresponding piecewise linear equations of the yield condition for particular cases are given in the form of tables. In solving specific boundary-value problems, we consider a circular cylindrical shell simply supported at its ends and loaded with a uniform internal pressure, for which the load-carrying capacity is determined in relation to the mechanical properties of composite components and some characteristic geometrical parameters. The results of numerical calculations are represented in the form of graphs. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 42, No. 5, pp. 655–666, September–October, 2006.     

A variational principle in a geometrically nonlinear theory of heterogeneous viscoelastic shells

The use of the hereditary theory for shells heterogeneous across their thickness is considered. A variational method is formulated for calculating thin anisotropic shells made of a material whose deformation behavior can be described by relations of the linear theory of viscoelasticity. In order to transform the corresponding functional into a form suitable for shells, some assumptions related to concepts of the theory of thin shells are introduced. In the capacity of Euler equations, physical relations, nonlinear equilibrium equations, and nonlinear boundary conditions are derived. The state equations are deduced for a multilayered shell. Translated from Mekhanika Kompozitnykh Materialov, Vol. 45, No. 2, pp. 231–240, March–April, 2009.     

Structure of nonlinear elastic relationships for the highly anisotropic layer of a nonthin shell

Laminated nonthin shells made of nonlinearly elastic fiber composites are considered. The composite material is assumed to be transversely isotropic in planes perpendicular to reinforcement. The asymptotic method and the condition of material stability are applied to analyze the structure of constitutive relations. To introduce a small parameter, the high stiffness in the reinforcement direction of the fiber composite is used. This allows us to obtain simplified constitutive relations containing functions with one or two arguments instead of five as in the initial general case. Kazan State Architectural Building Academy, Tatarstan, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 5, pp. 615–628, September–October, 1999.     

Nonlinear nonaxisymmetric deformation of composite shells of revolution

We discuss the results of the determination of the stress and displacement fields in nonaxisymmetrically loaded nonlinear-elastic shells of revolution. The original nonlinear system of equations is linearized in accordance with the method of variation of elastic parameters. The two-dimensional linear boundary-value problem is reduced to a sequence of one-dimensional problems, which are solved using a numerical method. We carry out an analysis of the stress-strain state of a conical shell made of a composite material of granular structure. Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, No. 37, 1994, pp. 80–83.     

复合材料三角形网格加筋圆锥壳体位移型稳定性方程及其总体稳定性分析

本文采用Donnell型扁壳理论,首先利用最小势能原理和广义平均筋条刚度法推导出用位移分量表示的复合材料三角形网格加筋叠层圆锥壳体的稳定性方程,考虑了蒙皮最一般的拉弯与拉扭耦合关系和加筋筋条的偏心效应,并讨论了该方程的基本性质.根据外压实验观察结果,通过选取适当的位移分量表达式,并运用Galerkin法分析了在均布外压作用下复合材料三角形网格加筋叠层圆锥壳体总体稳定性,得到了临界载荷的解析表达式,并对某一类C/E复合材料三角形内网格加筋圆锥壳体的临界外压进行了计算,所得理论值与实验结果很好地吻合.最后,讨论了有关参数对临界载荷的影响.本文所建立的新方程和所得结果对于航空航天结构非常有用.     

On the equations of thermoelasticity of thin shells with breaks in the middle surface

Applying the apparatus of generalized functions, we obtain a complete system of equations of thermoelasticity for thin shells with breaks. The shells are subject to heat sources located arbitrarily along a curve or throughout a region. We find the solution of the steady-state heat-conduction problem for an unbounded cylindrical shell with a break along a meridian. The results of numerical analysis are given. Translated fromMatematichni Metodi i Fiziko-mekhanichni Polya, Vol. 40, No. 1, 1997, pp. 135–139.     

Stability of Conical Shells of Metal Composites Beyond the Elastic Limit

The equations for integral instantaneous characteristics of composite materials consisting of elastoplastic fibers and matrix are derived based on the known hypotheses of uniform strain or stress fields. The constitutive relations for a layered shell are obtained. The numerical algorithm elaborated is used to solve the stability problem for conical boron-aluminum shells under external pressure and axial compression. It is shown that the shells of medium thickness lose their stability under loads whose magnitude depends on the plasticity of the binder. The plasticity has a decisive influence on the choice of the optimum directions of reinforcement. If the parameters of a shell are such that the buckling occurs beyond the elastic limit, the shell must be reinforced in the direction of precritical stresses. However, this is possible only upon separate action of loads.     

Analysis of contact stresses in structural joints of composite shell with steel banding

Based on the generalized Timoshenko-type shell theory, a numerical-analytical procedure for determining contact stresses from the interaction between a cylindrical composite shell and rigid bandings is proposed. Specific cases of loading and contact interaction (ideal contact through an adhesive interlayer) are considered. The contact problems are reduced to the solution of a Fredholm integral equation of the second-kind. A calculation analysis is performed. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 1, pp. 109–120, January–February, 2000.     

Dynamic stability of a porous cylindrical shell

This paper is devoted to a closed cylindrical shell made of a porous-cellular material. The mechanical properties vary continuously on the thickness of a shell. The mechanical model of porosity is as described as presented by Magnucki, Stasiewicz. A shell is simply supported on edges. On the ground of assumed displacement functions the deformation of shell is defined. The displacement field of any cross section and linear geometrical and physical relationships are assumed in cylindrical coordinate system. The components of deformation and stress state were found. Using the Hamilton's principle the system of differential equations of dynamic stability is obtained. The forms of unknown functions are assumed and the system of a differential equations is reduced to a simple ordinary equation of dynamic stability of shell (Mathieu's equation). The derived equation are used for solving a problem of dynamic stability of porous-cellular shell with intensity of load directed in generators of shell. The critical loads are derived for a family of porous shells. The unstable space of family porous shells is found. The influence a coefficient of porosity on the stability regions in Figures is presented. The results obtained for porous shell are compared to a homogeneous isotropic cylindrical shell. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)