The Elastoplastic Deformation of Variable-Thickness Shells of Revolution with Allowance for Geometric Nonlinearity

A solution is proposed to the problem on the nonlinear deformation of shells with a coordinate surface of revolution and thickness variable in two directions. Using the efficient method of linearization of physical equations together with the Bubnov–Vlasov–Kantorovich method makes it possible to reduce the dimension of the problem and to solve it with a satisfactory computational burden. A method based on parameter expansion of shell rigidities is proposed in the case where the thickness varies slightly along the circumferential coordinate. The solutions of several problems illustrating the procedure developed are presented     

Design of corrugated cylindrical shells under different end conditions

An approach to the solution of problems of statics for corrugated cylindrical shells with varying thickness is proposed. The solution is based on spline approximations along the generatrix and on the stable numerical method of discrete orthogonalization along the directrix. Problems on the stress-strain state of corrugated shells whose thickness varies along the directrix with different amplitudes and frequencies under different boundary conditions are solved. The effect of the boundary conditions, the type of end fixity, and the law of thickness variation on the parameters of the stress-strain state is analyzed. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 35, No. 9, pp. 38–46, September, 1999.     

Nonlinear natural frequency of shallow conical shells with variable thickness

IntroductionTheplatesandtheshellswithvariablethicknessarewidelyusedinengineering .Theproblemaboutstaticshasbeenstudiedbymanyscholars;therearemanyRefs .[1 -4 ]inthisfield .Papersaboutnonlineardynamicsaremuchless[5 ,6 ].Inthispaper,selectingthemaximumamplitudeinthecenterofshallowconicalshellswithvariablethicknessasperturbationparameter,thenonlinearnaturalfrequencyofshallowconicalshellswithvariablethicknessisobtainedbymethodgiveninRef.[7] .Thenonlinearnaturalfrequencyisnotonlyconnectedwiththeva…     

任意变厚度的旋转扁薄壳非线性稳定的幂函数解法

以幂函数为试函数,两次使用配点法成功地分离了耦合的大挠度方程,从而导出变厚度旋转扁壳非线性稳定的计算式。支座可以是弹性的。本文给出了均布或多项式分布荷载作用下,线性或多项式型变厚度的圆锥壳、球壳、余弦壳或四次多项式型旋转壳的上、下临界荷载。均布荷载作用下指数型变厚度球壳的上临界荷载同其他方法的结果作了比较。用配点法编写的程序具有收敛范围大、精度高、通用性强和计算时间少的优点。     

Nonaxisymmetric Thermoviscoelastoplastic Deformation of Shells of Revolution

An analysis is made of the basic results obtained at the S. P. Timoshenko Institute of Mechanics of the National Academy of Sciences of Ukraine in developing a theory and methods for thermoviscoelastic stress—strain analysis of flexible laminated shells of revolution with a thickness variable in two directions under nonaxisymmetric nonisothermal deformation along rectilinear and slightly curved paths, with the loading history taken into account     

Stress–strain state of nonthin orthotropic spherical shells of variable thickness

The stress–strain state of an orthotropic spherical shell with thickness varying in two coordinate directions is analyzed. Different boundary conditions are considered, and a refined problem statement is used. A numerical analytic method based on spline-approximation and discrete orthogonalization is developed. The stress–strain state of spherical orthotropic shells with variable thickness is studied     

Free vibrations of shallow nonthin shells with variable thickness and rectangular planform

The free vibrations of shallow orthotropic shells with variable thickness and rectangular planform are studied. The shear strains are taken into account. The spline approximation of unknown functions is used. The natural frequencies are calculated for different boundary conditions. The dependence of the natural frequencies on the curvature of the midsurface is examined. The natural frequencies of shells with constant and variable thickness are compared     

Spline-approximation solution of two-dimensional problems of statics for orthotropic conical shells in a refined formulation

An approach to solving two-dimensional stress-strain problems for orthotropic conical shells of variable thickness in a refined formulation is developed. The approach is based on the spline-approximation and the stable discrete-orthogonalization method, which is used to solve the one-dimensional problem. The dependence of the deflection and stresses on the thickness and apex angle of a shell of constant volume is given as an example __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 11, pp. 43–54, November 2007.     

Nonlinear bending of the shallow spherical shells with variable thickness under axisymmetrical loads

Based on the differential equation of the nonlinear bending of shallow sphericalshells with variable thickness under axisymmetrical loads,this paper studies thenumerical solution of the nonlinear differential equation by means of interpolatingmatrix method.The analysis of the results indicates that the suggested method is easyto implement and obtains the same high accuracy for both the displacements and theinternal forces.     

Thermoelastic bending of locally heated orthotropic shells

The thermoelastic bending of locally heated orthotropic shells is studied using the classical theory of thermoelasticity of thin shallow orthotropic shells and the method of fundamental solutions. Linear distribution of temperature over thickness and the Newton’s law of cooling are assumed. Numerical analysis is carried out for orthotropic shells of arbitrary Gaussian curvature made of a strongly anisotropic material. The behavior of thermal forces and moments near the zone of local heating is studied for two areas of thermal effect: along a coordinate axis and along a circle of unit radius. Generalized conclusions are drawn __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 3, pp. 80–85, March 2007.     

Analysis of the stress-strain state of noncircular cylindrical shells subject to thickness viration and weight retention

The stress-strain state of noncircular shells has been analyzed based upon solution of boundary value static problems of variable shell thickness using the methods of spline-collocation and discrete orthogonization. Shell weight was preserved depending on the degree of change in the thickness and the value of the eccentricity. Three classes of problems were considered in which the thickness varied along the generatrix, the guide, and in two coordinate directions; data are presented about the deflection and tangential force in the cross section under different values of the parameters. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev, Ukraine, Translated from Prikladnaya Mekhanika, Vol. 35, No. 6, pp. 39–47, June, 1999.     

Study Into the Effect of Circumferential Variation in Thickness and Load on the Deformation of Cylindrical Shells of Elliptic Cross Section

By solving the boundary-value stress–strain problems for cylindrical shells with an elliptical cross section and a thickness varying along the directrix, the effect of variability in the thickness and load on their deformation is studied. Tables and plots present the deflection and the bending moment calculated under various boundary and loading conditions.     

Stress Analysis of Orthotropic Noncircular Cylindrical Shells of Variable Thickness in a Refined Formulation

An approach is developed to solve stress–strain problems in a refined formulation for orthotropic cylindrical shells of variable thickness and noncircular cross section. It is shown, as an example, how the distributions of deflections and stresses depend on changes in the shell thickness at constant weight     

中厚圆柱壳在局部荷载下有限变形与屈曲分析

在柱壳的有限元计算中，采用Mindlin八结点杂交壳单元和增量荷载法，基于选择积分，缩减积分及完全积分三种积分模式编制了分层计算各种厚度板壳的有限元程序FEAM，并对中厚圆柱壳在局部法向均布荷载作用下的弹塑性有限变形和屈曲问题进行了分析和计算，算例表明，利用FEAM可对壳体屈曲的临界荷载及屈曲后结构的承载与形状改变作定性与定量的分析.     

Natural vibrations of thin conical panels of variable thickness

A numerical analytical approach is proposed to study the natural vibrations of thin isotropic conical shells with varying thickness. The approach is based on the spline-approximation of unknown functions. Open shells (panels) with different boundary conditions are considered. The effect of variable thickness on the dynamic characteristics is analyzed     

埋入水中旋转薄壳谐耦振分析的传递矩阵法

基于一般线弹性薄壳和势流理论,导出了旋转壳状态向量的一阶常微分矩阵方程和水动压力表达式,再借助齐次扩容技术和精细积分法,应用推广的传递矩阵法对埋入水中旋转薄壳的流固耦振进行了数值求解,并研究了一些因素对精度的影响.算例表明传递矩阵法和有限元方法相比不仅精度良好,而且有较高的计算效率.     

Optimal design of axisymmetric plastic shallow shells of von Mises material

An optimal design technique developed earlier for axisymmetric plates and circular cylindrical shells is accommodated for shallow spherical shells subjected to uniform transverse pressure. Material of the shells is assumed to be rigid-plastic obeying the von Mises yield condition and the associated deformation law. The post-yield behaviour of the shells is taken into account. The weight minimization is performed under the condition that the maximal deflection of the shell of variable thickness coincides with the deflection of the reference shell of constant thickness. The problem is transformed into a non-linear boundary value problem which is solved numerically.     

The influence of the reference geometry on the response of elastic shells

Within the scope of the nonlinear theory of an elastic Cosserat surface, this paper is mainly concerned with the influence of the reference geometry and the related aspects of material symmetry restriction on the response of thermoelastic shells. The significance of the effect of the reference geometry is discussed in the case of isotropic shells, which may be of variable thickness in a reference state.     

A finite element formulation for analysis of functionally graded plates and shells

Summary A finite element formulation is derived for the thermoelastic analysis of functionally graded (FG) plates and shells. The power-law distribution model is assumed for the composition of the constitutent materials in the thickness direction. The procedure adopted to derive the finite element formulation contains the analytical through-the-thickness integration inherently. Such formulation accounts for the large gradient of the material properties of FG plates and shells through the thickness without using the Gauss points in the thickness direction. The explicit through-the-thickness integration becomes possible due to the proper decomposition of the material properties into the product of a scalar variable and a constant matrix through the thickness. The nonlinear heat-transfer equation is solved for thermal distribution through the thickness by the Rayleigh-Ritz method. According to the results, the formulation accounts for the nonlinear variation in the stress components through the thickness especially for regions with a variation in martial propperties near the free surfaces.     

On the vibration of laminated nonhomogeneous orthotropic shells

In this paper, an analytical procedure is given to study the free vibration of the laminated homogeneous and non-homogeneous orthotropic conical shells with freely supported edges. The basic relations, the modified Donnell type motion and compatibility equations have been derived for laminated orthotropic truncated conical shells with variable Young’s moduli and densities in the thickness direction of the layers. By applying the Galerkin method, to the basic equations, the expressions for the dimensionless frequency parameter of the laminated homogeneous and non-homogeneous orthotropic truncated conical shells are obtained. The appropriate formulas for the single-layer and laminated complete conical and cylindrical shells made of homogeneous and non-homogeneous, orthotropic and isotropic materials are found as a special case. Finally, the influences of the non-homogeneity, the number and ordering of layers and the variations of the conical shell characteristics on the dimensionless frequency parameter are investigated. The results obtained for homogeneous cases are compared with their counterparts in the literature.