Postbuckling characteristics of angle-ply laminated truncated circular conical shells

The postbuckling characteristics of the angle-ply laminated composite conical shells subjected to the torsion, the external pressure, the axial compression, and the thermal loading considering uniform temperature change are studied using the semi-analytical finite element approach. The finite element formulation is based on the first-order shear deformation theory and the field consistency principle. The variations in the stiffness coefficients along the meridional direction due to the changes in the ply-angle and the ply-thickness of the filament wound conical shells are incorporated in the finite element formulation. The nonlinear governing equations are solved using the Newton–Raphson iteration procedure coupled with the displacement control method to trace the prebuckling followed by the postbuckling equilibrium path. The presence of asymmetric perturbation in the form of a small magnitude load spatially proportional to the linear buckling mode shape is considered to initiate the bifurcation of the shell deformation. The influence of semi-cone angle, ply-angle and number of circumferential waves on the prebuckling/postbuckling response of the anti-symmetric angle-ply laminated circular conical shells is investigated.     

Free vibrations of composite laminated doubly-curved shells and panels of revolution with general elastic restraints

A unified numerical analysis model is presented to solve the free vibration of composite laminated doubly-curved shells and panels of revolution with general elastic restraints by using the Fourier–Ritz method. The first-order shear deformation theory is adopted to conduct the analysis. The admissible function is acquired by using a modified Fourier series approach in which several auxiliary functions are added to a standard cosine Fourier series to eliminate all potential discontinuities of the displacement function and its derivatives at the edges. Furthermore, the general elastic restraint and kinematic compatibility and physical compatibility conditions are imitated by the boundary and coupling spring technique respectively when the composite laminated doubly-curved panels degenerate to the complete shells of revolution. Then, the desired results are solved by the variational operation. Large quantities of numerical examples are calculated about the free vibration of cross-ply and angle-ply composite laminated doubly-curved panels and shells with different geometric and material parameters. Through the sufficient conclusions obtained from the comparison, it can be seen that highly accurate solutions can be yielded with a little computational effort. To understand the influence of different boundary conditions, lamination schemes, material and geometrical parameters on the vibration characteristics, a series of parametric studies are carried out. Lastly, results for vibration of the composite laminated doubly-curved panels and shells subject to various kinds of boundary conditions and with different geometrical and material parameters are also presented firstly, which can provide the benchmark data for other studies conducted in the future.     

Investigation of Locally Loaded Multilayer Shells by a Mixed Finite-Element Method. 1. Geometrically Linear Statement

The Hu-Washizu functional is constructed for analyzing prestressed multilayer anisotropic Timoshenko-type shells. As unknown functions, six displacements and eleven strains of the faces of the shells are chosen. Based on mixed finite-element approximations, a numerical algorithm is developed for solving linear static problems of prestressed multilayer composite shells. The results of solving the well-known test problem on a cylindrical shell subjected to two opposite point forces and the problem on local loading of a toroidal multilayer rubber-cord shell are presented.     

Dynamic and static loss in stability of flexible spherical shells made out of a composite material

The dynamic and static stability of shallow spherical shells which are rectangular in a plane are investigated. It is assumed that the shell is made out of a composite material which is weakly shear resistant and hence the refined theories which allow for transverse shear deformations and rotational inertia are applied. The solutions which were obtained are compared with solutions founded on the basis of the Kirchhoff-Love theory. It is shown that the results which are obtained on the basis of the classical theory are high for both the static and dynamic loss in stability, and are qualitatively different from the results obtained using the refined theory. The solutions were obtained using the Bubnov-Galerkin method in the higher approximations.     

Boundary-Value Problems of the Theory of Thin and Nonthin Orthotropic Shells with Account of Nonlinearly Elastic Properties and Low Shear Rigidity of Composite Materials

The basic geometric and physical relations and resolving equations of the theory of thin and nonthin orthotropic composite shells with account of nonlinear properties and low shear rigidity of their materials are presented. They are derived based on two theories, namely the theory of anisotropic shells employing the Timoshenko or Kirchhoff-Love hypothesis and the nonlinear theory of elasticity and plasticity of anisotropic media in combination with the Lagrange variational principle. The procedure and algorithm for the numerical solution of nonlinear (linear) problems are based on the method of successive approximations, the difference-variational method, and the Lagrange multiplier method. Calculations of the stress-strain state for a spherical shell with a circular opening loaded with internal pressure are presented. The effect of transverse shear strains and physical nonlinearity of the material on the distribution of maximum deflections and circumferential stresses in the shell, obtained according to two variants of the shell theories, is studied. A comparison of the results of the problem solution in linear and nonlinear statements with and without account of the shell shear strains is given. The numerical data obtained for thin and nonthin (medium thick) composite shells are analyzed.     

反对称角铺设层合板的屈曲和后屈曲

本文以挠度为摄动参数,采用文[1]提供的摄动方法研究了四边简支的完善和非完善反对称角铺设层合板在面内压缩作用下的屈曲和后屈曲性态.本文讨论了面内边界条件、铺设角、铺层数以及初始几何缺陷对层合板后屈曲性态的影响.     

层合板壳脱层屈曲的有限元分析

通过建立一类新的参考面有限单元,得到适用于分析层合板壳脱层屈曲问题的有限元方法。指出了利用Mindlin假设意义下的变形协调条件,可以将大多数胜任层合板壳分析的一般板壳单元改造为相应的参考面单元。这一方法确保了位移场的合理性和协调条件的满足。为验证参考面单元的有效性,还对壳体脱层屈曲的几个算例作了数值分析。     

Contact interaction of composite shells,subjected to follower loads,with a rigid convex foundation

Based on a 7-parameter shell model, a numerical algorithm is developed for solving the contact problem for a multilayered composite shell lying on a rigid convex foundation, which is subjected to a follower pressure and undergoes arbitrarily large rotations. A new geometrically exact solid shell element is formulated, which permits one to solve the nonlinear deformation problem for thin-walled composite structures under unilateral contact constraints by using a small number of load steps. The calculation of a homogeneous ring and an angle-ply toroidal shell interacting with plane and cylindrical foundations is considered.     

Stress-strain state and stability of composite sandwich shells with a scaling zone between the core and facings

A finite element model is presented for analyzing the strength and stability of sandwich shells of arbitrary configuration with an adhesion failure zone between the core and one of the facings. The model is based on the assumptions that both facings are laminated Timoshenko-type composite shells, only transverse shear stresses in the core and normal stresses in the thickness direction have nonzero values, a free slip in the tangential plane in the adhesion failure zone and unilateral contact along the normal are possible, and the prebuckling state in the stability problem is linear. Biquadratic nine-node approximations for all functions and numerical integration were used. The displacements and rotation angles of the normals toward the facings as well as stresses in the core are taken as global degrees of freedom. The algebraic problem is solved using a special step-by-step procedure of determining the contact area in the scaling zone and employing unilateral constraints for some of the unknowns. Numerical examples are also given.Translated from Mekhanika Kompozitnykh Materialov, Vol. 29, No. 5, pp. 640–652, September–October, 1993.     

复合材料多层板壳大挠度非线性问题的迭代解法

在王震鸣等人提出的各向异性多层扁壳的大挠度方程的基础上,提出了复合材料多层板壳大挠度非线性问题的迭代解法。分析了四边简支的复合材料多层矩形扁壳,与小挠度线性理论解析解及有限元非线性解进行了对比。结果表明,载荷较小并发生小挠度时,所得的大挠度解和小挠度解析解非常接近,载荷较大时,所得解和有限元非线性解非常接近。     

层合板壳脱层曲面的有限元分析

通过建立一类新的参考面有限单元,得到适应于分析层合板壳脱层屈曲问题的有限元方法,指出了利用Ｍｉｎｄｌｉｎ假设意义下的变形协调条件,可以将大多数胜任层合板壳分析的一般板壳单元改造为相应的参考面单元,这一方法确保了位移场的合理性和协调条件满足,为验证参考而单元的有效性和协调还对壳体脱层屈曲的几个算例作了数值分析。     

Composite Approximations to the Solutions of the Orr-Sommerfeld Equation

The method of matched asymptotic expansions is used to derive composite approximations to the solutions of the Orr-Sommerfeld equation which satisfy Olver's completeness requirement. It is shown that the inner expansions can be obtained to all orders in terms of a certain class of generalized Airy functions, and these expansions are then used to derive approximations to the connection formulae. Because of the linearity of the problem it is possible and convenient to fix the normalization of the inner and outer expansions separately and then to relate them through the central matching coefficients. The Stokes multipliers can then be expressed in terms of the central matching coefficients and the coefficients which appear in the connection formulae. Once the inner and outer expansions have been matched they can be combined, if desired, to form composite approximations of either the additive or multiplicative type. For example, the ‘modified’ viscous solutions of Tollmien emerge in a natural way as first-order composite approximations obtained by multiplicative composition; similarly, the form of the ‘viscous correction’ to the singular inviscid solutions which I conjectured some years ago emerges as a first-order additive composite approximation. Because of the completeness requirement, however, these composite approximations are valid only in certain wedge shaped domains; approximations which are valid in the complementary sectors can then be obtained by the use of the connections formulae. The theory thus provides a relatively simple and explicit method of obtaining higher approximations, and its structure permits a direct comparison of the present results not only with the older heuristic theories but also with the comparison equation method.     

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.     

复合材料对称层合板单向拉伸与面内剪切下的三维应力分析

本文给出了单向拉伸与面向剪切载荷下复合材料对称层合板中心区域的应力和应变沿板厚的数值计算分布规律。计算结果表明，在斜交对称辅层的层合板中心区域层间界面附近存在着层间边界层效应。层间界面处纤维走向的突变导致局部的三维应力状态和很强的应力集中。     

Analysis of free damped vibrations of laminated composite cylindrical shells

Damped free vibrations of multilayered composite cylindrical shells are investigated. Vibration and damping analysis of cylindrical shells is performed by using the first-order shear deformation theory (FOSDT). Based on other researchers' works, two damping models are developed, i.e., the energy method (EM), and the method of complex eigenvalues (MCE). Several numerical examples of the damped free vibration problem of laminated composite cylindrical shells have been solved and comparison has been made with the results of other authors.Published in Mekhanika Kompozitnykh Materialov, Vol. 31, No. 5, pp. 646–659, September–October, 1995.     

Investigation of Locally Loaded Multilayer Shells by a Mixed Finite-Element Method. 2. Geometrically Nonlinear Statement

Based on mixed finite-element approximations, a numerical algorithm is developed for solving linear static problems of prestressed multilayer composite shells subjected to large displacements and arbitrarily large rotations. As the sought-for functions, six displacements and eleven strains of the shell faces are chosen, which allows us to use nonlinear deformation relationships exactly representing arbitrarily large displacements of the shell as a rigid body. The stiffness matrix of a shell element has a proper rank and is calculated based on exact analytical integration. The bilinear element developed does not allow false rigid displacements and is not subjected to the membrane, shear, or Poisson locking phenomenon. The results of solving the well-known test problem on a nonsymmetrically fixed circular arch subjected to a concentrated load and the problem on a locally loaded toroidal multilayer rubber-cord shell are presented.     

复合材料加筋薄壁圆锥壳体有限变形的混合型理论

本文利用变分原理和平均筋条刚度法,建立了在任意载荷作用下纵向和环向密加筋复合材料圆锥壳体有限变形的Donnell型理论.考虑了面板最一般的弯曲拉伸耦合关系和加筋筋条的偏心效应的影响.导出了平衡条件、边界条件和变形协调方程.给出了以应力函数和挠度函数表示的耦合形式的非性性变系数偏微分方程组.对于一些特殊情况,给出了相应的简化方程.     

Finite element dynamic analysis of unsymmetric composite laminated beams with shear effect and rotary inertia under the action of moving loads

The finite element dynamic response of an unsymmetric composite laminated orthotropic beam, subjected to moving loads, has been studied. One-dimensional finite element based on classical lamination theory, first-order shear deformation theory, and higher-order shear deformation theory having 16, 20 and 24 degrees of freedom, respectively, are developed to study the effects of extension, bending, and transverse shear deformation. The theories also account for the Poisson effect, thus, the lateral strains and curvatures can be expressed in terms of the axial and transverse strains and curvatures and the characteristic couplings (bend–stretch, shear–stretch and bend–twist couplings) are not lost. The dynamic response of symmetric cross-ply and unsymmetric angle-ply laminated beams under the action of a moving load have been compared to the results of an isotropic simple beam. The formulation also has been applied to the static and free vibration analysis.     

Stability and free vibration analyses of double-bonded micro composite sandwich cylindrical shells conveying fluid flow

In this study, based on Reddy cylindrical double-shell theory, the free vibration and stability analyses of double-bonded micro composite sandwich cylindrical shells reinforced by carbon nanotubes conveying fluid flow under magneto-thermo-mechanical loadings using modified couple stress theory are investigated. It is assumed that the cylindrical shells with foam core rested in an orthotropic elastic medium and the face sheets are made of composites with temperature-dependent material properties. Also, the Lorentz functions are applied to simulation of magnetic field in the thickness direction of each face sheets. Then, the governing equations of motions are obtained using Hamilton's principle. Moreover, the generalized differential quadrature method is used to discretize the equations of motions and solve them. There are a good agreement between the obtained results from this method and the previous studies. Numerical results are presented to predict the effects of size-dependent length scale parameter, third order shear deformation theory, magnetic intensity, length-to-radius and thickness ratios, Knudsen number, orthotropic foundation, temperature changes and carbon nanotubes volume fraction on the natural frequencies and critical flow velocity of cylindrical shells. Also, it is demonstrated that the magnetic intensity, temperature changes and carbon nanotubes volume fraction have important effects on the behavior of micro composite sandwich cylindrical shells. So that, increasing the magnetic intensity, volume fraction and Winkler spring constant lead to increase the dimensionless natural frequency and stability of micro shells, while this parameter reduce by increasing the temperature changes. It is noted that sandwich structures conveying fluid flow are used as sensors and actuators in smart devices and aerospace industries. Moreover, carotid arteries play an important role to high blood rate control that they have a similar structure with flow conveying cylindrical shells. In fact, the present study can be provided a valuable background for more research and further experimental investigation.     

Numerical elastic-plastic simulation of interlaminar stresses in a notched angle-ply thermoplastic composite laminate

A thermoplastic angle-ply AS4/PEEK laminate with a hole is considered. The interlaminar stresses along the hole edge at different interfaces under uniaxial extension are investigated. According to the symmetries of the structure and loading, a suitable finite-element model is developed. Utilizing a three-dimensional elastic-plastic finite-element procedure elaborated previously, a finite-element modeling of the interlaminar stresses in a thick angle-ply composite laminate is carried out. Based on the interlaminar stresses obtained, the dangerous locations of delamination initiation are predicted. The results obtained indicate that there is some relationship between the dangerous locations and fiber orientations in the adjacent layers, and it maybe inferred that the critical locations are near the regions where the hole edge is tangent to the fiber orientation in the layers adjacent to the interface. The interlaminar stresses at the same interfaces are not sensible to distances from the midplane of the laminate. Very high interlaminar tensile stresses are found to exist on the hole edge at the +25°/+25° or –25°/–25° interfaces, and delaminations can initiate there first. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 45, No. 3, pp. 427-440, May-June, 2009.