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.     

Non-linear buckling for the surface rectangular delamination of laminated piezoelectric shells

An analytical method is presented to study the non-linear buckling characteristic of rectangular local delamination near the surface of fiber-reinforced piezoelectric lamination shells under coupled mechanical and electric loads. The stacking sequence of fiber reinforced lamination shells with piezoelectric layers is considered as symmetry, but the stacking sequence of rectangular local delamination sub-shells is arbitrary. Based on the nonlinear displacement mode of delaminated sub-shells, the effects of electric fields, the geometrical, physical parameters and stacking sequences of piezoelectric laminated shells on the non-linear local buckling for rectangular delamination near the surface of piezoelectric laminated base-shells are solved.     

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.     

Explicit through-thickness integration schemes for geometric nonlinear analysis of laminated composite shells

Degenerated shell elements were found to be attractive in solving homogeneous shell problems. Direct extension of the same to layered shells becomes computationally inefficient as, in the computation of element matrices, 3-D numerical integration in each layer and summation over the layers have to be carried out. In order to make the formulation efficient, explicit through-thickness schemes have been devised for linear problems. The present paper deals with the extension of the same to geometric nonlinear problems with options of small and large rotations. The explicit through-thickness integration becomes possible due to the assumption on the variation of inverse Jacobian through the thickness. Depending on the assumptions, three different schemes under large and small rotation cases have been presented and their relative numerical accuracy and computational efficiency have been evaluated. It has been observed that there is no sacrifice on the numerical accuracy due to the assumptions leading to the explicit through-thickness integration, but at the same time, there is considerable saving in the computational time. The computational efficiency improves as the number of layers in the laminate increases. The small rotation formulation with the assumption of linear variation of Jacobian inverse across the thickness and based on further approximation regarding certain submatrices is seen to be computationally efficient, as applied to geometric nonlinear layered shell problems.     

Post buckling response of laminated composite plate on elastic foundation with random system properties

This paper deals with second order statistics of post buckling load of shear deformable laminated composite plates resting on linear elastic foundation with random system properties. The formulation is based on higher order shear deformation plate theory in general von Karman sense, which includes foundation effect using two-parameter Pasternak model. The random system equations are derived using the principal of virtual work. A finite element method is used for spatial descretization of the laminate with a reasonable accuracy. A perturbation technique has been the first time successfully combined with direct iterative technique by neglecting the changes in nonlinear stiffness matrix due to random variation of transverse displacements during iteration. The numerical results for the second order statistics of post buckling loads are obtained. A detailed study is carried out to highlight the characteristics of the random response and its sensitivity to different foundation parameters, the plate thickness ratio, the plate aspect ratio, the support condition, the stacking sequence and the lamination angle on the post buckling response of the laminate. The results have been compared with existing results and an independent Monte Carlo simulation.     

On the theories used for the wave propagation in laminated composite thin elastic shells

In this paper, the problem of propagation of free harmonic waves in cross-ply laminated thin elastic shells is considered. For this problem, a theoretical unification of the most commonly used, in physical and engineering applications, thin shell theories which take into consideration transverse shear deformation effects is presented. In more detail, the problem is formulated in such a way that by using some tracers, which have the form of Kronecker's deltas, the obtained stress-strain relations, constitutive equations and equations of motion produce, as special cases, the corresponding relations and equations of the transverse shear deformable analogs of Donnell's, Love's and Sanders' theories. Using an eigenvalue form solution of the equations of motion, a comparison of corresponding numerical results obtained on the basis of all of the afore-mentioned theories is made. Comparisons with corresponding results obtained on the basis of the classical thin shell theories of Donnell, Love, Sanders and Flugge are also made.

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Resumé On étudie un problème de propagation d'ondes harmoniques libres dans une fine coque cylindrique, élastique, composée de lamelles croisées. On présente une unification des théories les plus courantes que les ingénieurs et physiciens appliquent aux problèmes de coques minces sous considération de la déformation due au cisaillement transverse. En détails, le problème est formulé de telle façon qu'en utilisant des opérateurs de trace (sous forme du symbole de Kronecker) les relations obtenues: contrainte-déformation, équations constitutives et équations de mouvement donnent comme cas spéciaux les relations correspondantes et les équations des problèmes analogues (déformation de coques minces par cisaillement transverse) des théories de Donnell, Love et Sanders. En utilisant une solution aux valeurs propres des équations de mouvement, on compare les résultats numériques obtenus grâce aux théories mentionées ci-dessus aux résultats correspondants sur la base des théories classiques de Donnell, Love, Sander et Flugge.

     

Creep buckling of glass-reinforced plastic cyclindrical shells

The buckling modes of cylindrical shells made of a polymeric composite with creep properties are considered. The initial imperfections of the shell are characterized by a Fourier series. The time dependence of a large number of harmonics of the Fourier series is investigated by means of nonlinear equations of the Timoshenko type. It is established that some are damped, while others grow at an ever-increasing rate. It is shown that in the course of time the effective shape of the deflections is transformed and at the critical moment the shell buckles in a mode that differs from the shape of the initial deflections.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 4, pp. 697–703, July–August, 1971.