Analyzing the stress–strain state of thick cylindrical shells

Two approaches to the analysis of the stress–strain state of thick cylindrical shells are elaborated. The shell is divided by concentric cross-sectional circles into several coaxial cylindrical shells. Each of these shells has its own curvature determined on its midline. The stress–strain state of the original shell is described by satisfying the interface conditions between the component shells. The distribution of unknown functions throughout the thickness is determined by finding the analytic solution of a system of differential equations in the first approach and is approximated by polynomial functions in the second approach. The stress–strain state of thick shells is analyzed. It is revealed that the effect of reduction becomes stronger with increasing curvature     

Delamination growth for composite laminated cylindrical shells under external pressure

The delamination growth may occur in delaminated cylindrical shells under external pressure.This will lead to failure of structure.By using the variational principle of moving boundary and considering the contact effect between delamination regions,in this work,the delamination growth was investigated for cylindrical shells under the action of external pressure.At the same time,according to the Griffith criterion,the formulas of energy release rate along the delamination front were obtained.In the numerical calculation,the delamination growth of axisymmetrical laminated cylindrical shells was analyzed,and the effects of delamination sizes and depths,the geometrical parameters, the material properties,and the laminate stacking sequences on delamination growth were discussed.     

Spline-approximation solution of stress–strain problems for beveled cylindrical shells

The problem of bending of beveled circular cylindrical shells is solved by parametrizing the shell and reducing the two-dimensional boundary-value problem to a one-dimensional one by the spline-collocation method. This problem is solved by the stable discrete-orthogonalization method. The effect of the variability of the geometrical parameters on the displacement fields of circular cylinders is analyzed     

Buckling of geometrically imperfect cylindrical shells — definition of a buckling load

On the basis of extensive buckling tests and analytical and numerical buckling analyses for composite cylinders it became desirable to provide a recommendation for the most reliable evaluation of stability limits for imperfect CFRP cylinders subjected to axial compression. This paper reports on different approaches including linear, non-linear and dynamic non-linear FE analysis results and discusses the related effects and potential difficulties.     

Surface waves in a piezoelectric–semiconductor composite structure

The present work deals with the propagation of interfacial surface waves in a composite consisting of homogeneous, transversely isotropic, piezoelectric halfspace underlying a thin layer of non-piezoelectric semiconductor material. The mathematical model of the problem is depicted by partial differential equations of motion for the structure and boundary conditions to be satisfied at the interface and free surface of the composite. After obtaining formal wave solution of the model the secular equation that governs the propagation of surface waves in the considered composite structure has been derived in compact form. The numerical solution of secular equation is being carried out for the composites Si–CdSe, Ge–CdSe and Ge–PZT by employing functional iteration method along with irreducible Cardano method using MATLAB programming. The computer simulated results in respect of dispersion curves, attenuation coefficient and specific loss factor of energy dissipation are presented graphically for Si–CdSe composite to illustrate the analytical developments. We have extended our analysis to Ge–CdSe and Ge–PZT composites also. However, to avoid clustering of profiles and also to have clear understanding of the variations, the computer simulated values of phase velocity and attenuation coefficient are presented in tabular form for all three considered composite structures. This work may be useful for designing and construction of surface acoustic wave (SAW) devices and electronics industry.     

Identification of parameters of models of nonlinear deformation of isotropic and composite materials on the basis of calculations and experiments aimed at analyzing the dynamic behavior of cylindrical metal–plastic shells

A method for identification of material parameters of the constitutive relations of elastoplastic and viscoelastic deformation of isotropic and composite materials is developed. The method is based on minimizing the functional of the residue of results of numerical and experimental analysis of unsteady deformation of structural elements made of examined materials. The method is tested, and prospects of its application for determining material parameters of viscoelastic and elastoplastic models of nonlinear deformation of cylindrical metal–plastic shells under explosive loading are demonstrated.     

Dynamic stability recognition of cylindrical shallow shells in Kelvin–Voigt viscoelastic medium under transverse white noise excitation

Nonlinear Dynamics - This paper investigates the problem of delay-dependent dissipativity for a class of Markovian jump neural networks with a time-varying delay. A generalized integral inequality...     

A unified Chebyshev–Ritz formulation for vibration analysis of composite laminated deep open shells with arbitrary boundary conditions

In this paper, a unified Chebyshev–Ritz formulation is presented to investigate the vibrations of composite laminated deep open shells with various shell curvatures and arbitrary restraints, including cylindrical, conical and spherical ones. The general first-order shear deformation shell theory is employed to include the effects of rotary inertias and shear deformation. Under the current framework, regardless of boundary conditions, each of displacements and rotations of the open shells is invariantly expressed as Chebyshev orthogonal polynomials of first kind in both directions. Then, the accurate solutions are obtained by using the Rayleigh–Ritz procedure based on the energy functional of the open shells. The convergence and accuracy of the present formulation are verified by a considerable number of convergence tests and comparisons. A variety of numerical examples are presented for the vibrations of the composite laminated deep shells with various geometric dimensions and lamination schemes. Different sets of classical constraints, elastic supports as well as their combinations are considered. These results may serve as reference data for future researches. Parametric studies are also undertaken, giving insight into the effects of elastic restraint parameters, fiber orientation, layer number, subtended angle as well as conical angle on the vibration frequencies of the composite open shells.     

Formation of vortex breakdown in conical–cylindrical cavities

Numerical simulations in confined rotating flows were performed in this work, in order to verify and characterize the formation of the vortex breakdown phenomenon. Cylindrical and conical–cylindrical geometries, both closed, were used in the simulations. The rotating flow is induced by the bottom wall, which rotates at constant angular velocity. Firstly the numerical results were compared to experimental results available in references, with the purpose to verify the capacity of the computational code to predict the vortex breakdown phenomenon. Further, several simulations varying the parameters which govern the characteristics of the flows analyzed in this work, i.e., the Reynolds number and the aspect ratio, were performed. In these simulations, the limits for the transitional regime and the vortex breakdown formation were verified. Steady and transient cases, with and without turbulence modeling, were simulated. In general, some aspects of the process of vortex breakdown in conical–cylindrical geometries were observed to be different from that in cylinders.     

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     

Asymptotic homogenization modeling of smart composite generally orthotropic grid-reinforced shells: Part II– Applications

A comprehensive micromechanical model for the analysis of thin smart composite grid-reinforced shells with an embedded periodic grid of generally orthotropic cylindrical reinforcements that may also exhibit piezoelectric properties is developed and applied to examples of practical importance. Details on derivation of a general homogenized smart shell model are provided in Part I of this work. The present paper solves the obtained unit cell problems and develops expressions for the effective elastic, piezoelectric and thermal expansion coefficients for the grid reinforced smart composite shell. Thus obtained effective coefficients are universal in nature and can be used to study a wide variety of boundary value problems. The applicability of the model is illustrated by means of several examples including cylindrical reinforced smart composite shells, and multi-layer smart shells. The derived expressions allow tailoring the effective properties of a smart grid-reinforced shell to meet the requirements of a particular application by changing certain geometric or physical parameters.     

Orientation of cylindrical particles in gas–solid circulating fluidized bed

The orientation of cylindrical particles in a gas–solid circulating fluidized bed was investigated by establishing a three-dimensional Euler–Lagrange model on the basis of rigid kinetics, impact kinetics and gas–solid two-phase flow theory. The resulting simulation indicated that the model could well illustrate the orientation of cylindrical particles in a riser during fluidization. The influences of bed structure and operation parameters on orientation of cylindrical particles were then studied and compared with related experimental results. The simulation results showed that the majority of cylindrical particles move with small nutation angles in the riser, the orientation of cylindrical particles is affected more obviously by their positions than by their slenderness and local gas velocities. The simulation results well agree with experiments, thus validating the proposed model and computation.     

Asymptotic analysis of linearly elastic shells: ‘Generalized membrane shells’

We consider a family of linearly elastic shells indexed by their half-thickness , all having the same middle surface % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiaadofacqGH9aqpcqaHvpGAcaGGOaGafqyYdCNbaebacaGGPaaa% aa!4317!\[S = \varphi (\bar \omega )\], with % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiabew9aQjaacQdacuaHjpWDgaqeaiabgkOimlaadkfadaahaaWc% beqaaiaaikdaaaGccqGHsgIRcaWGsbWaaWbaaSqabeaacaaIZaaaaa% aa!4812!\[\varphi :\bar \omega \subset R^2 \to R^3 \], and clamped along a portion of their lateral face whose trace on S is % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiabew9aQjaacIcacqaHZoWzdaWgaaWcbaGaaGimaaqabaGccaGG% Paaaaa!41EB!\[\varphi (\gamma _0 )\], where % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiaacIcacqaHZoWzdaWgaaWcbaGaaGimaaqabaGccaGGPaaaaa!401F!\[(\gamma _0 )\] is a fixed portion of with length % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiaacIcacqaHZoWzdaWgaaWcbaGaaGimaaqabaGccaGGPaGaeyOp% a4JaaGimaaaa!41E1!\[(\gamma _0 ) > 0\]. Let % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiaacIcacqaHZoWzdaWgaaWcbaGaeqySdeMaeqOSdigabeaakiaa% cIcacqaH3oaAcaGGPaGaaiykaaaa!45AA!\[(\gamma _{\alpha \beta } (\eta ))\] be the linearized strain tensor of S. We make an essential geometric and kinematic assumption, according to which the semi-norm % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiaacYhacqGHflY1caGG8bWaa0baaSqaaiabeM8a3bqaaiaad2ea% aaaaaa!4345!\[| \cdot |_\omega ^M \] defined by % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiaacYhacqaH3oaAcaGG8bWaa0baaSqaaiabeM8a3bqaaiaad2ea% aaGccqGH9aqpdaGadeqaamaaqababaGaaiiFaiaacYhaaSqaaiabeg% 7aHfrbbjxAHXgaiuaacaWFSaGaeqOSdigabeqdcqGHris5aOGaeq4S% dCMaeqySdeMaeqOSdiMaaiikaiabeE7aOjaacMcacaGG8bGaaiiFam% aaDaaaleaacaWGmbWaaWbaaWqabeaacaaIYaaaaSGaaiikaiabeM8a% 3jaacMcaaeaacaaIYaaaaaGccaGL7bGaayzFaaWaaWbaaSqabeaaca% aIXaGaai4laiaaikdaaaaaaa!61F1!\[|\eta |_\omega ^M = \left\{ {\sum\nolimits_{\alpha ,\beta } {||} \gamma \alpha \beta (\eta )||_{L^2 (\omega )}^2 } \right\}^{1/2} \] is a norm over the space % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiaadAfacaGGOaGaeqyYdCNaaiykaiabg2da9maacmqabaGaeq4T% dGMaeyicI4SaamisamaaCaaaleqabaGaaGymaaaakiaacIcacqaHjp% WDcaGGPaGaai4oaiabeE7aOjabg2da9iaab+gacaqGUbGaeq4SdC2a% aSbaaSqaaiaabcdaaeqaaaGccaGL7bGaayzFaaaaaa!5361!\[V(\omega ) = \left\{ {\eta \in H^1 (\omega );\eta = {\text{on}}\gamma _{\text{0}} } \right\}\], excluding however the already analyzed membrane shells, where % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiabeo7aNnaaBaaaleaacaqGWaaabeaakiabg2da9iabgkGi2kab% eM8a3baa!42F8!\[\gamma _{\text{0}} = \partial \omega \] and S is elliptic. This new assumption is satisfied for instance if % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiabeo7aNnaaBaaaleaacaqGWaaabeaakiabgcMi5kabgkGi2kab% eM8a3baa!43B9!\[\gamma _{\text{0}} \ne \partial \omega \] and S is elliptic, or if S is a portion of a hyperboloid of revolution.We then show that, as 0, the averages % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaamaalaaabaGaaGymaaqaaiaaikdadaahaaWcbeqaaiabew7aLbaa% aaGcdaWdXaqaaiaadwhadaqhaaWcbaGaamyAaaqaaiabew7aLbaaki% aabsgacaWG4bWaa0baaSqaaiaaiodaaeaacqaH1oqzaaaabaGaeyOe% I0IaeqyTdugabaGaeqyTduganiabgUIiYdaaaa!4E28!\[\frac{1}{{2^\varepsilon }}\int_{ - \varepsilon }^\varepsilon {u_i^\varepsilon {\text{d}}x_3^\varepsilon } \] across the thickness of the shell of the covariant components u _i of the displacement of the points of the shell strongly converge in the completion V _M ^#() of V() with respect to the norm % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiaacYhacqGHflY1caGG8bWaa0baaSqaaiabeM8a3bqaaiaad2ea% aaaaaa!4345!\[| \cdot |_\omega ^M \], toward the solution of a generalized membrane shell problem. This convergence result also justifies the recent formal asymptotic approach of D. Caillerie and E. Sanchez-Palencia.The limit problem found in this fashion is sensitive, according to the terminology recently introduced by J.L. Lions and E. Sanchez-Palencia, in the sense that it possesses two unusual features: it is posed in a space that is not necessarily contained in a space of distributions, and its solution is highly sensitive to arbitrarily small smooth perturbations of the data.Under the same assumption, we also show that the average % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaamaalaaabaGaaGymaaqaaiaaikdadaahaaWcbeqaaiabew7aLbaa% aaGcdaWdXaqaaiaadwhadaqhaaWcbaGaamyAaaqaaiabew7aLbaaki% aabsgacaWG4bWaa0baaSqaaiaaiodaaeaacqaH1oqzaaaabaGaeyOe% I0IaeqyTdugabaGaeqyTduganiabgUIiYdaaaa!4E28!\[\frac{1}{{2^\varepsilon }}\int_{ - \varepsilon }^\varepsilon {u_i^\varepsilon {\text{d}}x_3^\varepsilon } \] where % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiaadwhadaahaaWcbeqaaiabew7aLbaakiabg2da9iaacIcacaWG% 1bWaa0baaSqaaiaadMgaaeaacqaH1oqzaaGccaGGPaaaaa!452C!\[u^\varepsilon = (u_i^\varepsilon )\], and the solution % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiabe67a4naaCaaaleqabaGaeqyTdugaaOGaeyicI4SaamOvamaa% BaaaleaacaWGlbaabeaakiaacIcacqaHjpWDcaGGPaaaaa!465B!\[\xi ^\varepsilon \in V_K (\omega )\] of Koiter's equations have the same principal part as 0 in the same space V _M () as above. For such generalized membrane shells, the two-dimensional shell model of W.T. Koiter is thus likewise justified.We also treat the case where % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiaacYhacqGHflY1caGG8bWaa0baaSqaaiabeM8a3bqaaiaad2ea% aaaaaa!4345!\[| \cdot |_\omega ^M \] is no longer a norm over V(), but is a norm over the space % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiaadAfadaWgaaWcbaGaam4saaqabaGccaGGOaGaeqyYdCNaaiyk% aiabg2da9maacmqabaGaeq4TdGMaeyypa0JaaiikaiabeE7aOnaaBa% aaleaacaWGPbaabeaakiaacMcacqGHiiIZcaWGibWaaWbaaSqabeaa% caaIXaaaaOGaaiikaiabeM8a3jaacMcacqGHxdaTcaWGibWaaWbaaS% qabeaacaaIYaaaaOGaaiikaiabeM8a3jaacMcacaGG7aGaeq4TdG2a% aSbaaSqaaiaadMgaaeqaaOGaeyypa0JaeyOaIy7aaSbaaSqaaiaadA% haaeqaaOGaeq4TdG2aaSbaaSqaaiaaiodaaeqaaOGaeyypa0JaaGim% aiGac+gacaGGUbGaeq4SdC2aaSbaaSqaaiaaicdaaeqaaaGccaGL7b% GaayzFaaaaaa!68B8!\[V_K (\omega ) = \left\{ {\eta = (\eta _i ) \in H^1 (\omega ) \times H^2 (\omega );\eta _i = \partial _v \eta _3 = 0\operatorname{on} \gamma _0 } \right\}\], thus also excluding the already analyzed flexural shells. Then a convergence theorem can still be established, but only in the completion of the quotient space V()/V ₀() with repect to % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiaacYhacqGHflY1caGG8bWaa0baaSqaaiabeM8a3bqaaiaad2ea% aaaaaa!4345!\[| \cdot |_\omega ^M \], where % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiaadAfadaWgaaWcbaGaaGimaaqabaGccaGGOaGaeqyYdCNaaiyk% aiabg2da9maacmqabaGaeq4TdGMaeyicI4SaamOvaiaacIcacqaHjp% WDcaGGPaGaai4oaiabeo7aNjabeg7aHjabek7aIjaacIcacqaH3oaA% caGGPaGaeyypa0JaaeimaiaabMgacaqGUbGaeqyYdChacaGL7bGaay% zFaaaaaa!5997!\[V_0 (\omega ) = \left\{ {\eta \in V(\omega );\gamma \alpha \beta (\eta ) = {\text{0in}}\omega } \right\}\].These convergence results, together with those that we already obtained for membrane and flexural shells, jointly with B. Miara in the second case, thus constitute an asymptotic analysis of linearly elastic shells in all possible cases.     

Vibration characteristics of a spherical–cylindrical–spherical shell by a domain decomposition method

A domain decomposition method is used to analyze the free and forced vibration characteristics of a spherical–cylindrical–spherical shell, based on Reissner–Naghdi's thin shell theory. The joined shell is divided into some cylindrical and spherical shell segments along the meridional (longitudinal) direction. Double mixed series, i.e., Fourier series and Chebyshev polynomials, are employed as the admissible displacement functions to obtain the discretized equation of motion for the joined shell. Numerical comparisons with the results derived by FEM and those available in the previous literature are made to validate the present method. Moreover, the effects of length-to-radius and radius-to-thickness ratios on the natural frequencies are also investigated.     

SPH modeling of fluid–solid interaction for dynamic failure analysis of fluid-filled thin shells

This work concerns the prediction of failure of a fluid-filled tank under impact loading, including the resulting fluid leakage. A water-filled steel cylinder associated with a piston is impacted by a mass falling at a prescribed velocity. The cylinder is closed at its base by an aluminum plate whose characteristics are allowed to vary. The impact on the piston creates a pressure wave in the fluid which is responsible for the deformation of the plate and, possibly, the propagation of cracks. The structural part of the problem is modeled using Mindlin–Reissner finite elements (FE) and Smoothed Particle Hydrodynamics (SPH) shells. The modeling of the fluid is also based on an SPH formulation. The problem involves significant fluid–structure interactions (FSI) which are handled through a master–slave-based method and the pinballs method. Numerical results are compared to experimental data.     

Propagation of a mode-III interfacial crack in a piezoelectric–piezomagnetic bi-material

The transient response of a semi-infinite mode-III interfacial crack propagating between piezoelectric (PE) and piezomagnetic (PM) half spaces is investigated in this paper. The integral transform method together with the Wiener–Hopf and Cagniard–de Hoop techniques is used to solve the mixed boundary value problem under consideration. The existence of generalized Maerfeld–Tournois interfacial wave is discussed and the solutions of the coupled fields are derived for four different cases of bulk shear wave velocity. The dynamic intensity factors of stress, electric displacement and magnetic induction as well as energy release rate (ERR) are obtained in explicit forms. The numerical results of the universal functions and dimensionless ERR for several different material combinations are presented and discussed in details. It is found that the Bleustein–Gulyaev (generalized Maerfeld–Tournois) waves dominate the dynamic characteristics of the interfacial crack propagation in PE–PM bi-material.     

Limiting deformability and strength of basalt–plastic shells under internal explosive loading

The dynamic strength and deformability of basalt–plastic specimens under single pulsed (explosive) loading are studied experimentally. The results obtained show that the basalt–plastic specimens possess high specific strength and their strength characteristics are close to those of similar tubular specimens from glassreinforced plastic based on a highmodulus glass fiber. It is found that a twofold increase in all geometrical dimensions of the specimens does not affect their specific carrying capacity.     

Control problems of Chen–Lee system by adaptive control method

Nonlinear Dynamics - This paper investigates the control problems of Chen–Lee system. Based on control theory of nonlinear systems, the adaptive controllers were proposed to achieve...     

Time-dependent thermoelastic creep analysis of rotating disk made of Al–SiC composite

Time-dependent creep stress redistribution analysis of rotating disk made of Al–SiC composite is investigated using Mendelson’s method of successive elastic solution. All mechanical and thermal properties except Poisson’s ratio are radial dependent based on volume fraction percent of SiC reinforcement. The material creep behavior is described by Sherby’s constitutive model using Pandey’s experimental results on Al–SiC composite. Loading is an inertia body force due to rotation and a distributed temperature field due to steady-state heat conduction from inner to outer surface of the disk. Using equations of equilibrium, stress strain, and strain displacement, a differential equation, containing creep strains, for displacement is obtained. History of stresses and deformations are calculated using method of successive elastic solution. It is concluded that the uniform distribution of SiC reinforcement does not considerably influence on stresses. However, the minimum and most uniform distribution of circumferential and effective thermoelastic stresses belongs to composite disk of aluminum with 0% SiC at inner surface and 40% SiC at outer surface. It has also been found that the stresses, displacement, and creep strains are changing with time at a decreasing rate so that after almost 50 years the solution approaches the steady-state condition.