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The chemical plating methods were used to prepare nanoshell Si/Cu composites. The methods delivered a high initial discharge and charge capacity of 1312.1 and 1008.8 mAh/g, respectively. The electrochemical properties of the composites retained about 662.6 mAh/g after 100 cycles. The Cu coating improved the electrical conductivity but hindered the direct contact of the Si particles and the electrolyte, which suppressed the SEI growth.

We are interested in the asymptotic analysis of the eigenvalue problem of clamped cylindrical shells. We analyze the lowest eigenvalues as a function of the shell thickness t, the asymptotic behavior of the respective eigenfunctions, and show how the different displacement components and parts of the energy scale in t. As a consequence, we are able to single out the numerical difficulties of the problem, which, surprisingly for a formally bending inhibited problem, include the presence of locking. Extensive numerical tests are included.

We prove a general adimensional energy estimate between the solution of the three-dimensional Lamé system on a thin clamped shell and a displacement reconstructed from the solution of the classical two-dimensional Koiter model. This estimate only involves the thickness parameter ε, constants attached to the mid-surface S, the two-dimensional energy of the solution of the Koiter model and "wavelengths" associated with this latter solution. This bound is in the same spirit as Koiter's heuristic estimate in Ref. 26 and can be viewed as an a posteriori estimation of the modeling error by means of the two-dimensional solution. It is general with respect to the geometry of the mid-surface S which is an arbitrary smooth manifold with boundary. Taking boundary layer terms into account, we prove that our estimates are sharp in the cases of plates and elliptic shells.

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A generalized conforming finite element theory was presented to satisfy the C¹ continuity condition for plate and shell element. The effectiveness of the theory in the linear analysis has been proved. This paper discusses the membrane locking phenomenon of shallow shell element based on the satisfaction of the requirement of rigid body motion, and a technique is developed to eliminate the membrane locking phenomenon. Accordingly a geometrically nonlinear generalized conforming rectangular shallow shell element with tangential degrees of freedom of midpoints of sides is formulated. Nonlinear numerical analysis of shell stability shows that the element exhibits high precision and fast convergence characteristics.

Presented here is an analytical solution to the free vibration problem of an isotropic cylindrical panel with SS2-type simply supported boundary conditions based on Reddy's third order shear deformation shell theory. Using the principle of virtual work, the Reddy's shell theory generates five highly coupled partial differential equations in terms of three unknown displacements and two unknown rotations. The partial differential equations in conjunction with the prescribed boundary conditions are solved using displacement functions expressed in terms of double Fourier series expansion. Cylindrical panels with various aspect and thickness ratios are considered in the study of convergence behavior and parametric variation of the eigenvalues. The eigenvalues and mode shapes obtained in this study are compared with those obtained from the finite element software package ANSYS. The hitherto unavailable analytical solutions can be used as benchmarks for checking the accuracy of various approximate methods such as the Rayleigh–Ritz, finite element and finite difference methods.

A study on the influence of meridional curvature on the buckling and postbuckling behavior of cross-ply laminated shells of revolution subjected to thermal and mechanical loads is carried out using the semianalytical finite element method. The nonlinear equations are solved using the Newton–Raphson iterative technique. The adaptive displacement control method is employed to trace the equilibrium path. Examined herein are the effects of positive and negative meridional curvature, the number of layers and the number of circumferential waves on the buckling/postbuckling behavior of cross-ply laminated, simply supported shells under thermal, external pressure, torsional and axial loadings. It is found that the critical load increases with the increase in the rise-to-radius ratio of positive meridional curvature shells for the loading cases considered. The critical temperature, torsional, axial loads decrease and the critical external pressure increases with increasing magnitude of the rise-to-radius ratio of negative meridional curvature shells. The postbuckling response of shells exposed to a uniform temperature rise is of a hardening nature for both positive and negative meridional curvature cases. Shells subjected to external pressure show a softening type of initial postbuckling response for positive meridional curvature, and a hardening type of postbuckling response for negative meridional curvature. The qualitative nature of postbuckling characteristics for torsional and axial loading cases may be softening, hardening or initially softening and later hardening, depending upon the combined influence of the rise-to-radius ratio, the number of circumferential waves and the number of layers.

The dynamics and stability of rotating circular cylindrical shells partially filled with ideal liquid is analyzed. The structural dynamics of the shell is modeled by using the first-order shear deformable shell theory and the flow inside the cylinder is simulated by a quasi 2D model based on the Navier–Stokes equations for ideal liquid. The fluid and structural models are combined using the nonpenetration condition of the flow on the wetted surface of the cylinder and the fluid pressure on the flexible shell. The obtained fluid–structure model is employed for the determination of the stable regions of the spinning frequency of the cylinder. A series of case studies are performed on the governing parameters of the instability of the cylinder and some conclusions are outlined.

To deal with the effect of liquid storage on the distribution of implosion, a fluid–solid coupling model is built for the shared nodes of implosion in the liquid storage tank. The displacement compatibility and acceleration and speed coupling are achieved between the implosion field (gas, liquid) and liquid storage tank. First, using this model, the implosion-generated overpressure distribution and structural response under the working condition of half filled tank are obtained. The results show that the overpressure, displacement and stress are high on the shell near the liquid level. Then, the effects of both the TNT equivalent and liquid level on implosion in the liquid storage tank are studied. As the TNT equivalent increases, the maximum overpressure, displacement and stress on the shell near the liquid level increase. Consequently, the maximum overpressure and displacement on the shell near the liquid level exceed those at the roof-to-shell connection of the tank. In contrast, as the liquid level increases, the maximum stress and displacement first increase near the shell. After reaching the peaks near half filled level, they begin to decrease. Only when the liquid reaches a certain level, it can have an attenuating effect on the overpressure at the bottom-to-shell connection. However, if the liquid level continues to rise beyond a certain threshold, the attenuating effect is no longer prominent.

Membranes have been popularly used in the fields of civil engineering and aerospace engineering. When wrinkled, a membrane loses its stiffness in the direction perpendicular to wrinkles and is more sensitive to wind loads. This paper numerically studied the wind-induced responses of a wrinkled membrane and their variations with respect to wind speed, wind direction and wrinkling deformation. Based on the stability theory of plates and shells, the wrinkling deformation of a rectangular membrane under shear was obtained by post-buckling analysis. Then, by using the wind load derived from a wind tunnel test, the dynamic responses of the wrinkled membrane were numerically analyzed for different wind speeds, wind directions and wrinkling deformations. The results indicate the following: (1) the displacement and extreme stresses of a membrane are gradually intensified with an increase in the wind speed; (2) the wind direction plays an important role in the displacement, but it has little effect on the stresses and (3) the displacement increases with the wrinkling deformation, and the extreme stresses are intensified with an increase in the pre-tension. This study on the wind-induced responses of a wrinkled membrane is helpful to the understanding of the complex behavior of a wrinkled membrane under wind loads while reducing the adverse effects of wrinkling deformation and ensuring the dynamic stability of membrane structures.

Segmentation of 3D cardiac images using a deformable elastic model of the heart proved to be significantly improved by applying special boundary conditions on the elastic model [15]. The purpose of this paper is to derive those boundary conditions by means of a rigourous convergence result. We consider a simplified two-layer elastic shell model and show that when the thickness ε of the thin external fibrous layer tends to 0 it can be replaced by the above mentioned boundary conditions on the internal layer. A mixed variational formulation of the problem in curvilinear coordinates is introduced. This formulation is then scaled in order to be defined over an ε-independent domain. Finally, several a priori estimations on the solution are obtained which enable us to pass to the limit and prove our result.

We study the dynamic fracture of thin-walled structure mainly due to impact and explosive loading. Therefore, we make use of a meshless smoothed particle hydrodynamics (SPH) shell formulation based on Mindlin–Reissner's theory. The formulation is an extension of the continuum-corrected and stabilized SPH method, so that thin structure can be modeled using only one particle characterizing mean position of shell surface. Fracture is based on separation of particles. We study tearing of pre-notched plates, fracture due to impact loading and dynamic fracture of cylindrical shells.

To determine strength allowables for cylinders–such as aircraft fuselages–made of fiber-matrix composites, practical analytical tools are needed to determine damage extent and residual strength around cutouts. A higher-order shell theory is used to analyze compressive and tensile loads on a graphite/epoxy laminated cylinder containing a square cutout. Failure in the fiber, matrix, or lamination is determinated by the Hashin failure criterion and modeled by reducing the appropriate stiffness terms. This results in a redistribution of stress, leading to further failure. Under fatigue loads, graphite/epoxy will lose stiffness as cycles increase. To model this effect of cyclic loading, the stiffness matrix is further reduced at the beginning of each cycle. Therefore, the static analysis can be used to predict damage under fatigue loading by representing several thousand fatigue cycles in a single computational cycle. In compression loading, the reduction in stiffness ultimately leads to geometric instability, or collapse. In tension, the reduction is stiffness–to account for fatigue–increases the displacements, but not the stress. Therefore, a strain-based criterion is added to induce macromechanical failure from the cyclic loading. The material damage propagates until failure of the curved panel occurs. The objective is not to model the micromechanical failure in the structure, but rather to determine the damage extent, stress redistribution, and residual strength of composite cylinders under fatigue loading.

In this paper the finite element procedure for analysing the postbuckling behaviours of shallow spherical shells is developed. The numerical simulations for the previously tested experimental data of pressurised thin-walled shallow spherical shells have been done by using a degenerated nine-node shell element with mixed interpolation functions. The nonlinear pre-buckling paths have been statically calculated, and then the corresponding postbuckling behaviours have also been obtained through nonlinear dynamic analysis. It is shown that if both an internal and an external viscous damping are considered, the good simulations even for the dynamic postbukling paths can be obtained.

A finite element analysis of a double layered shell with a circular hole is carried out using a commercial finite element software. The model proposed has been used to perform a stress analysis on three pipes with different sized hole. Moreover, thermal expansion has been implemented in the testing. For the purpose of the research, the elastic properties of the materials have been considered and the results compared with the authors’ previous publication. The outcome of the investigation will benefit towards the design of optimal and sustainable pipes with circular cut outs.