Behavior Of Thin Shells Research Articles

Stability and dynamics of scalar field thin-shell for renormalization group improved Schwarzschild black holes

In this paper, our main concern is to obtain the geometrical structure of a thin-shell through the match of inner flat and outer the renormalization group improved Schwarzschild black hole through a well-known cut and paste approach. Then, we are interested to discuss the dynamical configuration of thin-shell composed of a scalar field (massive and massless) through an equation of motion and Klein–Gordon’s equation. Finally, the stable configuration of thin-shell is observed through the linearized radial perturbation approach about equilibrium shell radius with a phantomlike equation of state, i.e., quintessence, dark energy, and phantom energy. It is noted that stable/unstable behavior of thin-shell is found after the expected position of the event horizon of an exterior manifold. It is concluded that the stability of a thin-shell is greater for the choice of Schwarzschild black hole as compared to the renormalized group of improved Schwarzschild black holes.

The Influence of Curvature on Convection in a Temperature‐Dependent Viscosity Fluid: Implications for the 2‐D and 3‐D Modeling of Moons

AbstractConvection in terrestrial bodies occurs within spherical shells described by the ratio, f, of their bounding radii. Previous studies that have modeled convection with a temperature‐dependent viscosity noted the strong effect of f on transition to the stagnant‐lid regime. Here we analyze stagnant‐lid convection in 2‐D and 3‐D systems with curvatures including relatively small‐core shells (f as small as 0.2) as well as in thin shell and plane‐layer cases. Several peculiarities of convection in a strongly temperature‐dependent viscosity fluid are identified for both high and low curvature systems. We demonstrate that effective Rayleigh numbers may differ by orders of magnitude in systems with different curvatures, when all other parameters are maintained at fixed values. Furthermore, as f is decreased, the nature of stagnant‐lid convection in small‐core bodies shows a divergence in the temperature and velocity fields found for 2‐D annulus and 3‐D spherical shell systems. In addition, substantial differences in the behavior of thin shell (f = 0.9) and plane‐layer (Cartesian geometry) models occur in both 2‐D and 3‐D, indicating that the latter (emulating a toroidal topology rather than spherical) may be inappropriate approximations for modeling variable viscosity convection in thin spherical shells. Our findings are especially relevant to understanding and accurately modeling the thermal structure that may exist in bodies characterized by thin shells (e.g., f = 0.9) or relatively small cores, such as shells comprising the Galilean satellites and other moons.

Effect of Loading Rate Dependence on Unstable Behavior of Thin-Shell Structured Beams under Axial Compression- Elucidation of Mechanism and Effect of Beam Aspect Ratio on Loading Rate Dependence

Effect of Loading Rate Dependence on Unstable Behavior of Thin-Shell Structured Beams under Axial Compression- Elucidation of Mechanism and Effect of Beam Aspect Ratio on Loading Rate Dependence

Incremental analysis of the nonlinear behavior of thin shells

The paper proposes a method of incremental loading for solving nonlinear problems of shell theory. A feature of this method is that the same algorithm is used before buckling, at the limit point, and after buckling. The method is based on the assumption that all the unknowns, including the load parameter, are on an equal footing. It is shown that the method can be used to solve algebraic equations with Cramer's rule involved to avoid numerical instability in the neighborhood of the limit point. Test problems confirm the validity of the approach

Postbuckling analysis of elastic shells of revolution considering mode switching and interaction

The postbuckling response of shells is known to exhibit complex phenomena including mode switching and interaction, particularly in the advanced postbuckling range. The existing literature contains many initial postbuckling analyses as well as advanced postbuckling analyses for a single buckling mode, but little work is available on the advanced postbuckling analysis of shells of revolution considering mode switching and interaction. In this paper, a numerical method for the advanced postbuckling analysis of thin shells of revolution subject to torsionless axisymmetric loads is presented, in which such mode switching and interaction are properly captured. Numerical results obtained using the present method for several typical problems not only demonstrate the capability of the method, but also lead to significant observations concerning the postbuckling behavior of thin shells of revolution. In particular, the results show that strong interaction between different harmonic modes may exist and the transition of deformation mode from one to another is gradual. Consequently, the conventional approach of finding the postbuckling path of a shell as the lower festoon curve of postbuckling paths of individual harmonic modes is not valid and is at best a convenient approximation.

Computer simulation of the buckling behavior of thin shells under quasi static loads

This paper concerns the theory and implementation of a numerical procedure that is capable of solving the collapse process of a structure when it is loaded past its ultimate carrying strength. The procedure is a combination of two generally available methods: A path following method for the quasi static part of the solutions and a transient method for the dynamic part. The simulation of a compression test on a thin walled cylindical shell with a local imperfection is provided to demonstrate the effectiveness of the strategy employed.

Full and von Karman geometrically nonlinear analyses of laminated cylindrical panels

A total Lagrangian-type nonlinear analysis for prediction of large deformation behavior of thick laminated composite cylindrical shells and panels is presented. The analysis, based on the hypothesis of layerwise linear displacement distribution through thickness, accounts for fully nonlinear kinematic relations, in contrast to the commonly used von Karman nonlinear strain approximation, so that stable equilibrium paths in the advanced nonlinear regime can be accurately predicted. The resulting degenerated surface-parallel quadratic (16-node) layer element, with 8 nodes on each of the top and bottom surfaces of each layer, has been implemented in conjunction with full and reduced numerical integration schemes to efficiently model both thin and thick shell behavior. The modified Newton-Raphson iterative scheme with Aitken acceleration factors is used to obtain hitherto unavailable numerical results corresponding to fully nonlinear behavior of the analyzed panels. A two-layer [0/90] thin/shallow clamped cylindrical panel is investigated to assess the convergence rate for full and reduced integration schemes and to check the accuracy of the present degenerate cylindrical shell layer element. Accuracy of the von Karman nonlinear approximation, currently employed in many investigations on buckling/postbuckling behavior of thin shells, is assessed, in the case of laminated thin cylindrical panels, by comparing the numerical results obtained using this approximation with those due to fully nonlinear kinematic relations, especially in the advanced stable postbuckling regime.

On the use of various shell theories in the analysis of axisymmetrically loaded circular containers

In shell literature there are several theories concerning the behavior of thin shells and a few regarding the behavior of thick and moderately thick shells. This paper is an attempt to bridge the gap that exists in the practicing engineer's mind as to when the validity of the theory of thin shells ceases and when that of thick shells begins. The problem of an axisymmetrically loaded container in the form of a cylindrical shell is analyzed, using both thick and thin shell theories for various values of t R and a recommendation is made regarding the bifurcation point between thin and thick shell theories.

Physical Strains in Nonlinear Thin Shell Theory

Expressions for the physical tangential and bending strains of nonlinear thin elastic shell theory in nonorthogonal coordinates are derived in a new, relatively compact form. The geometric and physical significance of the results is interpreted, where possible. In addition, the quantities describing the differential geometry of a deformed surface are also given. All results obtained are exact in the sense that no restrictions are imposed on the magnitude of strains in the derivations. The expressions for the nonlinear case are compared with the corresponding formulas of the linear theory. The results obtained together with further results to be published on the strains of the parallel surface, the statics of shells, and constitutive relations find direct application in the analysis of the nonlinear behavior of thin shells.