Dynamic Response Of Spherical Shell Research Articles

Investigation on dynamic response of thin spherical shells impacted by flat-nose projectile based on a novel damage model

Thin-shell structures are widely used in various engineering applications. It is essential to investigate the impact resistance of thin-shell structures, to provide theoretical support for engineering applications. Numerous impact tests have been conducted on thin spherical shells using ballistic guns. The effects of the impact velocity and shell thickness on the deformation and fracture of thin spherical shells are summarized. Moreover, a novel damage model based on statistic damage mechanics is proposed to better predict dynamic responses of thin shells impacted by projectiles. Considering that fracture surfaces are formed by void evolution and are affected by the stress states, the damage level is defined as the ratio of the statistical cross-sectional area of the voids to the cross-sectional area of the representative elements. Utilizing statistical methods, the incorporation of continuous void nucleation, ellipsoidal void growth, and the acceleration of dynamic void evolution are introduced into the novel damage model. Subsequently, numerical investigations of the dynamic response of spherical shells under impact are conducted based on the proposed damage model. The numerical results are consistent with the experimental results in terms of the depression deformations and strain signals. The effects of shell thickness and double-layer structures on the dynamic response of spherical shells are investigated via numerical simulations considering the novel damage model in detail. The results demonstrate that the proposed model can accurately predict the dynamic response of spherical shells impacted by flat-nose projectiles, thus serving as a valuable reference for engineering design.

Dynamic response of spherical shells subjected to the underwater impulse

The dynamic response of spherical shells under impact loads is investigated experimentally. The analysis focuses on the effects of flyer velocity, shell thickness, and shell curvature radius on shell deformation. The spherical shells are subjected to underwater shock waves of different intensities using a projectile-impact-based underwater shock tube. The dynamic response of the spherical shell is captured by the method of three-dimensional digital image correlation with high-speed photography. The response mechanism of the spherical shells is analyzed by the method of experiment and numerical simulations. The results show that the residual displacement of the center point of the target plate has a nonlinear relationship with the thickness and curvature radius of the target plate under the same underwater impact load. The slope of the residual displacement-curvature radius curve of the center point of the target plate increases with the decrease of the thickness under the same thickness, and the slope of the residual displacement-thickness curve of the center point of the target plate increases with the increase of the curvature radius under the same curvature radius. Quantitative structure–load–performance relation is carried out to facilitate the advanced study of metallic structures and guide the impact resistance design of spherical shells in marine structures.

Deformation and failure of thin spherical shells under dynamic impact loading: Experiment and analytical model

Thin curved shells are widely used in engineering. A shallow spherical shell is an effective representation of a curved shell affected by local impact loading. Therefore, the dynamic response of spherical shells under impact loading should be investigated to provide a design reference for curved shells applicable to engineering fields. In this study, the dynamic response and perforation of an aluminum spherical shell impacted by a cylindrical projectile were investigated theoretically. An isometric transformation was adopted to describe the major bending deformation of the spherical shell around the impact point. In addition, an edge region between the major bending part and an undeformed part was observed experimentally and described using a deformation mode. Hamilton's principle was adopted to derive the governing equations of the dynamic response of the impacted spherical shell. Furthermore, a viscoplastic strengthened model was introduced to describe the membrane force and bending moment of the perforation, whereas a rigid–plastic model was used to calculate the force and moment of the other parts of the spherical shell. The governing equations combined with the strengthened model were solved using the Runge–Kutta method. A comparison between the theoretical predictions and experimental results indicated a good agreement between them. Finally, the effects of the parameters set in the governing equations of the theoretical prediction were analyzed. We observed that the theoretical model predicted dimple radius more accurately than dimple depth. The dimple depth is linearly proportional to the impact velocity. In addition, the assumed sizes of the shear region of perforation only affect the ballistic limit and deformation generated by a velocity higher than the ballistic limit. The deformation and perforation of the impacted shell are almost independent of the initial width of the edge region of deformation. Additionally, we observed that the ballistic limit of the shell is linearly proportional to the shell thickness.

Modified numerical model for simulating fluid-filled structure response to underwater explosion with cavitation

In this paper, a numerical method is established to analyze the response of fluid-filled structure to underwater explosion with cavitation and the validation of the method is illustrated. In the present implementation, the second-order doubly asymptotic approximation (DAA2) other than curved wave approximation (CWA) is used to simulate non-reflecting boundary. Based on the method, the difference between DAA2 non-reflecting boundary and CWA non-reflecting boundary is investigated; then, the influence of internal fluid volume and the influence of cavitation on dynamic response of spherical shell are analyzed. Compared with CWA non-reflecting boundary, DAA2 non-reflecting boundary treats added mass effects better. When the internal fluid is full, the displacement and velocity of spherical shell decrease, but, when the internal fluid is half, the displacement and velocity of spherical shell increase. The effect of cavitation is more obvious at the trailing point than at the leading point of spherical shell.

Dynamic response of laminated orthotropic spherical shells including transverse shear deformation and rotatory inertia

In this paper, the equations of motion of axisymmetrically laminated cylindrical orthotropic spherical shells are derived. The effects of transverse shear deformation and rotatory inertia are considered. On this basis, the dynamic response of spherical shells under axisymmetric dynamic load is calculated using the finite difference method. The effects of material parameters, structural parameters and transverse shear deformation are discussed.

Non-linear static and dynamic response of spherical shells

In the present investigation an analytical technique using Chebyshev series expansion has been presented and used to study the non-linear transient behavior of shallow spherical shells with and without damping. The two coupled non-linear differential equation governing the shallow shell behavior are initially linearised using Taylor's series expansion. Results have been presented for three types of transient loadings, namely, step function, N-shaped pulse and sine wave pulse. It is shown that accurate results can be obtained using a five terms Chebyshev series expansion which is unlikely in the conventional methods.

Development of a Finite Element Model for a Guided Spherical Shell

A doubly curved anisymmetric spherical-shell finite element is utilized in order to predict the dynamic response of spherical shells for the Class V flextensional underwater acoustic transducer. The spherical shell is represented as a finite number of spherical frustra, joined at nodal circles. Norozhilov's “Thin Shell Theory” is applied and the element stiffness and mass matrices are derived and numerically integrated by utilizing Gauss-Legendre polynomials. The frequency coefficients of a spherical shell are defined. An IBM 360/75 computer is used for obtaining numerical results for varying thickness and opening angle, with guided clamped, guided pinned, clamped, and pinned boundary conditions. Numerical results for the Class V flextensional underwater transducer shell are included. Finally, a convergent test is carried out for a different number of finite elements for the Class V flextensional underwater transducer shell having pinned boundary conditions. The results agreed almost perfectly with earlier results obtained experimentally.