scholarly journals Strain Growth in a Finite-Length Cylindrical Shell Under Internal Pressure Pulse

2017 ◽  
Vol 139 (2) ◽  
Author(s):  
Qi Dong ◽  
Q. M. Li ◽  
Jinyang Zheng
Keyword(s):  
Cylindrical Shell ◽  
Boundary Conditions ◽  
Internal Pressure ◽  
Finite Length ◽  
Pressure Pulse ◽  
Elastic Response ◽  
Local Dynamic ◽  
Growth Phenomenon ◽  
Modal Coupling ◽  
Elastic Responses

Strain growth is a phenomenon observed in the elastic response of containment vessels subjected to internal blast loading. The local dynamic response of a containment vessel may become larger in a later stage than its response in the earlier stage. In order to understand the possible mechanisms of the strain growth phenomenon in a cylindrical vessel, dynamic elastic responses of a finite-length cylindrical shell with different boundary conditions subjected to internal pressure pulse are studied by finite-element simulation using LS-DYNA. It is found that the strain growth in a finite-length cylindrical shell with sliding–sliding boundary conditions is caused by nonlinear modal coupling. Strain growth in a finite-length cylindrical shell with free–free or simply supported boundary conditions is primarily caused by the linear modal superposition, possibly enhanced by the nonlinear modal coupling. The understanding of these strain growth mechanisms can guide the design of cylindrical containment vessels.

Investigation on the Mechanisms of Strain Growth in Cylindrical Containment Vessels Subjected to Internal Blast Loading

2008 ◽  
Author(s):  
Q. Dong ◽  
Q. M. Li ◽  
J. Y. Zheng
Keyword(s):  
Cylindrical Shells ◽  
Blast Loading ◽  
Elastic Response ◽  
Mode Shapes ◽  
Local Dynamic ◽  
Element Simulation ◽  
Growth Phenomenon ◽  
Modal Coupling ◽  
Internal Blast Loading ◽  
Elastic Responses

Strain growth is a phenomenon observed in the elastic response of containment vessels subjected to internal blast loading. The local dynamic response of a containment vessel may become larger in a later stage than its response in the earlier stage. In order to find out the possible mechanisms of the strain growth phenomenon, the natural frequencies and mode shapes of various vibration modes in cylindrical shells with different boundary conditions are obtained theoretically and numerically. The dynamic elastic responses of cylindrical shells subjected to internal blast loading are studied by theoretical analysis and finite element simulation using LS-DYNA. It is found that strain growth in cylindrical containment vessels is mainly caused by linear modal superposition and nonlinear modal coupling. The effects of the reflected blast shock waves and structural perturbation are discussed. The proposed theory for the strain growth mechanisms may guide the safe design of cylindrical containment vessels.

Dynamic thermo-elastic response of a discrete multi-layered cylindrical shell subjected to transient thermal loading

2008 ◽  
Vol 222 (4) ◽  
pp. 549-561 ◽  
Author(s):  
J Y Zheng ◽  
X D Wu ◽  
Y J Chen ◽  
G D Deng ◽  
Q M Li ◽  
...  
Keyword(s):  
Cylindrical Shell ◽  
Boundary Conditions ◽  
Thermal Loading ◽  
Elastic Response ◽  
Elastic Part ◽  
Dynamic Part ◽  
Layered Cylindrical Shell ◽  
Stress Boundary Conditions ◽  
Transient Thermal ◽  
Stress Boundary

Explosion containment vessels (ECVs) are used to fully contain the effects of explosion events. A discrete multi-layered cylindrical shell (DMC) consisting of a thin inner cylindrical shell and helically cross-winding flat steel ribbons has been proposed, which has obvious advantages of fabrication convenience and low costs. The applications of ECVs are closely associated with blast and thermal loads, and thus, it is important to understand the response of a DMC under transient thermal load in order to develop a design code and operation procedures for the use of DMC as ECV. In this paper, a mathematical model for the elastic response of a DMC subjected to thermal loading due to rapid heating is proposed. Based on the axisymmetric plane strain assumption, the displacement solution of the dynamic equilibrium equations of both inner shell and outer ribbon layer are decomposed into two parts, i.e. a thermo-elastic part satisfying inhomogeneous stress boundary conditions and a dynamic part for homogeneous stress boundary conditions. The thermo-elastic part is solved by a linear method and the dynamic part is determined by means of finite Hankel transform and Laplace transform. The thermo-elastic solution of a DMC is compared with the solution of a monobloc cylindrical shell, and numerical results are presented and discussed in terms of winding angle and material parameters.

Progress on Mechanisms of the Strain Growth Phenomenon in Containment Vessels

2012 ◽  
Author(s):  
Q. Dong ◽  
Y. Gu ◽  
B. Y. Hu
Keyword(s):  
Blast Loading ◽  
Elastic Response ◽  
Local Response ◽  
Response Characteristics ◽  
Initial Stage ◽  
Growth Phenomenon ◽  
Modal Coupling ◽  
Internal Blast Loading ◽  
Dynamic Response Characteristics ◽  
Mode Response

Strain growth is a phenomenon observed in the elastic response of containment vessels subjected to internal blast loading. The local response of the vessel may become larger in a later stage than its breathing mode response during the initial stage. The strain growth phenomenon has attracted great attention since it was first observed in 1976, and numerous researches have been conducted to investigate the mechanisms of the strain growth phenomenon in containment vessels. In this paper, some typical results on studying the mechanisms of strain growth in cylindrical and spherical containment vessels will be given, and the discovery of the mechanism of nonlinear modal coupling is especially highlighted. The present review may provide a good understanding on the dynamic response characteristics of cylindrical and spherical containment vessels subjected to internal blast loading.

Vibration and Stability of Cylindrical Shells Containing Flowing Fluid

2002 ◽  
Author(s):  
Igor Zolotarev
Keyword(s):  
Cylindrical Shell ◽  
Boundary Conditions ◽  
Finite Length ◽  
Natural Frequencies ◽  
Critical Flow ◽  
Thin Shells ◽  
Fluid Viscosity ◽  
Critical Flow Velocity ◽  
Flowing Fluid ◽  
The Stability

Natural frequencies and the thresholds for loosing the stability of thin-walled cylindrical shell conveying by flowing fluid are theoretically studied. Potential flow theory for fluid and 3D theory for thin shells are used. The shells of finite length are considered for the different case of boundary conditions at the edges of the shell, and their influence on the critical flow velocities for flutter are demonstrated. The fundamental importance of boundary conditions considered for fixing the edges of the cylindrical shell of finite length is shown. When the clamped - simply supported boundary conditions are assumed, the critical flow velocity for flutter is very low, even if the energy dissipation due to the fluid viscosity was taken into account.

scholarly journals Elastostatics of Bernoulli–Euler Beams Resting on Displacement-Driven Nonlocal Foundation

Nanomaterials ◽  
2021 ◽  
Vol 11 (3) ◽  
pp. 573
Author(s):  
Marzia Sara Vaccaro ◽  
Francesco Paolo Pinnola ◽  
Francesco Marotti de Sciarra ◽  
Raffaele Barretta
Keyword(s):  
Boundary Conditions ◽  
Structural Engineering ◽  
Beam Deflection ◽  
Soil Reaction ◽  
Differential Problem ◽  
Reaction Field ◽  
Ill Posed ◽  
Elastic Responses ◽  
Benchmark Solutions ◽  
Well Posed

The simplest elasticity model of the foundation underlying a slender beam under flexure was conceived by Winkler, requiring local proportionality between soil reactions and beam deflection. Such an approach leads to well-posed elastostatic and elastodynamic problems, but as highlighted by Wieghardt, it provides elastic responses that are not technically significant for a wide variety of engineering applications. Thus, Winkler’s model was replaced by Wieghardt himself by assuming that the beam deflection is the convolution integral between soil reaction field and an averaging kernel. Due to conflict between constitutive and kinematic compatibility requirements, the corresponding elastic problem of an inflected beam resting on a Wieghardt foundation is ill-posed. Modifications of the original Wieghardt model were proposed by introducing fictitious boundary concentrated forces of constitutive type, which are physically questionable, being significantly influenced on prescribed kinematic boundary conditions. Inherent difficulties and issues are overcome in the present research using a displacement-driven nonlocal integral strategy obtained by swapping the input and output fields involved in Wieghardt’s original formulation. That is, nonlocal soil reaction fields are the output of integral convolutions of beam deflection fields with an averaging kernel. Equipping the displacement-driven nonlocal integral law with the bi-exponential averaging kernel, an equivalent nonlocal differential problem, supplemented with non-standard constitutive boundary conditions involving nonlocal soil reactions, is established. As a key implication, the integrodifferential equations governing the elastostatic problem of an inflected elastic slender beam resting on a displacement-driven nonlocal integral foundation are replaced with much simpler differential equations supplemented with kinematic, static, and new constitutive boundary conditions. The proposed nonlocal approach is illustrated by examining and analytically solving exemplar problems of structural engineering. Benchmark solutions for numerical analyses are also detected.

Free vibration analysis of three-layer thin cylindrical shell with variable thickness two-dimensional FGM middle layer under arbitrary boundary conditions

2021 ◽  
pp. 109963622110204
Author(s):  
Xue-Yang Miao ◽  
Chao-Feng Li ◽  
Yu-Lin Jiang ◽  
Zi-Xuan Zhang
Keyword(s):  
Cylindrical Shell ◽  
Boundary Conditions ◽  
Volume Fraction ◽  
Ritz Method ◽  
Admissible Function ◽  
Free Vibration Analysis ◽  
Middle Layer ◽  
Two Dimensional ◽  
Arbitrary Boundary ◽  
Arbitrary Boundary Conditions

In this paper, a unified method is developed to analyze free vibrations of the three-layer functionally graded cylindrical shell with non-uniform thickness. The middle layer is composed of two-dimensional functionally gradient materials (2D-FGMs), whose thickness is set as a function of smooth continuity. Four sets of artificial springs are assigned at the ends of the shells to satisfy the arbitrary boundary conditions. The Sanders’ shell theory is used to obtain the strain and curvature-displacement relations. Furthermore, the Chebyshev polynomials are selected as the admissible function to improve computational efficiency, and the equation of motion is derived by the Rayleigh–Ritz method. The effects of spring stiffness, volume fraction indexes, configuration on of shell, and the change in thickness of the middle layer on the modal characteristics of the new structural shell are also analyzed.

Approximate Formulas for Cylindrical Shell Free Vibration Based on Vlasov’s and Enhanced Vlasov’s Semi-Momentless Theory

2018 ◽  
Author(s):  
Igor Orynyak ◽  
Yaroslav Dubyk
Keyword(s):  
Cylindrical Shell ◽  
Boundary Conditions ◽  
Circular Cylindrical Shell ◽  
Equations Of Motion ◽  
Middle Surface ◽  
Axial Direction ◽  
Mode Shapes ◽  
Natural Mode ◽  
Transverse Deflection ◽  
Approximate Formulas

Simple approximate formulas for the natural frequencies of circular cylindrical shells are presented for modes in which transverse deflection dominates. Based on the Donnell-Mushtari thin shell theory the equations of motion of the circular cylindrical shell are introduced, using Vlasov assumptions and Fourier series for the circumferential direction, an exact solution in the axial direction is obtained. To improve the results assumptions of Vlasov’s semimomentless theory are enhanced, i.e. we have used only the hypothesis of middle surface inextensibility to obtain a solution in axial direction. Nonlinear characteristic equations and natural mode shapes, are derived for all type of boundary conditions. Good agreement with experimental data and FEM is shown and advantage over the existing formulas for a variety of boundary conditions is presented.

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