A Dynamic Shell Theory Coupling Thickness Stress Wave Effects With Gross Structural Response

1973 ◽  
Vol 40 (3) ◽  
pp. 731-735 ◽  
Author(s):  
S. E. Benzley ◽  
J. R. Hutchinson ◽  
S. W. Key
Keyword(s):  
Stress Wave ◽  
Shell Theory ◽  
Cylindrical Shells ◽  
Structural Response ◽  
Early Time ◽  
Stress Wave Propagation ◽  
Late Time ◽  
The Finite Element Method ◽  
Wave Effects ◽  
Circumferential Displacement

A theory for thick cylindrical shells is presented that couples the early time thickness stress wave propagation with higher-order shell theory equations. The formulation completely describes the continuum response in the thickness direction for “early time” considerations while representing the circumferential response with a high-order circumferential displacement assumption. Late time (structural response) equations are developed to continue the analysis after thickness effects are no longer important. The finite-element method is used to obtain solutions of the theory. Calculations are presented which show that thickness stress need not be included for cylindrical shells with h/R ratios less than 0.2.

DYNAMIC STABILITY OF A BEAM ON AN ELASTIC FOUNDATION INCLUDING STRESS WAVE EFFECTS

2012 ◽  
Vol 04 (02) ◽  
pp. 1250017 ◽  
Author(s):  
YING LIU ◽  
G. LU
Keyword(s):  
Dynamic Stability ◽  
Elastic Foundation ◽  
Stress Wave ◽  
Axial Load ◽  
Elastic Beam ◽  
Beam Theory ◽  
Stress Wave Propagation ◽  
Bernoulli Beam ◽  
Wave Effects ◽  
Euler Bernoulli Beam

This paper examines the dynamic stability of an elastic beam on the elastic foundation, in which the stress wave effect is taken into account. Based on Euler–Bernoulli beam theory, the dynamic response of the elastic beam on the elastic foundation to a small transverse perturbation is analyzed. By considering the stress wave propagation in the beam and the constraint of the elastic foundation, the critical bifurcation condition of elastic beam is derived, and the critical axial load of the elastic beam is predicted. Furthermore, the effects of the elastic foundation and the beam length on buckling condition are discussed by using numeric examples. Finally, an approximate solution of critical axial load for elastic beam on the elastic foundation is provided, which may be used to investigate elastic beam buckling problem.

The Effect of Plate Curvature on the Influence of Macroscale Geometric Voids in Controlling Stress Wave Propagation

2020 ◽  
Author(s):  
C. S. Florio
Keyword(s):  
Wave Propagation ◽  
Stress Wave ◽  
Plane Stress ◽  
Cylindrical Shells ◽  
Reaction Force ◽  
Stress Waves ◽  
Stress Wave Propagation ◽  
Axial Impact ◽  
Plate Curvature ◽  
Metal Plates

Abstract Much work has been done to create and understand means to control the propagation of acoustic and light waves through materials and structures. The ability to perform similar studies on the control of stress waves has implications not only for the development of capabilities to disrupt stress waves in order to limit their damage, but also to direct stress waves in order to tailor the behavior of a structure for a specific functional goal. Recent studies have demonstrated the use of voids and inclusions of varying size, geometry, arrangement, and composition in structures to attenuate impact forces or cloak stress waves in thin, flat, plane stress plates. However, many structures that may benefit from these wave modification methods are comprised of cylindrical shells. It is not currently known how well the techniques to control wave propagation and trends identified in plane stress plates can be applied to structures with cylindrical shells. Therefore, this study develops and uses computational modeling methods to examine the modification and control of stress waves induced by an axial impact load in metal plates of varying curvature through the inclusion of macroscale voids. Methods are developed and used in this work to study the response of metal plates of varying curvature with and without voids of different shapes and arrangement to axial impact loads. The response is quantified through the magnitude of the fixed end reaction force and through normal oscillations of discrete points along the length of the plate. Fast Fourier transformation and wavelet coherence techniques are used to understand both the time-averaged and time-dependent oscillation behavior. Correlations are drawn between plate curvature and void design on the control of the propagation of stress waves. The knowledge gained can help guide the understanding design of these stress wave modification features.

Effects of Anisotropy in Axisymmetric Cylindrical Shells

1967 ◽  
Vol 34 (3) ◽  
pp. 659-666 ◽  
Author(s):  
S. T. Gulati ◽  
F. Essenburg
Keyword(s):  
Cylindrical Shell ◽  
Shear Deformation ◽  
Transverse Shear ◽  
Shell Theory ◽  
Circular Cylindrical Shell ◽  
Cylindrical Shells ◽  
Practical Importance ◽  
Transverse Shear Deformation ◽  
Circumferential Displacement

The solution of the problem of the generally anisotropic axisymmetric circular cylindrical shell is obtained employing a recent shell theory given by Naghdi. The practical importance of the presence of the circumferential displacement components and the twisting couple arising due to the presence of anisotropy, as well as the significance of the inclusion of the coupled effects of transverse shear deformation and anisotropy, are illustrated by a specific example.

Non-Linear Dynamic Analysis of Cylindrical Shells Subjected to a Flowing Fluid

2000 ◽  
Author(s):  
A. A. Lakis ◽  
A. Selmane ◽  
C. Dupuis
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Shell Theory ◽  
Cylindrical Shells ◽  
Empty Shell ◽  
The Finite Element Method ◽  
Linear Dynamic ◽  
Stiffness Matrices ◽  
Non Linear ◽  
Element Method

Abstract A theory is presented to predict the influence of non-linearities associated with the wall of the shell and with the fluid flow on the dynamic of elastic, thin, orthotropic open and closed cylindrical shells submerged and subjected to an internal and external fluid. The open shells are assumed to be freely simply-supported along their curved edges and to have arbitrary straight edge boundary conditions. The method developed is a hybrid of thin shell theory, fluid theory and the finite element method. The solution is divided into four parts. In part one, the displacement functions are obtained from Sanders’ linear shell theory and the mass and linear stiffness matrices for the empty shell are obtained by the finite element procedure. In part two, the modal coefficients derived from the Sanders-Koiter non-linear theory of thin shells are obtained for these displacement functions. Expressions for the second and third order non-linear stiffness matrices of the empty shell are then determined through the finite element method. In part three a fluid finite element is developed, the model requires the use of a linear operator for the velocity potential and a linear boundary condition of impermeability. With the non-linear dynamic pressure, we develop in the fourth part three non-linear matrices for the fluid. The non-linear equation of motion is then solved by the fourth-order Runge-Kutta numerical method. The linear and non-linear natural frequency variations are determined as a function of shell amplitudes for different cases.

scholarly journals Vibration of rotating circular cylindrical shells with distributed springs

2021 ◽  
Vol 37 ◽  
pp. 346-358
Author(s):  
Fuchun Yang ◽  
Xiaofeng Jiang ◽  
Fuxin Du
Keyword(s):  
Boundary Conditions ◽  
Galerkin Method ◽  
Shell Theory ◽  
Rotation Speed ◽  
Cylindrical Shells ◽  
Free Vibrations ◽  
Governing Equations ◽  
Natural Response ◽  
Circular Cylindrical Shells ◽  
The Galerkin Method

Abstract Free vibrations of rotating cylindrical shells with distributed springs were studied. Based on the Flügge shell theory, the governing equations of rotating cylindrical shells with distributed springs were derived under typical boundary conditions. Multicomponent modal functions were used to satisfy the distributed springs around the circumference. The natural responses were analyzed using the Galerkin method. The effects of parameters, rotation speed, stiffness, and ratios of thickness/radius and length/radius, on natural response were also examined.

FEM Stress Analysis and Strength of Scarf Adhesive Joints of Similar Adherend Subjected to Impact Tensile Loadings

2007 ◽  
Author(s):  
Toshiyuki Sawa ◽  
Yuya Hirayama ◽  
He Dan
Keyword(s):  
Young’S Modulus ◽  
Principal Stress ◽  
Stress Wave ◽  
Young's Modulus ◽  
Three Dimensional ◽  
Maximum Principal Stress ◽  
Adhesive Joints ◽  
Stress Wave Propagation ◽  
Adhesive Thickness ◽  
Three Dimensional Finite Element

The stress wave propagation and stress distribution in scarf adhesive joints have been analyzed using three-dimensional finite element method (FEM). The FEM code employed was LS-DYNA. An impact tensile loading was applied to the joint by dropping a weight. The effect of the scarf angle, Young’s modulus of the adhesive and adhesive thickness on the stress wave propagations and stress distributions at the interfaces have been examined. As the results, it was found that the point where the maximum principal stress becomes maximum changes between 52 degree and 60 degree under impact tensile loadings. The maximum value of the maximum principal stress increases as scarf angle decreases, Young’s modulus of the adhesive increases and adhesive thickness increases. In addition, Experiments to measure the strains and joint strengths were compared with the calculated results. The calculated results were in fairly good agreements with the experimental results.

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