scholarly journals The Elastic-Plastic Response of Thin Spherical Shells to Internal Blast Loading

1960 ◽  
Vol 27 (1) ◽  
pp. 139-144 ◽  
Author(s):  
W. E. Baker
Keyword(s):  
Numerical Solutions ◽  
Equations Of Motion ◽  
Analytic Solutions ◽  
Plastic Response ◽  
Transient Pressure ◽  
Elastic Plastic ◽  
Small Deflection ◽  
Thin Spherical Shell ◽  
Internal Blast Loading ◽  
Good Agreement

In this paper, the theory is developed for the elastic-plastic response of a thin spherical shell to spherically symmetric internal transient pressure loading. Analytic solutions are obtained to the linear, small-deflection equations of motion for shell materials which exhibit various degrees of strain-hardening. Numerical solutions obtained by digital computer are also presented for the equations for large deflections obtained by accounting for shell thinning and increase in radius during deformation. The theory is compared with experiment, and is shown to be in good agreement.

scholarly journals Resonant Stellar Orbits in Spiral Galaxies

1975 ◽  
Vol 69 ◽  
pp. 237-244
Author(s):  
P. O. Vandervoort
Keyword(s):  
Excellent Agreement ◽  
Spiral Galaxy ◽  
Harmonic Balance ◽  
Spiral Galaxies ◽  
Numerical Solutions ◽  
Equations Of Motion ◽  
Analytic Solutions ◽  
Stellar Orbits ◽  
Method Of Harmonic Balance ◽  
Resonance Phenomena

This paper reviews a series of investigations of the orbits of stars in the regions of the Lindblad resonances of a spiral galaxy. The analysis is formulated in an epicyclic approximation. Analytic solutions of the epicyclic equations of motion are obtained by the method of harmonic balance of Bogoliubov and Mitropolsky. These solutions represent the resonance phenomena exhibited by the orbits in generally excellent agreement with numerical solutions.

The steady flow due to a rotating sphere at low and moderate Reynolds numbers

1980 ◽  
Vol 101 (2) ◽  
pp. 257-279 ◽  
Author(s):  
S. C. R. Dennis ◽  
S. N. Singh ◽  
D. B. Ingham
Keyword(s):  
Reynolds Number ◽  
Numerical Solutions ◽  
Equations Of Motion ◽  
Reynolds Numbers ◽  
Low Reynolds Numbers ◽  
Finite Set ◽  
Flow Variables ◽  
Theoretical Results ◽  
Radial Variable ◽  
Good Agreement

The problem of determining the steady axially symmetrical motion induced by a sphere rotating with constant angular velocity about a diameter in an incompressible viscous fluid which is at rest at large distances from it is considered. The basic independent variables are the polar co-ordinates (r, θ) in a plane through the axis of rotation and with origin at the centre of the sphere. The equations of motion are reduced to three sets of nonlinear second-order ordinary differential equations in the radial variable by expanding the flow variables as series of orthogonal Gegenbauer functions with argument μ = cosθ. Numerical solutions of the finite set of equations obtained by truncating the series after a given number of terms are obtained. The calculations are carried out for Reynolds numbers in the range R = 1 to R = 100, and the results are compared with various other theoretical results and with experimental observations.The torque exerted by the fluid on the sphere is found to be in good agreement with theory at low Reynolds numbers and appears to tend towards the results of steady boundary-layer theory for increasing Reynolds number. There is excellent agreement with experimental results over the range considered. A region of inflow to the sphere near the poles is balanced by a region of outflow near the equator and as the Reynolds number increases the inflow region increases and the region of outflow becomes narrower. The radial velocity increases with Reynolds number at the equator, indicating the formation of a radial jet over the narrowing region of outflow. There is no evidence of any separation of the flow from the surface of the sphere near the equator over the range of Reynolds numbers considered.

A Coarse Model for the Multiaxial Elastic-Plastic Response of Ductile Porous Materials

2019 ◽  
Vol 86 (8) ◽  
Author(s):  
Andreas Schiffer ◽  
Panagiotis Zacharopoulos ◽  
Dennis Foo ◽  
Vito L. Tagarielli
Keyword(s):  
Mechanical Response ◽  
Hydrostatic Stress ◽  
Parent Material ◽  
Porous Solids ◽  
Plastic Response ◽  
Elastic Plastic ◽  
Numerical Studies ◽  
Coarse Model ◽  
Modeling Strategy ◽  
Good Agreement

We propose a modeling strategy to predict the mechanical response of porous solids to imposed multiaxial strain histories. A coarse representation of the microstructure of a porous material is obtained by subdividing a volume element into cubic cells by a regular tessellation; some of these cells are modeled as a plastically incompressible elastic-plastic solid, representing the parent material, while the remaining cells, representing the pores, are treated as a weak and soft compressible solid displaying densification behavior at large compressive strains. The evolution of homogenized deviatoric and hydrostatic stress is explored for different porosities by finite element simulations. The predictions are found in good agreement with previously published numerical studies in which the microstructural geometry was explicitly modeled.

Wave Propagation in Tapered Vessels: New Analytic Solutions That Account for Vessel Distensibility and Fluid Compressibility

2013 ◽  
Vol 136 (1) ◽  
Author(s):  
George Papadakis
Keyword(s):  
Numerical Solutions ◽  
Analytic Solutions ◽  
Temporal And Spatial Variation ◽  
Low Frequencies ◽  
Analytic Expressions ◽  
Wave Forms ◽  
Wall Deformation ◽  
Temporal And Spatial ◽  
Good Agreement ◽  
Fluid Compressibility

The central aim of this paper is to contribute to the theoretical analysis and understanding of the effect of vessel tapering on the propagation of pressure and velocity wave forms. To this end, it presents new analytic expressions for the temporal and spatial variation of these two variables that account for weak fluid compressibility. It extends previous work in which only the effect of wall deformation (i.e., vessel distensibility) was taken into account. The solutions are derived in the frequency domain and can account for the steady solution component (d.c. component) obtained by taking the asymptotic limit for very low frequencies. It is shown that the effect of compressibility makes the equations more complex but it is still possible to derive closed form analytic solutions in terms of Bessel functions of orders 1/3 and 4/3. The analytical solutions are compared with full 3D fluid structure interaction (FSI) simulations for the case of propagation of a step pressure variation at the inlet of a tapered vessel. Good agreement is observed between the 1D analytical and 3D numerical solutions.

Large-Deformation Response of Deep Circular Arches to Radial Magnetomotive Forces

1978 ◽  
Vol 20 (6) ◽  
pp. 335-343 ◽  
Author(s):  
S. T. S. Al-Hassani ◽  
M. S. J. Hashmi
Keyword(s):  
High Speed ◽  
Numerical Technique ◽  
Equations Of Motion ◽  
High Energy ◽  
Plastic Response ◽  
Deformation Response ◽  
Single Turn ◽  
Impulsive Forces ◽  
Induced Currents ◽  
Good Agreement

Circular-arch specimens were produced from aluminium rings. By using suitable rigid inserts in a ring, only a small portion of it was allowed to deform freely. The rings were subjected to uniformly-distributed, radially-inward-directed impulsive forces. The forces were generated by a high-energy electrical discharge through a single-turn coil which surrounded the ring. The induced currents in the ring were high enough to engender large, transient, radially-directed magnetomotive forces which caused gross plastic deformation. The elastic–plastic response of the arches was predicted by using a finite-difference numerical technique to solve the equations of motion. The analysis allows for circumferential and shear forces, as well as large changes in geometry. It also incorporates strain-hardening, but it ignores the influence of rotary inertia. High-speed photographs were used to record the transient shape of the collapsing arches. These were found to be in good agreement with the predicted profiles.

Wave Propagation in Tapered Vessels: New Analytic Solutions That Account for Vessel Distensibility and Fluid Compressibility

2013 ◽  
Author(s):  
George Papadakis
Keyword(s):  
Bessel Functions ◽  
Numerical Solutions ◽  
Analytic Solutions ◽  
Temporal And Spatial Variation ◽  
Low Frequencies ◽  
Wave Forms ◽  
Wall Deformation ◽  
Temporal And Spatial ◽  
Good Agreement ◽  
Fluid Compressibility

The central aim of this paper is to contribute to the understanding of the effect of vessel tapering on the propagation of pressure and velocity wave forms. It presents new analytic solutions for the temporal and spatial variation of these two variables that account for weak fluid compressibility. It extends previous work of the author in which only the effect of wall deformation (i.e. vessel distensibility) was taken into account. The solutions are derived in the frequency domain and can account for the steady solution component (d.c. component) obtained by taking the asymptotic value for very low frequencies. It is shown that the effect of compressibility makes the equations more complex but it is still possible to derive closed form analytic solutions in terms of Bessel functions of orders 1/3 and 4/3. The analytical solutions are compared with 3D FSI simulations for the case of propagation of a step pressure variation at the inlet of a tapered vessel. Good agreement is observed between the 1D analytical and 3D numerical solutions.

Modelling the morning glory of the Gulf of Carpentaria

2002 ◽  
Vol 454 ◽  
pp. 1-20 ◽  
Author(s):  
ANNE PORTER ◽  
NOEL F. SMYTH
Keyword(s):  
Numerical Solutions ◽  
Equations Of Motion ◽  
Simple Wave ◽  
Morning Glory ◽  
Pressure Jump ◽  
Large Wave ◽  
Long Wave ◽  
Westerly Direction ◽  
Cape York ◽  
Good Agreement

The morning glory is a meteorological phenomenon which occurs in northern Australia and takes the form of a series of roll clouds. The morning glory is generated by the interaction of nocturnal seabreezes over Cape York Peninsula and propagates in a south-westerly direction over the Gulf of Carpentaria. In the present work, it is shown that the morning glory can be modelled by the resonant flow of a two-layer fluid over topography, the topography being the mountains of Cape York Peninsula. In the limit of a deep upper layer, the equations of motion reduce to a forced Benjamin–Ono equation. In this context, resonant means that the underlying flow velocity of the seabreezes is near a linear long-wave velocity for one of the long-wave modes. The morning glory is then modelled by the undular bore (simple wave) solution of the modulation equations for the Benjamin–Ono equation. This modulation solution is compared with full numerical solutions of the forced Benjamin–Ono equation and good agreement is found when the wave amplitudes are not too large. The reason for the difference between the numerical and modulation solutions for large wave amplitude is also discussed. Finally, the predictions of the modulation solution are compared with observational data on the morning glory and good agreement is found for the pressure jump due to the lead wave of the morning glory, but not for the speed and half-width of this lead wave. The reasons for this are discussed.

NUMERICAL SIMULATION OF SEISMIC DISTURBANCES

Geophysics ◽  
1966 ◽  
Vol 31 (1) ◽  
pp. 33-49 ◽  
Author(s):  
J. T. Cherry ◽  
W. R. Hurdlow
Keyword(s):  
Numerical Solutions ◽  
Numerical Technique ◽  
Continuum Hypothesis ◽  
Equations Of Motion ◽  
Yield Condition ◽  
Small Time ◽  
Tensile Failure ◽  
Time Step ◽  
Elastic Plastic ◽  
Cylindrically Symmetric

This paper presents the results from a Lagrangian numerical scheme of calculating cylindrically symmetric, elastic‐plastic, transient disturbances. The numerical technique involves transforming the Eulerian equations of motion containing a cylindrically symmetric stress tensor into Lagrangian coordinates. These transformed equations are then differenced in the Lagrangian coordinate system. Therefore, a given instantaneous stress field determines the accelerations of the points in the Lagrangian mesh. These accelerations are allowed to act over a small time‐step so that the mesh becomes distorted. This distortion determines the change in strain at a point; the strain change is related to a stress change by Hooke’s law. This new stress is used to determine new accelerations. If the material behaves plastically, then the stresses are adjusted so that a von Mises yield condition is satisfied. Five numerical solutions of various elastic‐plastic wave propagation problems are presented; these solutions agree extremely well with their corresponding analytic and experimental solutions. A shear and tensile failure mechanism is presented that is consistent with the continuum hypothesis. This mechanism gives good results when applied to NTS alluvium. Data for hard rock are not yet available.

scholarly journals MODELING LONGSHORE CURRENTS FOR FIELD SITUATIONS

1982 ◽  
Vol 1 (18) ◽  
pp. 100
Author(s):  
Seetharama R. Vemulakonda ◽  
James R. Houston ◽  
H. Lee Butler
Keyword(s):  
North Carolina ◽  
Numerical Models ◽  
Equations Of Motion ◽  
Analytic Solutions ◽  
Computational Costs ◽  
Nearshore Circulation ◽  
Longshore Currents ◽  
Field Situation ◽  
Reasonable Cost ◽  
Good Agreement

There is a growing need for generalized numerical models for longshore currents and nearshore circulation that solve the complete equations of motion, are flexible in the formulations chosen for various terms, and can be applied to field situations at a reasonable cost. The development and application of one such model is described in this paper. The model was first tested by comparing its results to known analytic solutions and experimental data. There was good agreement. It was next applied to a field situation near Oregon Inlet, North Carolina. The results appeared to be reasonable and the computational costs were modest.

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