The Elastic-Plastic Analysis of Tubes—III: Shakedown Analysis

1992 ◽  
Vol 114 (2) ◽  
pp. 229-235 ◽  
Author(s):  
W. Jiang
Keyword(s):  
Steady State ◽  
Centrifugal Force ◽  
Kinematic Hardening ◽  
Steady States ◽  
Shakedown Analysis ◽  
Elastic Plastic ◽  
External Pressures ◽  
Plastic Analysis ◽  
Elastic Shakedown ◽  
Steady State Solutions

This paper presents an investigation of the shakedown behavior of tubes subjected to cyclic centrifugal force and temperature, and sustained internal and external pressures. It is found that the steady states can always be attained as a result of the kinematic hardening. Then, when shakedown occurs, the stresses and strains will cycle between the cooling state and the heating state. The steady-state solutions for the cases of elastic shakedown and reversed plasticity are discussed and given in this paper.

The Elastic-Plastic Analysis of Tubes—IV: Thermal Ratchetting

1992 ◽  
Vol 114 (2) ◽  
pp. 236-245 ◽  
Author(s):  
W. Jiang
Keyword(s):  
Steady State ◽  
Plastic Strain ◽  
Centrifugal Force ◽  
Kinematic Hardening ◽  
Elastic Plastic ◽  
External Pressures ◽  
Plastic Analysis ◽  
Steady Solutions ◽  
Number Of Cycles

This paper continues the investigation of the shakedown behavior of tubes subjected to cyclic centrifugal force and temperature, and sustained internal and external pressures. It is found that when ratchetting occurs, the plastic strain builds up with each cycle, but finally reaches a steady state after a large number of cycles for kinematic hardening materials. The steady solutions for three kinds of ratchetting behavior are found and given in this paper.

Elastic-Plastic Analysis of Fretting Contacts

2015 ◽  
Vol 642 ◽  
pp. 248-252
Author(s):  
Chang Hung Kuo
Keyword(s):  
Kinematic Hardening ◽  
Carbon Steels ◽  
Plastic Behavior ◽  
Rule Based ◽  
Elastic Plastic ◽  
Hardening Rule ◽  
Chaboche Model ◽  
Plastic Analysis ◽  
Finite Element Procedure ◽  
Elastic Shakedown

A finite element procedure is implemented for the elastic-plastic analysis of carbon steels subjected to reciprocating fretting contacts. The nonlinear kinematic hardening rule based on Chaboche model is used to model the cyclic plastic behavior in fretting contacts. The results show that accumulation of plastic strains, i.e. ratchetting, may occur near the contact edge while elastic shakedown is likely to take place in substrate.

Swirling flow states in finite-length diverging or contracting circular pipes

2017 ◽  
Vol 819 ◽  
pp. 678-712 ◽  
Author(s):  
Zvi Rusak ◽  
Yuxin Zhang ◽  
Harry Lee ◽  
Shixiao Wang
Keyword(s):  
Steady State ◽  
Numerical Simulations ◽  
Finite Length ◽  
Vortex Breakdown ◽  
Steady States ◽  
Inviscid Limit ◽  
Circular Pipes ◽  
Outlet Flow ◽  
Separation Zones ◽  
Steady State Solutions

The dynamics of inviscid-limit, incompressible and axisymmetric swirling flows in finite-length, diverging or contracting, long circular pipes is studied through global analysis techniques and numerical simulations. The inlet flow is described by the profiles of the circumferential and axial velocity together with a fixed azimuthal vorticity while the outlet flow is characterized by a state with zero radial velocity. A mathematical model that is based on the Squire–Long equation (SLE) is formulated to identify steady-state solutions of the problem with special conditions to describe states with separation zones. The problem is then reduced to the columnar (axially-independent) SLE, with centreline and wall conditions for the solution of the outlet flow streamfunction. The solution of the columnar SLE problem gives rise to the existence of four types of solutions. The SLE problem is then solved numerically using a special procedure to capture states with vortex-breakdown or wall-separation zones. Numerical simulations based on the unsteady vorticity circulation equations are also conducted and show correlation between time-asymptotic states and steady states according to the SLE and the columnar SLE problems. The simulations also shed light on the stability of the various steady states. The uniqueness of steady-state solutions in a certain range of swirl is proven analytically and demonstrated numerically. The computed results provide the bifurcation diagrams of steady states in terms of the incoming swirl ratio and size of pipe divergence or contraction. Critical swirls for the first appearance of the various types of states are identified. The results show that pipe divergence promotes the appearance of vortex-breakdown states at lower levels of the incoming swirl while pipe contraction delays the appearance of vortex breakdown to higher levels of swirl and promotes the formation of wall-separation states.

scholarly journals The viscous froth model: steady states and the high-velocity limit

2009 ◽  
Vol 465 (2108) ◽  
pp. 2391-2405 ◽  
Author(s):  
S. J. Cox ◽  
D. Weaire ◽  
G. Mishuris
Keyword(s):  
Steady State ◽  
High Velocity ◽  
Steady States ◽  
Two Dimensional ◽  
Isolated Points ◽  
Physical Effects ◽  
Straight Lines ◽  
Steady State Solutions ◽  
Finite Extent

The steady-state solutions of the viscous froth model for foam dynamics are analysed and shown to be of finite extent or to asymptote to straight lines. In the high-velocity limit, the solutions consist of straight lines with isolated points of infinite curvature. This analysis is helpful in the interpretation of observations of anomalous features of mobile two-dimensional foams in channels. Further physical effects need to be adduced in order to fully account for these.

scholarly journals The Geometry of Power Systems Steady-State Equations– Part I: Power Surface

2020 ◽  
pp. 37-46
Author(s):  
B. Ayuev ◽  
V. Davydov ◽  
P. Erokhin ◽  
V. Neuymin ◽  
A. Pazderin
Keyword(s):  
Steady State ◽  
Power Systems ◽  
Power System ◽  
Power Flow ◽  
Analytical Study ◽  
State Theory ◽  
Steady States ◽  
State Equations ◽  
Feasibility Region ◽  
Steady State Solutions

Steady-state equations play a fundamental role in the theory of power systems and computation practice. These equations are directly or mediately used almost in all areas of the power system state theory, constituting its basis. This two-part study deals with a geometrical interpretation of steady-state solutions in a power space. Part I considers steady states of the power system as a surface in the power space. A power flow feasibility region is shown to be widely used in power system theories. This region is a projection of this surface along the axis of a slack bus active power onto a subspace of other buses power. The findings have revealed that the obtained power flow feasibility regions, as well as marginal states of the power system, depend on a slack bus location. Part II is devoted to an analytical study of the power surface of power system steady states.

scholarly journals Steady states of thin film droplets on chemically heterogeneous substrates

2020 ◽  
Vol 85 (6) ◽  
pp. 980-1020
Author(s):  
Weifan Liu ◽  
Thomas P Witelski
Keyword(s):  
Thin Films ◽  
Steady State ◽  
Finite Size ◽  
Steady States ◽  
One Dimension ◽  
Asymptotic Estimates ◽  
Perturbation Expansions ◽  
Flux Boundary Conditions ◽  
Axisymmetric Solutions ◽  
Steady State Solutions

Abstract We study steady-state thin films on chemically heterogeneous substrates of finite size, subject to no-flux boundary conditions. Based on the structure of the bifurcation diagram, we classify the 1D steady-state solutions that exist on such substrates into six different branches and develop asymptotic estimates for the steady states on each branch. Using perturbation expansions, we show that leading-order solutions provide good predictions of the steady-state thin films on stepwise-patterned substrates. We show how the analysis in one dimension can be extended to axisymmetric solutions. We also examine the influence of the wettability contrast of the substrate pattern on the linear stability of droplets and the time evolution for dewetting on small domains. Results are also applied to describe 2D droplets on hydrophilic square patches and striped regions used in microfluidic applications.

Lower Bound Methods in Elastic-Plastic Shakedown Analysis

2010 ◽  
Author(s):  
Wolf Reinhardt ◽  
Reza Adibi-Asl
Keyword(s):  
Lower Bound ◽  
Plastic Material ◽  
Shakedown Analysis ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Efficient Calculation ◽  
Asme Code ◽  
Elastic Shakedown ◽  
Plastic Shakedown

Several methods were proposed in recent years that allow the efficient calculation of elastic and elastic-plastic shakedown limits. This paper establishes a uniform framework for such methods that are based on perfectly-plastic material behavour, and demonstrates the connection to Melan’s theorem of elastic shakedown. The paper discusses implications for simplified methods of establishing shakedown, such as those used in the ASME Code. The framework allows a clearer assessment of the limitations of such simplified approaches. Application examples are given.

The Elastic-Plastic Analysis of Tubes—I: General Theory

1992 ◽  
Vol 114 (2) ◽  
pp. 213-221 ◽  
Author(s):  
W. Jiang
Keyword(s):  
General Theory ◽  
Constitutive Equations ◽  
Kinematic Hardening ◽  
Elastic Plastic ◽  
Hardening Rule ◽  
Plastic Analysis ◽  
Made In

A study is made in this paper of the elastic-plastic analysis of tubes subjected to various loads and temperatures. The kinematic hardening rule is used in the analysis and constitutive equations are developed for the tube problems. By piecing several elastic and plastic solutions together, various tube problems can be solved in closed forms.

scholarly journals On the crossing of intermediate unstable steady state solutions for thermal ignition in a sphere

2001 ◽  
Vol 43 (1) ◽  
pp. 77-85 ◽  
Author(s):  
R. O. Weber ◽  
G. C. Wake ◽  
H. S. Sidhu ◽  
G. N. Mercer ◽  
B. F. Gray ◽  
...  
Keyword(s):  
Steady State ◽  
Unit Sphere ◽  
Steady States ◽  
Temperature Profiles ◽  
Thermal Ignition ◽  
Unstable Steady State ◽  
Steady State Temperature ◽  
Parameter Values ◽  
Steady State Solutions ◽  
Unstable Intermediate

AbstractSteady state solutions for spontaneous thermal ignition in a unit sphere are considered. The multiplicity of unstable, intermediate, steady state, temperature profiles is calculated and shown for selected parameter values. The crossing of the temperature profiles corresponding to the unstable, intermediate, steady states is exhibited in a particular case and is proven in general using elementary ideas from analysis. Estimates of the location of crossing points are given.

THE STABILITY OF SPATIALLY NONHOMOGENEOUS STEADY STATES IN A TUBULAR CHEMICAL REACTOR

1993 ◽  
Vol 03 (06) ◽  
pp. 1477-1486
Author(s):  
JAMES M. ROTENBERRY ◽  
ANTONMARIA A. MINZONI
Keyword(s):  
Steady State ◽  
Peclet Number ◽  
Chemical Reactor ◽  
Higher Order ◽  
Steady States ◽  
Complex Conjugate ◽  
Heat Of Reaction ◽  
Péclet Number ◽  
The Stability ◽  
Steady State Solutions

We study the axial heat and mass transfer in a highly diffusive tubular chemical reactor in which a simple reaction is occurring. The steady state solutions of the governing equations are studied using matched asymptotic expansions, the theory of dynamical systems, and by calculating the solutions numerically. In particular, the effect of varying the Peclet and Damköhler numbers (P and D) is investigated. A simple expression for the approximate location of the transition layer for large Peclet number is derived and its accuracy tested against the numerical solution. The stability of the steady states is examined by calculating the eigenvalues and eigenfunctions of the linearized equations. It is shown that a Hopf bifurcation of the CSTR model (i.e., the limit as the P approaches zero) can be continued up to order 1 in the Peclet number. Furthermore, it is shown numerically that for appropriate values of the Peclet number, the Damköhler number, and B (the heat of reaction) these Hopf bifurcations merge with the limit points of an "S–shaped" bifurcation curve in a higher order singularity controlled by the Bogdanov–Takens normal form. Consequently, there must exist a finite amplitude, nonuniform, stable periodic solution for parameter values near this singularity. The existence of higher order degeneracies is also explored. In particular, it is shown for D ≪ 1 that no value of P exists where two pairs of complex conjugate eigenvalues of the steady state solutions can cross the imaginary axis simultaneously.

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