Shakedown in Elastic-Plastic Systems Under Dynamic Loadings

1972 ◽  
Vol 39 (2) ◽  
pp. 416-421 ◽  
Author(s):  
Hwa-Shan Ho
Keyword(s):  
Numerical Procedure ◽  
Direct Search ◽  
Plastic Work ◽  
The Other ◽  
Inertia Force ◽  
Basic Tendency ◽  
Finite Amount ◽  
General Proof ◽  
Elastic Plastic ◽  
Dynamic Loadings

Following the derivations of Koiter, who gave a general proof of Melan’s shakedown theorem for elastic-plastic systems under quasi-static reversible parametric loadings, it is shown here that the inclusion of the inertia force due to dynamic loadings does not change the basic tendency for the system to shakedown, if it can. Because of the validity of this shakedown theorem, the problem of designing a system under dynamic loadings and with only a finite amount of allowable plastic work can be transformed into a quasi-static, elastic counterpart. For the case of proportional loadings, two methods for solving the “compounded” shakedown load are proposed. One is called the “Method of Zero Work;” the other, involving a systematic numerical procedure, is called the “Method of Direct Search.” The concept of “optimum preloading” is also introduced.

scholarly journals Tail-Actuator Propulsion Device for Aquatic Robot

2006 ◽  
Vol 18 (1) ◽  
pp. 89-96 ◽  
Author(s):  
Andrea Manuello Bertetto ◽  
◽  
Maurizio Ruggiu
Keyword(s):  
Mathematical Model ◽  
Numerical Procedure ◽  
Numerical Data ◽  
Operating Principle ◽  
The Other ◽  
Kinematics And Dynamics ◽  
Experimental Characterization ◽  
Fish Propulsion ◽  
Geometrical Dimensions ◽  
Simplified Mathematical Model

In this paper an aquatic device inspired to the fish propulsion is proposed. At the first, the operating principle of the fluidic actuator and its experimental characterization are presented. Then, the results of numerous tests carried out on the integrated tail-actuator device are shown either in terms of thrust exerted or as biomorphism of its kinematics. The tests were run at several driven frequencies with different fins depending on their geometrical dimensions and compliances. On the other hand, a simplified mathematical model of the propulsion system, based on the calculation of the instantaneous tail kinematics and dynamics by means of a numerical procedure, is proposed with the aim of simulating performances either in terms of thrust exerted or kinematics behavior. Finally a discussion about the results obtained and a comparison between experimental and numerical data are presented.

Ductile Crack Propagation Simulation of a Cylinder With a Through-Wall Circumferential Flaw Under Excessive Cyclic Torsion Loading

2014 ◽  
Author(s):  
Kiminobu Hojo ◽  
Daigo Watanabe ◽  
Shinichi Kawabata ◽  
Yasufumi Ametani
Keyword(s):  
Cyclic Loading ◽  
Crack Growth ◽  
Rotation Angle ◽  
Fe Analysis ◽  
The Other ◽  
J Integral ◽  
Ductile Crack ◽  
Elastic Plastic ◽  
Cyclic Torsion ◽  
Ductile Crack Growth

A lot of applications of elastic plastic FE analysis to flawed structural fracture behaviors of mode I have been investigated. On the other hand the analysis method has not been established for the case of the excessive cyclic torsion loading with mode II or III fracture. The authors tried simulating the fracture behavior of a cylinder-shaped specimen with a through-walled circumferential flaw subjected to excessive monotonic or cyclic loading by using elastic plastic FE analysis. Chaboche constitutive equation of the used FE code Abaqus was applied to estimate the elastic plastic cyclic behavior. As a result in the case of monotonic loading without crack extension, the relation of torque-rotation angle of the experiment was estimated well by the simulation. Also J-integral by the Abaqus’ function agreed with a simplified J-equation using the calculated torque-rotation angle relation. On the other hand under load controlled cyclic loading associated with ductile crack growth, the calculated torque-rotation angle relation did not agree with the experimental one because of high sensitivity of the used stress-strain curve. J-integral from Abaqus code did not increase regardless of the accumulated crack growth and plastic zone. Several simplified ΔJ calculations tried to explain the experimental ductile crack growth and it seemed that da/dN-ΔJ relation follows the Paris’ law. From these examinations an estimation procedure of the structures under excessive cyclic loading was proposed.

scholarly journals Approximate Solution of a Fourth Order Weakly Non-Linear Differential System with Strong Damping and Slowly Varying Coefficients by Unified KBM Method

1970 ◽  
Vol 34 (1) ◽  
pp. 71-82
Author(s):  
M Alhaz Uddin ◽  
MA Sattar
Keyword(s):  
Approximate Solution ◽  
Differential System ◽  
Fourth Order ◽  
Initial Conditions ◽  
Numerical Procedure ◽  
The Other ◽  
Oscillatory Process ◽  
Strong Damping ◽  
Varying Coefficients ◽  
Kbm Method

The unified Krylov-Bogoliubov-Mitropolskii (KBM) method is used for determining theanalytical approximate solution of a fourth order weakly nonlinear differential system with strongdamping and slowly varying coefficients when a pair of eigen-values of the unperturbed equationis a multiple (approximately or perfectly) of the other pair or pairs. In a damped case, one of thenatural frequencies of the linearized equation may be a multiple of the other. The analytical firstorder approximate solution for different initial conditions shows a good coincidence with thoseobtained by the numerical procedure. The method is illustrated by an example.Key words: Perturbation method; Weak nonlinearity; Oscillatory process; Strong damping; Varying coefficientsDOI: 10.3329/jbas.v34i1.5493Journal of Bangladesh Academy of Sciences, Vol.34, No.1, 71-82, 2010

Damping and Inertia Coefficients for Two Open Ends Squeeze Film Dampers With a Central Groove: Measurements and Predictions

2012 ◽  
Vol 134 (10) ◽  
Author(s):  
Luis San Andrés
Keyword(s):  
Short Length ◽  
Operating Conditions ◽  
The Other ◽  
System Stability ◽  
Squeeze Film ◽  
Inertia Force ◽  
Frequency Domain Method ◽  
Force Coefficients ◽  
Squeeze Film Dampers ◽  
Static Eccentricity

Aircraft engine rotors are particularly sensitive to rotor imbalance and sudden maneuver loads, since they are always supported on rolling element bearings with little damping. Most engines incorporate squeeze film dampers (SFDs) as means to dissipate mechanical energy from rotor vibrations and to ensure system stability. The paper quantifies experimentally the forced performance of a SFD comprising two parallel film lands separated by a deep central groove. Tests are conducted on two open ends SFDs, both with diameter D = 127 mm and nominal radial clearance c = 0.127 mm. One damper has film lands with length L = 12.7 mm (short length), while the other has 25.4 mm land lengths. The central groove has width L and depth 3/4 L. A light viscosity lubricant flows into the central groove via three orifices, 120 deg apart and then through the film lands to finally exit to ambient. In operation, a static loader pulls the bearing to various eccentric positions and electromagnetic shakers excite the test system with periodic loads to generate whirl orbits of specific amplitudes. A frequency domain method identifies the SFD damping and inertia force coefficients. The long damper generates six times more damping and about three times more added mass than the short length damper. The damping coefficients are sensitive to the static eccentricity (up to ∼ 0.5 c), while showing lesser dependency on the amplitude of whirl motion (up to 0.2 c). On the other hand, inertia coefficients increase mildly with static eccentricity and decrease as the amplitude of whirl motion increases. Cross-coupled force coefficients are insignificant for all imposed operating conditions on either damper. Large dynamic pressures recorded in the central groove demonstrate the groove does not isolate the adjacent squeeze film lands, but contributes to the amplification of the film lands’ reaction forces. Predictions from a novel SFD model that includes flow interactions in the central groove and feed orifices agree well with the test force coefficients for both dampers. The test data and predictions advance current knowledge and demonstrate that SFD-forced performance is tied to the lubricant feed arrangement.

Comparison of the Effects of Density and Sound Speed Variation in the Propagation of Planar Transient Waves

1992 ◽  
Vol 114 (3) ◽  
pp. 409-414
Author(s):  
J. H. Ginsberg
Keyword(s):  
Differential Equations ◽  
Material Properties ◽  
Sound Speed ◽  
Heterogeneous Media ◽  
Numerical Procedure ◽  
Mean Value ◽  
The Other ◽  
Transient Waves ◽  
One Dimensional ◽  
Spatial Grid

When expressed in the form of characteristic differential equations, the laws governing propagation of linear one-dimensional waves through heterogeneous media show that the only properties of significance are the sound speed c and the acoustic impedance ρc, either of which may vary spatially. The former occurs in the differential equations governing the (curved) characteristics, while the latter appears in the differential equations governing the evolution of particle velocity and stress along the characteristics. The present study employs an inherently stable finite difference representation of the characteristic equations, in which the spatial grid is obtained by evaluating the intersections in space-time of constant time lines with comparable increments of the characteristic variables. The numerical procedure is used to follow the propagation of a single-lobe sine pulse in cases where only ρ or c fluctuates spatially about a mean value while the other property is constant, and compares those results to the case were both material properties vary. Nonconstancy of c is shown to cause temporal shifts in waveforms, while spatial variation of ρc causes attenuation and distortion of the waveform.

COMPUTING MINKOWSKI SUMS OF PLANE CURVES

1995 ◽  
Vol 05 (04) ◽  
pp. 413-432 ◽  
Author(s):  
ANIL KAUL ◽  
RIDA T. FAROUKI
Keyword(s):  
Algebraic Curve ◽  
Numerical Procedure ◽  
The Other ◽  
Minkowski Sum ◽  
Plane Curves ◽  
Parametric Curves ◽  
Implicit Equation ◽  
Minkowski Sums ◽  
High Degree ◽  
The Given

The Minkowski sum of two plane curves can be regarded as the area generated by sweeping one curve along the other. The boundary of the Minkowski sum consists of translated portions of the given curves and/or portions of a more complicated curve, the “envelope” of translates of the swept curve. We show that the Minkowski-sum boundary is describable as an algebraic curve (or subset thereof) when the given curves are algebraic, and illustrate the computation of its implicit equation. However, such equations are typically of high degree and do not offer a practical basis for tracing the boundary. For the case of polynomial parametric curves, we formulate a simple numerical procedure to address the latter problem, based on constructing the Gauss maps of the given curves and using them to identifying “corresponding” curve segments that are to be summed. This yields a set of discretely-sampled arcs that constitutes a superset of the Minkowski-sum boundary, and can be regarded as a planar graph. To extract the true boundary, we present a method for identifying and “trimming” away extraneous arcs by systematically traversing this graph.

scholarly journals Energetic criterion in general elastic-plastic fracture mechanics

1993 ◽  
Vol 15 (1) ◽  
pp. 16-20
Author(s):  
Bui Huu Dan
Keyword(s):  
Experimental Data ◽  
Energy Balance ◽  
Fracture Mechanics ◽  
Crack Growth ◽  
Numerical Procedure ◽  
Slip Model ◽  
Elastic Plastic

From the analyzing the equation of energy balance for cracked bodies during the crack growth the energetic criterion is formulated for general elastic-plastic fracture mechanics. The numerical procedure should be realized by using the slip model of polycrystalline plasticity and the experimental data.

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