On the Principle of Haar and von Karman in Statically Determinate Problems of Plasticity

1957 ◽  
Vol 24 (3) ◽  
pp. 461-463
Author(s):  
Leo Finzi
Keyword(s):  
Energy Density ◽  
Elastic Energy ◽  
Yield Condition ◽  
Variational Formula ◽  
Stress Strain ◽  
Von Karman ◽  
The One ◽  
Von Kármán

Abstract It is shown that a variational formula similar to the one expressing the principle of Haar and von Karman in the statically determinate problems of plasticity holds independently of the stress-strain relations and yield condition. In the variation of the elastic energy the part connected with the variation of the field must be distinguished from the part connected with the variation of the energy density. These points are illustrated by an example.

Existence of a sharp transition in the peak propulsive efficiency of a low- pitching foil

2016 ◽  
Vol 800 ◽  
pp. 307-326 ◽  
Author(s):  
Anil Das ◽  
Ratnesh K. Shukla ◽  
Raghuraman N. Govardhan
Keyword(s):  
Power Coefficient ◽  
Energetic Cost ◽  
Mean Power ◽  
Thrust Coefficient ◽  
Propulsive Efficiency ◽  
Von Karman ◽  
Wide Range ◽  
The Mean ◽  
The One ◽  
Von Kármán

We perform a comprehensive characterization of the propulsive performance of a thrust generating pitching foil over a wide range of Reynolds ($10\leqslant Re\leqslant 2000$) and Strouhal ($St$) numbers using a high-resolution viscous vortex particle method. For a given $Re$, we show that the mean thrust coefficient $\overline{C_{T}}$ increases monotonically with $St$, exhibiting a sharp rise as the location of the inception of the wake asymmetry shifts towards the trailing edge. As a result, the propulsive efficiency too rises steeply before attaining a maximum and eventually declining at an asymptotic rate that is consistent with the inertial scalings of $St^{2}$ for $\overline{C_{T}}$ and $St^{3}$ for the mean power coefficient, with the latter scaling holding, quite remarkably, over the entire range of $Re$. We find the existence of a sharp increase in the peak propulsive efficiency ${\it\eta}_{max}$ (at a given $Re$) in the $Re$ range of 50 to approximately 1000, with ${\it\eta}_{max}$ increasing rapidly from about 1.7 % to the saturated asymptotic value of approximately $16\,\%$. The $St$ at which ${\it\eta}_{max}$ is attained decreases progressively with $Re$ towards an asymptotic limit of $0.45$ and always exceeds the one for transition from a reverse von Kármán to a deflected wake. Moreover, the drag-to-thrust transition occurs at a Strouhal number $St_{tr}$ that exceeds the one for von Kármán to reverse von Kármán transition. The $St_{tr}$ and the corresponding power coefficient $\overline{C_{p,}}_{tr}$ are found to be remarkably consistent with the simple scaling relationships $St_{tr}\sim Re^{-0.37}$ and $\overline{C_{p,}}_{tr}\sim Re^{-1.12}$ that are derived from a balance of the thrust generated from the pitching motion and the drag force arising out of viscous resistance to the foil motion. The fact that the peak propulsive efficiency degrades appreciably only below $Re\approx 10^{3}$ establishes a sharp lower threshold for energetically efficient thrust generation from a pitching foil. Our findings should be generalizable to other thrust-producing flapping foil configurations and should aid in establishing the link between wake patterns and energetic cost of thrust production in similar systems.

scholarly journals Stochastic Intermittency Fields in a von Kármán Experiment

Symmetry ◽  
2021 ◽  
Vol 13 (9) ◽  
pp. 1752
Author(s):  
Jürgen Schmiegel ◽  
Flavio Pons
Keyword(s):  
Time Series ◽  
Energy Dissipation ◽  
Turbulent Flow ◽  
Turbulence Intensity ◽  
Statistical Properties ◽  
Close Resemblance ◽  
Von Karman ◽  
The One ◽  
Von Kármán

We discuss the application of stochastic intermittency fields to describe and analyse the statistical properties of time series of the generalised turbulence intensity in an anisotropic and inhomogeneous turbulent flow and provide a parsimonious description of the one-, two-, and three-point statistics. In particular, we show that the three-point correlations can be predicted from observed two-point statistics. Our analysis is motivated by observed stylised features of the energy dissipation in homogeneous and isotropic situations where these statistical properties are well represented within the framework of stochastic intermittency fields. We find a close resemblance and conclude that stochastic intermittency fields may be relevant in more general situations.

An Extension of Burzyński Hypothesis of Material Effort Accounting for the Third Invariant of Stress Tensor

2011 ◽  
Vol 56 (2) ◽  
pp. 503-508 ◽  
Author(s):  
R. Pęcherski ◽  
P. Szeptyński ◽  
M. Nowak
Keyword(s):  
Stress Tensor ◽  
Elastic Energy ◽  
Yield Condition ◽  
The Third ◽  
Third Invariant ◽  
Lode Angle

An Extension of Burzyński Hypothesis of Material Effort Accounting for the Third Invariant of Stress Tensor The aim of the paper is to propose an extension of the Burzyński hypothesis of material effort to account for the influence of the third invariant of stress tensor deviator. In the proposed formulation the contribution of the density of elastic energy of distortion in material effort is controlled by Lode angle. The resulted yield condition is analyzed and possible applications and comparison with the results known in the literature are discussed.

scholarly journals Target metric and Shell Shaping

2021 ◽  
Vol 8 (1) ◽  
pp. 13-25
Author(s):  
Gloria Rita Argento ◽  
Stefano Gabriele ◽  
Luciano Teresi ◽  
Valerio Varano
Keyword(s):  
Elastic Energy ◽  
Elastic Shell ◽  
The Other ◽  
The One

Abstract We exploit the possibility of deforming a shell by assigning a target metric, which, for 2D structures, is decomposed into the first and second target fundamental-forms. As well known, an elastic shell may change its shape under two different kinds of actions: one are the loadings, the other one are the distortions, also known as the pre-strains. Actually, the target fundamental forms prescribe a sought shape for the solid, and the metric effectively realized is the one that minimizes the distance, measured through an elastic energy, between the target and the actual fundamental forms. The proposed method is very effective in deforming shells.

scholarly journals The two-dimensional hydrodynamical theory of moving aerofoils. IV

1947 ◽  
Vol 188 (1015) ◽  
pp. 439-463
Keyword(s):  
Stability Problem ◽  
Two Dimensional ◽  
Centre Of Gravity ◽  
First Approximation ◽  
Von Karman ◽  
Moving Cylinder ◽  
Period Equation ◽  
The Stability ◽  
Von Kármán ◽  
Hydrodynamical Theory

In the first part of this paper opportunity has been taken to make some adjustments in certain general formulae of previous papers, the necessity for which appeared in discussions with other workers on this subject. The general results thus amended are then applied to a general discussion of the stability problem including the effect of the trailing wake which was deliberately excluded in the previous paper. The general conclusion is that to a first approximation the wake, as usually assumed, has little or no effect on the reality of the roots of the period equation, but that it may introduce instability of the oscillations, if the centre of gravity of the element is not sufficiently far forward. During the discussion contact is made with certain partial results recently obtained by von Karman and Sears, which are shown to be particular cases of the general formulae. An Appendix is also added containing certain results on the motion of a vortex behind a moving cylinder, which were obtained to justify certain of the assumptions underlying the trail theory.

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