scholarly journals Numerical Studies on the Design of Self-Resetting Active Bistable Cross-Shaped Structure for Morphing Applications

Proceedings ◽  
2020 ◽  
Vol 64 (1) ◽  
pp. 16
Author(s):  
P. M. Anilkumar ◽  
A. Haldar ◽  
S. Scheffler ◽  
B. N. Rao ◽  
R. Rolfes
Keyword(s):  
Stable Equilibrium ◽  
Fibre Composite ◽  
Equilibrium Shape ◽  
Middle Portion ◽  
Stable Equilibrium State ◽  
Control Effort ◽  
Unsymmetric Laminates ◽  
Numerical Studies ◽  
Finite Element Package ◽  
Equilibrium Shapes

Multistable structures that possess more than one elastically stable equilibrium state are highly attractive for advanced shape-changing (morphing) applications due to the nominal control effort required to maintain the structure in any of its specific stable shapes. The aim of the paper is to develop a bistable cross-shaped structure consisting of symmetric and unsymmetric laminate actuated using Macro Fibre Composite (MFC) actuators. The critical snap-through voltages required to change the shapes are investigated in a commercially available finite element package. The use of MFC actuators to snap the bistable laminate from one equilibrium shape to another and back again (self-resetting) is demonstrated. A new cross-shaped design of active bistable laminate with MFC actuators is proposed where the cross-shape consist of four rectangles on the four legs and a square on the middle portion. All the rectangles are made up of unsymmetric laminates, and the central portion is designed with a symmetric laminate. MFC actuators are bonded on both sides of the four legs to trigger snap-through and snap-back actions. An attempt is made to address the possible design difficulties arising from the additional stiffness contribution by MFC layers on the naturally cured equilibrium shapes of cross-shaped bistable laminates.

Mechanics of membrane–membrane adhesion

2011 ◽  
Vol 16 (8) ◽  
pp. 872-886 ◽  
Author(s):  
Ashutosh Agrawal
Keyword(s):  
Lipid Vesicles ◽  
Spontaneous Curvature ◽  
Interface Conditions ◽  
Point Boundary ◽  
Lagrange Equations ◽  
Equilibrium Conditions ◽  
Numerical Studies ◽  
Curvature Elasticity ◽  
Equilibrium Shapes ◽  
Membrane Adhesion

Curvature elasticity is used to derive the equilibrium conditions that govern the mechanics of membrane–membrane adhesion. These include the Euler–Lagrange equations and the interface conditions which are derived here for the most general class of strain energies permissible for fluid surfaces. The theory is specialized for homogeneous membranes with quadratic ‘Helfrich’-type energies with non-uniform spontaneous curvatures. The results are employed to solve four-point boundary value problems that simulate the equilibrium shapes of lipid vesicles that adhere to each other. Numerical studies are conducted to investigate the effect of relative sizes, osmotic pressures, and adhesion-induced spontaneous curvature on the morphology of adhered vesicles.

Equilibrium dynamics in a model of growth and spatial agglomeration

2021 ◽  
pp. 1-26
Author(s):  
Shota Fujishima ◽  
Daisuke Oyama
Keyword(s):  
Economic Activity ◽  
Capital Accumulation ◽  
Time Preference ◽  
Stable Equilibrium ◽  
Spillover Effects ◽  
Spatial Equilibrium ◽  
Stable Equilibrium State ◽  
Macroeconomic Variables ◽  
Equilibrium Dynamics ◽  
Endogenous Growth Model

Abstract We present a multiregional endogenous growth model in which forward-looking agents choose their regions to live in, in addition to consumption and capital accumulation paths. The spatial distribution of economic activity is determined by the interplay between production spillover effects and urban congestion effects. We characterize the global stability of the spatial equilibrium states in terms of economic primitives such as agents’ time preference and intra- and interregional spillovers. We also study how macroeconomic variables at the stable equilibrium state behave according to the structure of the spillover network.

scholarly journals Entropy Generation Rate in a Chemically Reacting System

1993 ◽  
Vol 115 (3) ◽  
pp. 208-212 ◽  
Author(s):  
E. P. Gyftopoulos ◽  
G. P. Beretta
Keyword(s):  
Equilibrium State ◽  
Entropy Generation ◽  
Chemical Potential ◽  
Stable Equilibrium ◽  
Entropy Generation Rate ◽  
Stable Equilibrium State ◽  
Microscopic Reversibility ◽  
Chemical Reaction Mechanisms ◽  
Chemically Reacting ◽  
Surrogate System

For a nonchemical-equilibrium state of an isolated system A that has r constituents with initial amounts na = {n1a, n2a, …, nra}, and that is subject to τ chemical reaction mechanisms, temperature, pressure, and chemical potentials cannot be defined. As time evolves, the values of the amounts of constitutents vary according to the stoichiometric relations ni(t) = nia + Σj=1τ νi(j) εj(t), where νi(j) is the stoichiometric coefficient of the ith constituent in the j-reaction mechanism and εj(t) the reaction coordinate of the jth reaction at time t. For such a state, we approximate the values of all the properties at time t with the corresponding properties of the stable equilibrium state of a surrogate system B consisting of the same constituents as A with amounts equal to ni(t) for i = 1, 2, …, r, but experiencing no chemical reactions. Under this approximation, the rate of entropy generation is given by the expression S˙irr = ε˙ · Y, where ε˙ is the row vector of the τ rates of change of the reaction coordinates, ε˙ = { ε˙1, …, ε˙τ }, Y the column vector of the τ ratios aj/Toff for j = 1, 2, …, τ, aj = −Σi=1r νi(j) μi,off, that is, the jth affinity of the stable equilibrium state of the surrogate system B, and μi,off, and Toff are the chemical potential of the ith constituent and the temperature of the stable equilibrium state of the surrogate system. Under the same approximation, by further assuming that ε˙ can be represented as a function of Y only that is, ε˙(Y), with ε˙(0) = 0 for chemical equilibrium, we show that ε˙ = L·Y + (higher order terms in Y), where L is a τ × τ matrix that must be non-negative definite and symmetric, that is, such that the matrix elements Lij satisfy the Onsager reciprocal relations, Lij = Lji. It is noteworthy that, for the first time, the Onsager relations are proven without reference to microscopic reversibility. In our view, if a process is irreversible, microscopic reversibility does not exist.

scholarly journals Finite-dimensional maps describing the dynamics of a logistic equation with delay

2019 ◽  
Vol 487 (6) ◽  
pp. 611-616
Author(s):  
S. D. Glyzin ◽  
S. A. Kashchenko
Keyword(s):  
Numerical Simulation ◽  
Equilibrium State ◽  
Stable Equilibrium ◽  
Dynamic Properties ◽  
Logistic Equation ◽  
Mathematical Ecology ◽  
Stable Equilibrium State ◽  
Finite Dimensional ◽  
Equation With Delay ◽  
Dynamics Of Populations

This article discusses a family of maps that are used in the numerical simulation of a logistic equation with delay. This equation and presented maps are widely used in problems of mathematical ecology as models of the dynamics of populations. The paper compares the dynamic properties of the trajectories of these mappings and the original equation with delay. It is shown that the behavior of the solutions of maps can be quite complicated, while the logistic equation with delay has only a stable equilibrium state or cycle.

Size-Dependent Equilibrium Shapes of Solid Pb Inclusions in Al

1997 ◽  
Vol 3 (S2) ◽  
pp. 629-630
Author(s):  
U. Dahmen ◽  
E. Johnson ◽  
S.Q. Xiao ◽  
S. Paciornik ◽  
A. Johansen
Keyword(s):  
Size Dependence ◽  
Equilibrium Shape ◽  
Alloy System ◽  
Lattice Parameter ◽  
Al Alloys ◽  
Size Dependent ◽  
Interfacial Energies ◽  
Relative Extent ◽  
Equilibrium Shapes ◽  
Melting And Solidification

Small Pb inclusions in Al have been studied by a number of investigators because the alloy system offers the possibility of observing the processes of melting and solidification directly. Both solids are fee, and the mutual solubility of solid Pb and Al is negligible. Despite a large difference in lattice parameter, it has been found that inclusions follow a parallel-cube orientation relationship and their equilibrium shape is a cuboctahedron, bounded by ﹛111﹜ and ﹛100﹜ facets [1]. Following Herring, the relative extent of the two types of facet directly indicates a ratio of interfacial energies γl00/γ111- However, recent investigations have shown that for inclusions in the range of a few to a few tens of nanometers the equilibrium shape becomes a function of size [2].In the present work, this size dependence of the equilibrium shape has been investigated further. Al alloys with about lat.% Pb were prepared by rapid solidification or by ion implantation, and equilibrated by annealing at about 300°C.

Thermodynamic Definition and Quantum-Theoretic Pictorial Illustration of Entropy

1998 ◽  
Vol 120 (2) ◽  
pp. 154-160 ◽  
Author(s):  
E. P. Gyftopoulos
Keyword(s):  
Equilibrium State ◽  
Thermodynamic Equilibrium ◽  
Stable Equilibrium ◽  
Variable Temperature ◽  
Cyclic Change ◽  
Stable Equilibrium State ◽  
Change Of State ◽  
Laws Of Thermodynamics ◽  
External Forces ◽  
Work Done

Cannot analyzed an engine operating between two reservoirs. Through a peculiar mode of reasoning, he found the correct optimum shaft work done during a cyclic change of state of the engine. Clausius justified Carnot’s result by enunciating two laws of thermodynamics, and introducing the concept of entropy as a ratio of heat and temperature of a thermodynamic equilibrium state. In this paper, we accomplish five purposes: (i) We consider a Carnot engine. By appropriate algebraic manipulations we express Carnot’s optimum shaft work in terms of available energies or exergies of the end states of one reservoir with respect to the other, and Clausius’ entropy S in terms of the energies and available energies of the same and states. (ii) We consider the optimum shaft work done during a cyclic change of state of an engine operating between a reservoir, and a system with fixed amounts of constituents and fixed volume, but variable temperature. We express the optimum shaft work in terms of the available energies of the end states of the system, and Clausius’ entropy in terms of the energies and available energies of the same end states. Formally, the entropy expression is identical to that found for the Carnot engine, except that here the change of state of the system is not isothermal. (iii) We consider the optimum shaft work done during a cyclic change of state of a general engine operating between a reservoir R and system A which initially is in any state A1, stable or thermodynamic equilibrium or not stable equilibrium. In state A1, the values of the amounts of constituents are n1, and the value of the volume is V1 whereas, in the final state A0, n0 ≠ n1 and V0 ≠ V1 Using the laws of thermodynamics presented by Gyftopoulos and Beretta, we prove that such an optimum exists, call it generalized available energy with respect to R, and use it together with the energy to define a new property Σ1 We note that the expression for Σ is formally identical to and satisfies the same criteria as Clausius’ entropy S. The only difference is that Σ applies to all states, whereas Clausius’ S applies only to stable equilibrium states. So we call Σ entropy and denote it by S (iv) We use the unified quantum theory of mechanics and thermodynamics developed by Hatsopoulos and Gyftopoulos, and find a quantum theoretic expression for S in terms of the density operator ρ that yields all the probabilities associated with measurement results. (v) We note that the quantumtheoritic expression for S can be interpreted as a measure of the shape of an atom, molecule, or other system because ρ can be though of as such a shape, and provide pictorial illustrations of this interpretation. For given values of energy E, amounts of constituents n, and volume V, the value of the measure is zero for all shapes that correspond to projectors (wave functions), positive for density operators that are not projectors, and the largest for the ρ that corresponds to the unique stable equilibrium state determined by the given E, n, and V. Accordingly, spontaneous entropy generation occurs as a system adapts its shape to conform to the internal and external forces. Beginning with an arbitrary initial ρ this adaptation continues only until no further spontaneous change of shape can occur, that is, only until a stable equilibrium state is reached.

Shape training of Ge precipitates in an Al-1.8at% Ge alloy

1994 ◽  
Vol 52 ◽  
pp. 690-691
Author(s):  
S. Hinderberger ◽  
S. Q. Xiao ◽  
K. H. Westmacott ◽  
U. Dahmen
Keyword(s):  
Room Temperature ◽  
Equilibrium Shape ◽  
Bulk Sample ◽  
Temperature Cycling ◽  
Orientation Relationships ◽  
Rich Variety ◽  
Direct Observations ◽  
Equilibrium Shapes ◽  
Ice Water

Ge precipitates in Al are known to form in a rich variety of shapes and orientation relationships. In this work it is shown that initial non-equilibrium shapes such as plates, laths, needles and tetrahedra can be induced to change to the equilibrium shape of an octahedron by proper temperature cycling. Analysis of this effect in bulk samples was complemented by direct observations of its mechanisms during in-situ temperature cycling.A bulk sample of an Al-1.8at%Ge alloy was solid solution annealed at 420°C for 2h, quenched in ice water, pre-aged at room temperature for 72h and then annealed for 5h at 250°C. Subsequently, part of the sample was repeatedly cycled between 250°C and 360°C. TEM specimens were prepared from both the cycled and non-cycled bulk sample by conventional electropolishing and examined in a JEOL 200CX electron microscope. The in-situ temperature cycling was carried out in a Kratos 1.5 MeV HVEM equipped with a double tilt heating stage.

Development and Characterizations of Liquid Bridge Based Microstereolithography (LBMSL) System

2017 ◽  
Author(s):  
Yanfeng Lu ◽  
Jeongwoo Lee ◽  
Sumanth Kashyap ◽  
Md. Omar Faruk Emon ◽  
Jae-Won Choi
Keyword(s):  
Layer Thickness ◽  
Liquid Bridge ◽  
Stable Equilibrium ◽  
Equilibrium Shape ◽  
Fabrication Process ◽  
Material Consumption ◽  
Oxygen Inhibition ◽  
The Relationship ◽  
Fabrication Time

In this work, a novel liquid bridge based microstereolithography (LBMSL) was proposed and developed. The liquid bridge was first introduced into the MSL process by replacing the vat, allowing the entire fabrication process to occur within the liquid bridge. The liquid bridge was studied theoretically and experimentally in order to obtain the stable equilibrium shape and the relationship between the height and the volume of the liquid bridge. Using the LBMSL process, the fabrication layer thickness of 0.5 μm was reached. This could not be easily achieved in the vat-based MSL due to the oxygen inhibition to the photopolymer. Fabrication of a photopolymer with a viscosity of 3000 cP was tested and significant results were obtained. Compared with the vat-based MSL, the material consumption in LBMSL was reduced and the fabrication time was improved greatly, in particular, when using higher viscous materials.

EQUILIBRIUM CONFIGURATIONS OF ADHERING TUBULAR VESICLES UNDER EXTERNAL LOADS

2006 ◽  
Vol 20 (10) ◽  
pp. 1201-1210
Author(s):  
DONG NI ◽  
HUIJI SHI ◽  
YAJUN YIN
Keyword(s):  
Theoretical Model ◽  
Boundary Conditions ◽  
External Force ◽  
Equilibrium Shape ◽  
Lipid Vesicles ◽  
Equilibrium Configurations ◽  
Applied Forces ◽  
Equilibrium Shapes ◽  
External Loads

A theoretical model is developed to describe the influence of external loads on the equilibrium shapes of adhering tubular lipid vesicles. In the case of nonspecific adhesion, the equilibrium shape equations and boundary conditions are derived through the method analogous to previous research. For a range of applied forces, locally stable bound shapes are simulated. Along with the increase or decrease the external force, the process for adhering vesicle disengaging from or sprawling to the substrate is predicted and analyzed.

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