On Nonuniqueness and Stability in Barber’s Model of Thermoelastic Contact

1996 ◽  
Vol 63 (3) ◽  
pp. 582-586 ◽  
Author(s):  
Z. S. Olesiak ◽  
Yu. A. Pyryev
Keyword(s):  
Boundary Conditions ◽  
Thermal Resistance ◽  
Numerical Solutions ◽  
Computational Simulation ◽  
Nonstationary Problem ◽  
Number Of Solutions ◽  
Thermoelastic Contact ◽  
Resistance Function ◽  
Special Cases ◽  
Unstable Solutions

In the recent our paper we have derived an algorithm which lets us find numerical solutions of special cases of a nonstationary problem of thermoelasticity with imperfect boundary conditions of Barber’s model. In this paper we show the results of computational simulation for a case of the thermal resistance function. We have obtained a number of solutions for different situations and have discussed the unique, nonunique, stable, and unstable solutions. We have found cases when the unique and nonunique solutions alternate. The results have been presented in the form of diagrams.

Thin Rectangular Plates on Elastic Foundation

1952 ◽  
Vol 19 (3) ◽  
pp. 361-368
Author(s):  
H. J. Fletcher ◽  
C. J. Thorne
Keyword(s):  
Boundary Conditions ◽  
Rectangular Plate ◽  
Elastic Foundation ◽  
Numerical Solutions ◽  
The Other ◽  
Rectangular Plates ◽  
Transverse Loads ◽  
Sine Transform ◽  
Special Cases ◽  
Plates On Elastic Foundation

Abstract The deflection of a thin rectangular plate on an elastic foundation is given for the case in which two opposite edges have arbitrary but given deflections and moments. Six important cases of boundary conditions on the remaining two edges are treated. The solution is given for general transverse loads which are continuous in one direction and sectionally continuous in the other. By use of the sine transform the solution is obtained as a single trigonometric series. Numerical solutions are obtained for six special cases.

Postbuckling Behavior of Rectangular Plates With Small Initial Curvature Loaded in Edge Compression

1959 ◽  
Vol 26 (3) ◽  
pp. 407-414
Author(s):  
Noboru Yamaki
Keyword(s):  
Boundary Conditions ◽  
Numerical Solutions ◽  
Thin Plates ◽  
Large Deflections ◽  
Effective Width ◽  
Rectangular Plates ◽  
Postbuckling Behavior ◽  
Initial Curvature ◽  
Special Cases ◽  
Fundamental Equations

Abstract The solution of Marguerre’s fundamental equations for large deflections of thin plates with slight initial curvature is presented for the case of a rectangular plate subjected to edge compression. The problem is solved under eight different boundary conditions, combining two kinds of loading conditions and four kinds of supporting conditions. Numerical solutions are obtained for square plates with and without initial deflection, and the connections of deflection, edge shortening, and effective width of the plate with applied loads are clarified. The solutions here obtained include as special cases those investigated by Levy and Coan.

scholarly journals Effects of Loading and Boundary Conditions on the Performance of Ultrasound Compressional Viscoelastography: A Computational Simulation Study to Guide Experimental Design

Materials ◽  
2021 ◽  
Vol 14 (10) ◽  
pp. 2590
Author(s):  
Che-Yu Lin ◽  
Ke-Vin Chang
Keyword(s):  
Boundary Conditions ◽  
Simulation Study ◽  
Viscoelastic Properties ◽  
Measurement Accuracy ◽  
Computational Simulation ◽  
Vertical Direction ◽  
Fixation Method ◽  
Element Analysis ◽  
Sample Container

Most biomaterials and tissues are viscoelastic; thus, evaluating viscoelastic properties is important for numerous biomedical applications. Compressional viscoelastography is an ultrasound imaging technique used for measuring the viscoelastic properties of biomaterials and tissues. It analyzes the creep behavior of a material under an external mechanical compression. The aim of this study is to use finite element analysis to investigate how loading conditions (the distribution of the applied compressional pressure on the surface of the sample) and boundary conditions (the fixation method used to stabilize the sample) can affect the measurement accuracy of compressional viscoelastography. The results show that loading and boundary conditions in computational simulations of compressional viscoelastography can severely affect the measurement accuracy of the viscoelastic properties of materials. The measurement can only be accurate if the compressional pressure is exerted on the entire top surface of the sample, as well as if the bottom of the sample is fixed only along the vertical direction. These findings imply that, in an experimental validation study, the phantom design should take into account that the surface area of the pressure plate must be equal to or larger than that of the top surface of the sample, and the sample should be placed directly on the testing platform without any fixation (such as a sample container). The findings indicate that when applying compressional viscoelastography to real tissues in vivo, consideration should be given to the representative loading and boundary conditions. The findings of the present simulation study will provide a reference for experimental phantom designs regarding loading and boundary conditions, as well as guidance towards validating the experimental results of compressional viscoelastography.

scholarly journals Regular approximation of singular Sturm–Liouville problems with eigenparameter dependent boundary conditions

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Maozhu Zhang ◽  
Kun Li ◽  
Hongxiang Song
Keyword(s):  
Boundary Conditions ◽  
Operator Theory ◽  
Resolvent Convergence ◽  
Spectral Inclusion ◽  
Regular Approximation ◽  
Special Cases ◽  
Abstract Operator ◽  
Norm Resolvent Convergence ◽  
Sturm Liouville ◽  
Spectral Exactness

AbstractIn this paper we consider singular Sturm–Liouville problems with eigenparameter dependent boundary conditions and two singular endpoints. The spectrum of such problems can be approximated by those of the inherited restriction operators constructed. Via the abstract operator theory, the strongly resolvent convergence and norm resolvent convergence of a sequence of operators are obtained and it follows that the spectral inclusion of spectrum holds. Moreover, spectral exactness of spectrum holds for two special cases.

scholarly journals Impurity induced scale-free localization

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Linhu Li ◽  
Ching Hua Lee ◽  
Jiangbin Gong
Keyword(s):  
Boundary Conditions ◽  
Skin Effect ◽  
Reciprocal Lattice ◽  
Periodic Boundary Conditions ◽  
Open Boundary ◽  
Open Boundary Conditions ◽  
Translational Invariance ◽  
Scale Free ◽  
Special Cases ◽  
Simulation Results

AbstractNon-Hermitian systems have been shown to have a dramatic sensitivity to their boundary conditions. In particular, the non-Hermitian skin effect induces collective boundary localization upon turning off boundary coupling, a feature very distinct from that under periodic boundary conditions. Here we develop a full framework for non-Hermitian impurity physics in a non-reciprocal lattice, with periodic/open boundary conditions and even their interpolations being special cases across a whole range of boundary impurity strengths. We uncover steady states with scale-free localization along or even against the direction of non-reciprocity in various impurity strength regimes. Also present are Bloch-like states that survive albeit broken translational invariance. We further explore the co-existence of non-Hermitian skin effect and scale-free localization, where even qualitative aspects of the system’s spectrum can be extremely sensitive to impurity strength. Specific circuit setups are also proposed for experimentally detecting the scale-free accumulation, with simulation results confirming our main findings.

scholarly journals Coupled Systems of Sequential Caputo and Hadamard Fractional Differential Equations with Coupled Separated Boundary Conditions

Symmetry ◽  
2018 ◽  
Vol 10 (12) ◽  
pp. 701 ◽  
Author(s):  
Suphawat Asawasamrit ◽  
Sotiris Ntouyas ◽  
Jessada Tariboon ◽  
Woraphak Nithiarayaphaks
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Coupled Systems ◽  
Uniqueness Of Solutions ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Hadamard Fractional Differential Equations ◽  
Special Cases ◽  
Separated Boundary Conditions ◽  
Fractional Differential

This paper studies the existence and uniqueness of solutions for a new coupled system of nonlinear sequential Caputo and Hadamard fractional differential equations with coupled separated boundary conditions, which include as special cases the well-known symmetric boundary conditions. Banach’s contraction principle, Leray–Schauder’s alternative, and Krasnoselskii’s fixed-point theorem were used to derive the desired results, which are well-illustrated with examples.

scholarly journals Numerical Boundary Conditions for Solar Magnetic Hydrodynamic Flows Using the Method of Characteristics

1996 ◽  
Vol 154 ◽  
pp. 149-153
Author(s):  
S. T. Wu ◽  
A. H. Wang ◽  
W. P. Guo
Keyword(s):  
Boundary Conditions ◽  
Method Of Characteristics ◽  
Numerical Solutions ◽  
The Self ◽  
Time Dependent ◽  
Solar Plasma ◽  
The Method Of Characteristics ◽  
Mhd Simulations ◽  
Self Consistent ◽  
Dynamic Structures

AbstractWe discuss the self-consistent time-dependent numerical boundary conditions on the basis of theory of characteristics for magnetohydrodynamics (MHD) simulations of solar plasma flows. The importance of using self-consistent boundary conditions is demonstrated by using an example of modeling coronal dynamic structures. This example demonstrates that the self-consistent boundary conditions assure the correctness of the numerical solutions. Otherwise, erroneous numerical solutions will appear.

scholarly journals The effect of surface tension on steadily translating bubbles in an unbounded Hele-Shaw cell

2017 ◽  
Vol 473 (2201) ◽  
pp. 20170050 ◽  
Author(s):  
Christopher C. Green ◽  
Christopher J. Lustri ◽  
Scott W. McCue
Keyword(s):  
Surface Tension ◽  
Numerical Solutions ◽  
Bubble Velocity ◽  
Number Of Solutions ◽  
Branch Number ◽  
Single Solution ◽  
Countably Infinite ◽  
Prime Function ◽  
Hele Shaw Cell ◽  
Effect Of Surface

New numerical solutions to the so-called selection problem for one and two steadily translating bubbles in an unbounded Hele-Shaw cell are presented. Our approach relies on conformal mapping which, for the two-bubble problem, involves the Schottky-Klein prime function associated with an annulus. We show that a countably infinite number of solutions exist for each fixed value of dimensionless surface tension, with the bubble shapes becoming more exotic as the solution branch number increases. Our numerical results suggest that a single solution is selected in the limit that surface tension vanishes, with the scaling between the bubble velocity and surface tension being different to the well-studied problems for a bubble or a finger propagating in a channel geometry.

Microprocessor Silicon Die Temperature Prediction by Simplified Boundary Conditions

2015 ◽  
Author(s):  
Koji Nishi ◽  
Tomoyuki Hatakeyama ◽  
Shinji Nakagawa ◽  
Masaru Ishizuka
Keyword(s):  
Heat Transfer ◽  
Heat Conduction ◽  
Boundary Conditions ◽  
Thermal Resistance ◽  
Hot Spot ◽  
Three Dimensional ◽  
Thermal Design ◽  
Target Temperature ◽  
One Dimensional ◽  
Thermal Network

The thermal network method has a long history with thermal design of electronic equipment. In particular, a one-dimensional thermal network is useful to know the temperature and heat transfer rate along each heat transfer path. It also saves computation time and/or computation resources to obtain target temperature. However, unlike three-dimensional thermal simulation with fine pitch grids and a three-dimensional thermal network with sufficient numbers of nodes, a traditional one-dimensional thermal network cannot predict the temperature of a microprocessor silicon die hot spot with sufficient accuracy in a three-dimensional domain analysis. Therefore, this paper introduces a one-dimensional thermal network with average temperature nodes. Thermal resistance values need to be obtained to calculate target temperature in a thermal network. For this purpose, thermal resistance calculation methodology with simplified boundary conditions, which calculates thermal resistance values from an analytical solution, is also introduced in this paper. The effectiveness of the methodology is explored with a simple model of the microprocessor system. The calculated result by the methodology is compared to a three-dimensional heat conduction simulation result. It is found that the introduced technique matches the three-dimensional heat conduction simulation result well.

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