scholarly journals Discrete-to-continuum limits of planar disclinations

2021 ◽  
Vol 27 ◽  
pp. 23
Author(s):  
Pierluigi Cesana ◽  
Patrick van Meurs
Keyword(s):  
Boundary Condition ◽  
Nearest Neighbor ◽  
Materials Science ◽  
Additional Term ◽  
Density Theorem ◽  
Special Boundary ◽  
Relaxation Methods ◽  
Planar Domains ◽  
Special Boundary Condition ◽  
Numerical Minimization

In materials science, wedge disclinations are defects caused by angular mismatches in the crystallographic lattice. To describe such disclinations, we introduce an atomistic model in planar domains. This model is given by a nearest-neighbor-type energy for the atomic bonds with an additional term to penalize change in volume. We enforce the appearance of disclinations by means of a special boundary condition. Our main result is the discrete-to-continuum limit of this energy as the lattice size tends to zero. Our proof relies on energy relaxation methods. The main mathematical novelty of our proof is a density theorem for the special boundary condition. In addition to our limit theorem, we construct examples of planar disclinations as solutions to numerical minimization of the model and show that classical results for wedge disclinations are recovered by our analysis.

Ermittlung der magnetischen Widerstandsänderung und der HALL-Spannung mittels eines Widerstandsnetzwerkes

1963 ◽  
Vol 18 (1) ◽  
pp. 44-51 ◽  
Author(s):  
C. B. Burckhardt ◽  
M. J. O. Strutt
Keyword(s):  
Magnetic Field ◽  
Boundary Condition ◽  
Boundary Value Problem ◽  
Iterative Process ◽  
Boundary Value ◽  
Special Method ◽  
Special Boundary ◽  
Free Boundaries ◽  
Special Boundary Condition ◽  
The Magnetic Field

The potential of a semiconductor slab in a magnetic field satisfies LAPLACE'S equation ΔV= 0. The magnetic field causes a special boundary condition at the free boundaries. It is shown how this boundary value problem is solved by means of a resistance-network and feeding currents. For obtaining stability of the iterative process the feeding currents have to be calculated by a special method. The accuracy of the solutions obtained is good, as comparison with calculation (square slab) and measurements (square gyrator) shows. Further possibilities of application are suggested.

scholarly journals Experimental and Theoretical Research on Bending Behavior of Photovoltaic Panels with a Special Boundary Condition

Energies ◽  
2018 ◽  
Vol 11 (12) ◽  
pp. 3435 ◽  
Author(s):  
Tengyuan Zhang ◽  
Lingzhi Xie ◽  
Yongxue Li ◽  
Tapas Mallick ◽  
Qingzhu Wei ◽  
...  
Keyword(s):  
Boundary Condition ◽  
Closed Form Solution ◽  
Form Solution ◽  
Theoretical Research ◽  
Systematic Research ◽  
Special Boundary ◽  
Governing Equations ◽  
Simply Supported ◽  
Special Boundary Condition ◽  
Bending Behavior

Currently, the photovoltaic (PV) panels widely manufactured on market are composed of stiff front and back layers and the solar cells embedded in a soft polymeric interlayer. The wind and snow pressure are the usual loads to which working PV panels need to face, and it needs the panels keep undamaged under those pressure when they generate electricity. Therefore, an accurate and systematic research on bending behavior of PV panels is important and necessary. In this paper, classical lamination theory (CLT) considering soft interlayer is applied to build governing equations of the solar panel. A Rayleigh–Rita method is modified to solve the governing equations and calculate the static deformation of the PV panel. Different from many previous researches only analyzing simply supported boundary condition for four edges, a special boundary condition which consists of two opposite edges simply supported and the others two free is studied in this paper. A closed form solution is derived out and used to do the numerical calculation. The corresponding bending experiments of PV panels are completed. Comparing the numerical results with experiment results, the accuracy of the analytical solutions are verified.

Design of a numerical model of lung by means of a special boundary condition in the truncated branches

2016 ◽  
Vol 33 (6) ◽  
pp. e2830 ◽  
Author(s):  
Ana F. Tena ◽  
Joaquín Fernández ◽  
Eduardo Álvarez ◽  
Pere Casan ◽  
D. Keith Walters
Keyword(s):  
Boundary Condition ◽  
Numerical Model ◽  
Special Boundary ◽  
Special Boundary Condition

scholarly journals Mixed boundary conditions in the relaxational treatment of biharmonic problems (plane strain or stress)

1947 ◽  
Vol 189 (1019) ◽  
pp. 535-543 ◽  
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Plane Strain ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Elastic Plates ◽  
Relaxation Methods ◽  
Valuable Alternative ◽  
Engineering Problems ◽  
Biharmonic Problems

Relaxation methods have already been applied to the solution of four problems of (i) extension and (ii) flexure of flat elastic plates, in which ( a ) displacement or ( b ) traction is specified at the boundary. Here the method is adapted to the case in which the two types of boundary condition are mixed, where photo-elastic methods are difficult to apply. Two examples are treated by relaxation methods, and the results obtained indicate that this method may be a valuable alternative in engineering problems.

scholarly journals Comparison between Vortex-In-Cell and Vortex Particle Methods on Two-Dimensional Problem

AVIA ◽  
2021 ◽  
Vol 3 (1) ◽  
Author(s):  
C X Canh ◽  
L R Zuhal ◽  
H Muhammad
Keyword(s):  
Boundary Condition ◽  
Numerical Methods ◽  
Nearest Neighbor ◽  
Particle Method ◽  
Vortex Method ◽  
Particle Methods ◽  
Immersed Boundary ◽  
Two Dimensional ◽  
N Body Problem ◽  
Vortex Particle

This research is concerned with the two-dimensional vortex method (VM) solvers. We develop and investigate the performance of the Vortex-In-Cell (VIC) and Vortex Particle Method (VPM) which are well known as the VM’s family members. The advantage of these both methods are that we can accelerate velocity computation procedure, an N-body problem in numerical methods, by using Fast Fourier Transform (FFT) and Fast Multipole Method (FMM), respectively. In addition, the viscous calculation process in VPM can be accelerated by using a scheme of Nearest Neighbor Particle Searching (NNPS) algorithms. Moreover, the no-through boundary condition treatment issue can be easily handled by using an immersed boundary condition for both methods. The accuracy and numerical cost of both numerical methods will be examined by simulating flow over an Impulsively Started Circular Cylinder and comparisons

Finite Element Modeling of Plane-Strain Strip Drawing With Interface Friction

1988 ◽  
Vol 110 (2) ◽  
pp. 101-110 ◽  
Author(s):  
S. C-Y. Lu ◽  
P. K. Wright
Keyword(s):  
Boundary Condition ◽  
Finite Element ◽  
Plane Strain ◽  
Large Strain ◽  
Interface Velocity ◽  
Velocity Model ◽  
Interface Friction ◽  
Special Boundary Condition ◽  
Drawing Die ◽  
Strip Drawing

Numerical results of plane-strain strip drawing are presented emphasizing the interfacial friction conditions between workmaterial and drawing die. The results are based on a large-strain elasto-plastic finite element code with a special boundary condition capability to treat interface friction. Two different modeling approaches are developed. In the interface velocity model, finite element solutions are based on the velocity boundary conditions along the die-work interface measured through transparent sapphire dies. In the interface traction model, a technique called “General Linear Boundary Condition,” is developed to incorporate many different existing friction models. Predicted values of drawing force, die separating force, global friction, and residual stresses from both models are favorably compared with the corresponding experimental measurements.

scholarly journals A simplified approach to the window gasket modeling for window strength calculation

Vestnik MGSU ◽  
2021 ◽  
pp. 317-330
Author(s):  
Ivan S. Aksenov ◽  
Aleksandr P. Konstantinov
Keyword(s):  
Boundary Condition ◽  
Reaction Force ◽  
Element Model ◽  
Structural Behavior ◽  
Simplified Approach ◽  
Various Boundary Conditions ◽  
Special Boundary Condition ◽  
Urgent Task ◽  
Static Operation ◽  
Deformed State

Introduction. The study of the influence of window deformations on their performance characteristics is an urgent task. This problem is related to the issues of window elements static operation under the combined action of wind and temperature loads. It is proposed to use the capabilities of modern finite element modeling programs to analyze the window static operation. One of the problems is the modeling of an elastic window gaskets. Materials and methods. Computation of a gasket structural behavior in the direct formulation is associated with significant computational costs. In this article it is proposed a simplified method which allows taking into account the gasket mechanical work when creating window fine element model in the COMSOL Multiphysics software. For this purpose, the dependence of the gasket reaction force on the degree of its compression was obtained; this dependence was used to create a special boundary condition that imitates the force transfer from one window element to another through the gasket. Results. Two test computations were carried out with the same loads and grip conditions: in one, the gasket was modeled directly, in the other, it was replaced by the boundary condition described above. The results showed good agreement between the computations, moreover the second one needed much less time. Conclusions. Scientific foundations of window design should be based on modern research methods including computer modeling. Creating a computer model of the window static operation will allow us to consider in detail its deformed state and operational characteristics under various boundary conditions. The method proposed in this article for modeling the gasket structural behavior will be useful in achieving this aim.

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