How to save a bad element with weak boundary conditions

2006 ◽  
Vol 35 (5) ◽  
pp. 477-484 ◽  
Author(s):  
Emmanuel Hanert ◽  
Vincent Legat
Keyword(s):  
Boundary Conditions ◽  
Weak Boundary ◽  
Weak Boundary Conditions

Elasticity Solutions to Nonbuckling Serpentine Ribbons

2016 ◽  
Vol 84 (2) ◽  
Author(s):  
Shixuan Yang ◽  
Shutao Qiao ◽  
Nanshu Lu
Keyword(s):  
Boundary Conditions ◽  
Electronic Materials ◽  
Beam Theory ◽  
Stretchable Electronics ◽  
Curved Beam ◽  
Weak Boundary ◽  
The Matrix ◽  
Elasticity Solutions ◽  
Weak Boundary Conditions ◽  
Total Curve

Stretchable electronics have found wide applications in bio-mimetic and bio-integrated electronics attributing to their softness, stretchability, and conformability. Although conventional electronic materials are intrinsically stiff and brittle, silicon and metal membranes can be patterned into in-plane serpentine ribbons for enhanced stretchability and compliance. While freestanding thin serpentine ribbons may easily buckle out-of-plane, thick serpentine ribbons may remain unbuckled upon stretching. Curved beam (CB) theory has been applied to analytically solve the strain field and the stiffness of freestanding, nonbuckling serpentine ribbons. While being able to fully capture the strain and stiffness of narrow serpentines, the theory cannot provide accurate solutions to serpentine ribbons whose widths are comparable to the arc radius. Here we report elasticity solutions to accurately capture nonbuckling, wide serpentine ribbons. We have demonstrated that weak boundary conditions are sufficient for solving Airy stress functions except when the serpentine’s total curve length approaches the ribbon width. Slightly modified weak boundary conditions are proposed to resolve this difficulty. Final elasticity solutions are fully validated by finite element models (FEM) and are compared with results obtained by the curved beam theory. When the serpentine ribbons are embedded in polymer matrices, their stretchability may be compromised due to the fact that the matrix can constrain the in-plane rotation of the serpentine. Comparison between the analytical solutions for freestanding serpentines and the FEM solutions for matrix-embedded serpentines reveals that matrix constraint remains trivial until the matrix modulus approaches that of the serpentine ribbon.

Modes of deformation and weak boundary conditions in wedge indentation

2012 ◽  
Vol 2 (2) ◽  
pp. 47-50 ◽  
Author(s):  
Narayan Sundaram ◽  
Yang Guo ◽  
Srinivasan Chandrasekar
Keyword(s):  
Boundary Conditions ◽  
Weak Boundary ◽  
Wedge Indentation ◽  
Weak Boundary Conditions ◽  
Image Position

Abstract

Changing the symmetry of a homogeneous instability with a change in temperature in a stationary shear flow of a nematic with weak boundary conditions in an electromagnetic field

2012 ◽  
Vol 9 (2) ◽  
pp. 101-106
Author(s):  
I.Sh Nasibullayev
Keyword(s):  
Electromagnetic Field ◽  
Liquid Crystal ◽  
Shear Flow ◽  
Boundary Conditions ◽  
Nematic Liquid Crystal ◽  
Numerical Study ◽  
Weak Boundary ◽  
Weak Boundary Conditions

In this work, a numerical study is made of the induced switching symmetry of a homogeneous instability by temperature in a stationary shear flow of a nematic liquid crystal under electromagnetic field with weak boundary conditions.

scholarly journals A Flexible Boundary Procedure for Hyperbolic Problems: Multiple Penalty Terms Applied in a Domain

2014 ◽  
Vol 16 (2) ◽  
pp. 345-358 ◽  
Author(s):  
Jan Nordström ◽  
Qaisar Abbas ◽  
Brittany A. Erickson ◽  
Hannes Frenander
Keyword(s):  
Finite Difference ◽  
Boundary Conditions ◽  
Finite Difference Methods ◽  
Difference Operators ◽  
Hyperbolic Problems ◽  
Order Of Accuracy ◽  
Weak Boundary ◽  
Difference Methods ◽  
Weak Boundary Conditions ◽  
High Order Finite Difference

AbstractA new weak boundary procedure for hyperbolic problems is presented. We consider high order finite difference operators of summation-by-parts form with weak boundary conditions and generalize that technique. The new boundary procedure is applied near boundaries in an extended domain where data is known. We show how to raise the order of accuracy of the scheme, how to modify the spectrum of the resulting operator and how to construct non-reflecting properties at the boundaries. The new boundary procedure is cheap, easy to implement and suitable for all numerical methods, not only finite difference methods, that employ weak boundary conditions. Numerical results that corroborate the analysis are presented.

BOUNDARY CONDITIONS AND EXISTENCE RESULTS FOR LEVERMORE'S MOMENTS SYSTEM

2000 ◽  
Vol 10 (01) ◽  
pp. 127-152 ◽  
Author(s):  
P. LE TALLEC ◽  
J. P. PERLAT
Keyword(s):  
Boltzmann Equation ◽  
Boundary Conditions ◽  
Mathematical Analysis ◽  
Existence Results ◽  
Hyperbolic Structure ◽  
Dissipation Inequality ◽  
Moment Expansion ◽  
Linearized Problem ◽  
Flux Boundary Conditions ◽  
Weak Boundary Conditions

This paper considers the 14 moment expansion of the Boltzmann equation proposed by D. Levermore. After a brief review of this model, we derive weak boundary conditions compatible with the hyperbolic structure of the model, and express in average the microscopic boundary conditions imposed to the gas. This choice of half flux boundary conditions is justified by a mathematical analysis of the resulting linearized problem. Using standard parabolic regularization arguments and a specific dissipation inequality, we prove that the linearized problem has a unique solution.

Use of the Magnetostatic Analogue In Electromagnetic Lens Engineering

1970 ◽  
Vol 28 ◽  
pp. 360-361
Author(s):  
John W. Coleman
Keyword(s):  
Boundary Conditions ◽  
High Performance ◽  
Force Fields ◽  
Optical Design ◽  
Direct Conversion ◽  
Design Engineering ◽  
Design Data ◽  
Scalar Potentials ◽  
Geometric Elements ◽  
At Will

In the design engineering of high performance electromagnetic lenses, the direct conversion of electron optical design data into drawings for reliable hardware is oftentimes difficult, especially in terms of how to mount parts to each other, how to tolerance dimensions, and how to specify finishes. An answer to this is in the use of magnetostatic analytics, corresponding to boundary conditions for the optical design. With such models, the magnetostatic force on a test pole along the axis may be examined, and in this way one may obtain priority listings for holding dimensions, relieving stresses, etc..The development of magnetostatic models most easily proceeds from the derivation of scalar potentials of separate geometric elements. These potentials can then be conbined at will because of the superposition characteristic of conservative force fields.

A digital vocal tract simulator with boundary conditions at lips and glottis

1981 ◽  
Vol 64 (11) ◽  
pp. 18-26 ◽  
Author(s):  
Tetsuya Nomura ◽  
Nobuhiro Miki ◽  
Nobuo Nagai
Keyword(s):  
Boundary Conditions ◽  
Vocal Tract
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