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 ◽  
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Abstract

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.

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.

Trend to spatial homogeneity for solutions to semilinear damped wave equations

1987 ◽  
Vol 105 (1) ◽  
pp. 117-126 ◽  
Author(s):  
J. Solà-Morales ◽  
M. València
Keyword(s):  
Boundary Conditions ◽  
Wave Equations ◽  
Lipschitz Constant ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
Spatial Homogeneity ◽  
Homogeneous Solutions ◽  
Spatially Homogeneous ◽  
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SynopsisThe semilinear damped wave equationssubject to homogeneous Neumann boundary conditions, admit spatially homogeneous solutions (i.e. u(x, t) = u(t)). In order that every solution tends to a spatially homogeneous one, we look for conditions on the coefficients a and d, and on the Lipschitz constant of f with respect to u.

The Heat Equation for the -Neumann Problem, II

1988 ◽  
Vol 40 (2) ◽  
pp. 502-512 ◽  
Author(s):  
Richard Beals ◽  
Nancy K. Stanton
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Neumann Problem ◽  
Elliptic Boundary ◽  
Neumann Boundary ◽  
Hermitian Manifold ◽  
Neumann Boundary Conditions ◽  
Compact Manifolds ◽  
Elliptic Boundary Value ◽  
Image Position

Let Ω be a compact complex n + 1-dimensional Hermitian manifold with smooth boundary M. In [2] we proved the following.THEOREM 1. Suppose satisfies condition Z(q) with 0 ≦ q ≦ n. Let □p,q denote the -Laplacian on (p, q) forms onwhich satisfy the -Neumann boundary conditions. Then as t → 0;,(0.1)(If q = n + 1, the -Neumann boundary condition is the Dirichlet boundary condition and the corresponding result is classical.)Theorem 1 is a version for the -Neumann problem of results initiated by Minakshisundaram and Pleijel [8] for the Laplacian on compact manifolds and extended by McKean and Singer [7] to the Laplacian with Dirichlet or Neumann boundary conditions and by Greiner [5] and Seeley [9] to elliptic boundary value problems on compact manifolds with boundary. McKean and Singer go on to show that the coefficients in the trace expansion are integrals of local geometric invariants.

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