scholarly journals Patch‐Smoother and Multigrid for the Dual Formulation for Linear Elasticity

2021 ◽  
Author(s):  
Gabriele Rovi ◽  
Rolf Krause
Keyword(s):  
Linear Elasticity ◽  
Dual Formulation

Computing cell tractions from particle displacements on silicone rubber substrata

1994 ◽  
Vol 52 ◽  
pp. 162-163
Author(s):  
Tim Oliver ◽  
Akira Ishihara ◽  
Ken Jacobsen ◽  
Micah Dembo
Keyword(s):  
Plane Stress ◽  
Linear Elasticity ◽  
Silicone Rubber ◽  
Mathematical Analysis ◽  
Elastic Recovery ◽  
Video Images ◽  
Cell Traction Forces ◽  
Latex Beads ◽  
Cell Traction ◽  
Better Than

In order to better understand the distribution of cell traction forces generated by rapidly locomoting cells, we have applied a mathematical analysis to our modified silicone rubber traction assay, based on the plane stress Green’s function of linear elasticity. To achieve this, we made crosslinked silicone rubber films into which we incorporated many more latex beads than previously possible (Figs. 1 and 6), using a modified airbrush. These films could be deformed by fish keratocytes, were virtually drift-free, and showed better than a 90% elastic recovery to micromanipulation (data not shown). Video images of cells locomoting on these films were recorded. From a pair of images representing the undisturbed and stressed states of the film, we recorded the cell’s outline and the associated displacements of bead centroids using Image-1 (Fig. 1). Next, using our own software, a mesh of quadrilaterals was plotted (Fig. 2) to represent the cell outline and to superimpose on the outline a traction density distribution. The net displacement of each bead in the film was calculated from centroid data and displayed with the mesh outline (Fig. 3).

scholarly journals A Note on the Decomposition Methods for Support Vector Regression

2002 ◽  
Vol 14 (6) ◽  
pp. 1267-1281 ◽  
Author(s):  
Shuo-Peng Liao ◽  
Hsuan-Tien Lin ◽  
Chih-Jen Lin
Keyword(s):  
Support Vector Regression ◽  
Decomposition Method ◽  
Decomposition Methods ◽  
Support Vector ◽  
Dual Formulation ◽  
Working Set ◽  
Number Of Iterations

The dual formulation of support vector regression involves two closely related sets of variables. When the decomposition method is used, many existing approaches use pairs of indices from these two sets as the working set. Basically, they select a base set first and then expand it so all indices are pairs. This makes the implementation different from that for support vector classification. In addition, a larger optimization subproblem has to be solved in each iteration. We provide theoretical proofs and conduct experiments to show that using the base set as the working set leads to similar convergence (number of iterations). Therefore, by using a smaller working set while keeping a similar number of iterations, the program can be simpler and more efficient.

Locking-Free and Gradient-Robust $${\varvec{H}}({{\,\mathrm{{\text {div}}}\,}})$$-Conforming HDG Methods for Linear Elasticity

2021 ◽  
Vol 86 (3) ◽  
Author(s):  
Guosheng Fu ◽  
Christoph Lehrenfeld ◽  
Alexander Linke ◽  
Timo Streckenbach
Keyword(s):  
Linear Elasticity

scholarly journals A linear-elasticity-based mesh moving method with no cycle-to-cycle accumulated distortion

2021 ◽  
Author(s):  
Patrícia Tonon ◽  
Rodolfo André Kuche Sanches ◽  
Kenji Takizawa ◽  
Tayfun E. Tezduyar
Keyword(s):  
Linear Elasticity ◽  
Solid Surfaces ◽  
Moving Mesh ◽  
Test Case ◽  
Half Cycle ◽  
Arbitrary Lagrangian Eulerian ◽  
Interface Motion ◽  
Mesh Motion ◽  
Ale Methods ◽  
Moving Mesh Methods

AbstractGood mesh moving methods are always part of what makes moving-mesh methods good in computation of flow problems with moving boundaries and interfaces, including fluid–structure interaction. Moving-mesh methods, such as the space–time (ST) and arbitrary Lagrangian–Eulerian (ALE) methods, enable mesh-resolution control near solid surfaces and thus high-resolution representation of the boundary layers. Mesh moving based on linear elasticity and mesh-Jacobian-based stiffening (MJBS) has been in use with the ST and ALE methods since 1992. In the MJBS, the objective is to stiffen the smaller elements, which are typically placed near solid surfaces, more than the larger ones, and this is accomplished by altering the way we account for the Jacobian of the transformation from the element domain to the physical domain. In computing the mesh motion between time levels $$t_n$$ t n and $$t_{n+1}$$ t n + 1 with the linear-elasticity equations, the most common option is to compute the displacement from the configuration at $$t_n$$ t n . While this option works well for most problems, because the method is path-dependent, it involves cycle-to-cycle accumulated mesh distortion. The back-cycle-based mesh moving (BCBMM) method, introduced recently with two versions, can remedy that. In the BCBMM, there is no cycle-to-cycle accumulated distortion. In this article, for the first time, we present mesh moving test computations with the BCBMM. We also introduce a version we call “half-cycle-based mesh moving” (HCBMM) method, and that is for computations where the boundary or interface motion in the second half of the cycle consists of just reversing the steps in the first half and we want the mesh to behave the same way. We present detailed 2D and 3D test computations with finite element meshes, using as the test case the mesh motion associated with wing pitching. The computations show that all versions of the BCBMM perform well, with no cycle-to-cycle accumulated distortion, and with the HCBMM, as the wing in the second half of the cycle just reverses its motion steps in the first half, the mesh behaves the same way.

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