scholarly journals On the honeycomb conjecture for Robin Laplacian eigenvalues

2019 ◽  
Vol 21 (02) ◽  
pp. 1850007 ◽  
Author(s):  
Dorin Bucur ◽  
Ilaria Fragalà
Keyword(s):  
Torsional Rigidity ◽  
Cluster Problem ◽  
Laplacian Eigenvalues ◽  
Convexity Assumption ◽  
Robin Laplacian ◽  
Cheeger Sets ◽  
Optimal Cluster

We prove that the optimal cluster problem for the sum/the max of the first Robin eigenvalue of the Laplacian, in the limit of a large number of convex cells, is asymptotically solved by (the Cheeger sets of) the honeycomb of regular hexagons. The same result is established for the Robin torsional rigidity. In the specific case of the max of the first Robin eigenvalue, we are able to remove the convexity assumption on the cells.

CHASSIS TORSIONAL RIGIDITY: VALIDATION OF FEA DATA BY EXPERIMENTAL TEST

2019 ◽  
Author(s):  
Luís Fernando Marzola da Cunha ◽  
Matheus Lisboa Cardoch Valdes ◽  
Rhander Viana ◽  
Danilo dos Santos Oliveira ◽  
Luiz Eduardo Rodrigues Vieira
Keyword(s):  
Experimental Test ◽  
Torsional Rigidity

scholarly journals Analytical solution for torsion of cylindrical orthotropic annular wedge-shaped bars reinforced by thin shells

2021 ◽  
Author(s):  
István Ecsedi ◽  
Attila Baksa
Keyword(s):  
Analytical Solution ◽  
Cross Section ◽  
Analytical Method ◽  
Torsional Rigidity ◽  
Circular Ring ◽  
Thin Shells ◽  
Elastic Wedge ◽  
Curved Boundary ◽  
Cylindrically Orthotropic ◽  
Boundary Surfaces

AbstractThis paper deals with the Saint-Venant torsion of elastic, cylindrically orthotropic bar whose cross section is a sector of a circular ring shaped bar. The cylindrically orthotropic homogeneous elastic wedge-shaped bar strengthened by on its curved boundary surfaces by thin isotropic elastic shells. An analytical method is presented to obtain the Prandtl’s stress function, torsion function, torsional rigidity and shearing stresses. A numerical example illustrates the application of the developed analytical method.

On the Laplacian Eigenvalues of Gn,p

2007 ◽  
Vol 16 (6) ◽  
pp. 923-946 ◽  
Author(s):  
AMIN COJA-OGHLAN
Keyword(s):  
Random Graphs ◽  
Spectral Gap ◽  
Degree Sequences ◽  
Laplacian Eigenvalues ◽  
Combinatorial Laplacian ◽  
Laplacian Spectra

We investigate the Laplacian eigenvalues of sparse random graphs Gnp. We show that in the case that the expected degree d = (n-1)p is bounded, the spectral gap of the normalized Laplacian $\LL(\gnp)$ is o(1). Nonetheless, w.h.p. G = Gnp has a large subgraph core(G) such that the spectral gap of $\LL(\core(G))$ is as large as 1-O (d−1/2). We derive similar results regarding the spectrum of the combinatorial Laplacian L(Gnp). The present paper complements the work of Chung, Lu and Vu [8] on the Laplacian spectra of random graphs with given expected degree sequences. Applied to Gnp, their results imply that in the ‘dense’ case d ≥ ln2n the spectral gap of $\LL(\gnp)$ is 1-O (d−1/2) w.h.p.

Analysis of Twisting Stiffness for a Multifiber Composite Layer

1974 ◽  
Vol 41 (3) ◽  
pp. 658-662 ◽  
Author(s):  
C. W. Bert ◽  
S. Chang
Keyword(s):  
Cross Section ◽  
Least Squares Method ◽  
Rectangular Cross Section ◽  
Torsional Rigidity ◽  
Composite Layer ◽  
Circular Cross Section ◽  
Relaxation Method ◽  
Fiber Composites ◽  
Numerical Results ◽  
Torsion Problem

The twisting stiffness of a rectangular cross section consisting of a single row of solid circular cross-section fibers embedded in a matrix is analyzed. The problem is formulated as a Dirichlet torsion problem of a multielement region and solved by the boundary-point least-squares method. Numerical results for a single-fiber square cross section compare favorably with previous relaxation-method results. New numerical results for three and five-fiber composites suggest that the torsional rigidity of a multifiber composite can be approximated from the torsional rigidities of single and three-fiber models.

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