7,198 research outputs found
The mechanics of delamination in fiber-reinforced composite materials. Part 2: Delamination behavior and fracture mechanics parameters
Based on theories of laminate anisotropic elasticity and interlaminar fracture, the complete solution structure associated with a composite delamination is determined. Fracture mechanics parameters characterizing the interlaminar crack behavior are defined from asymptotic stress solutions for delaminations with different crack-tip deformation configurations. A numerical method employing singular finite elements is developed to study delaminations in fiber composites with any arbitrary combinations of lamination, material, geometric, and crack variables. The special finite elements include the exact delamination stress singularity in its formulation. The method is shown to be computationally accurate and efficient, and operationally simple. To illustrate the basic nature of composite delamination, solutions are shown for edge-delaminated (0/-0/-0/0) and (+ or - 0/+ or - 0/90/90 deg) graphite-epoxy systems under uniform axial extenstion. Three-dimensional crack-tip stress intensity factors, associated energy release rates, and delamination crack-closure are determined for each individual case. The basic mechanics and mechanisms of composite delamination are studied, and fundamental characteristics unique to recently proposed tests for interlaminar fracture toughness of fiber composite laminates are examined
Spectral radius, index estimates for Schrodinger operators and geometric applications
In this paper we study the existence of a first zero and the oscillatory
behavior of solutions of the ordinary differential equation ,
where are functions arising from geometry. In particular, we introduce a
new technique to estimate the distance between two consecutive zeros. These
results are applied in the setting of complete Riemannian manifolds: in
particular, we prove index bounds for certain Schr\"odinger operators, and an
estimate of the growth of the spectral radius of the Laplacian outside compact
sets when the volume growth is faster than exponential. Applications to the
geometry of complete minimal hypersurfaces of Euclidean space, to minimal
surfaces and to the Yamabe problem are discussed.Comment: 48 page
Conformal Wasserstein distances: comparing surfaces in polynomial time
We present a constructive approach to surface comparison realizable by a
polynomial-time algorithm. We determine the "similarity" of two given surfaces
by solving a mass-transportation problem between their conformal densities.
This mass transportation problem differs from the standard case in that we
require the solution to be invariant under global M\"{o}bius transformations.
We present in detail the case where the surfaces to compare are disk-like; we
also sketch how the approach can be generalized to other types of surfaces.Comment: 23 pages, 3 figure
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