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Effects of localized elliptical (circular being a special case) cylindrical surface flaws in laminated composite plates are investigated by using C°-type triangular composite plate elements, formulated on the assumptions of transverse inextensibility and layer-wise constant shear-angle theory (LCST). Numerical results for a cross-ply laminate compromised by the presence of an external part-through elliptical/circular cylindrical slot indicate the existence of severe cross-sectional warping in the vicinity of the surface flaw and plate boundaries. Furthermore, three-dimensional nature of the stress concentration factor in the neighborhood of the elliptical or circular cylinder shaped surface flaw boundary is clearly exhibited. Besides, very high stress concentration factors are found in the layer weakened by the surface flaw. Most importantly, the effects of stress singularity in the neighborhood of the circumferential re-entrant corner lines of the elliptical/circular cylindrical surface flaws, weakening laminated composite plates, are numerically assessed, because of their role in crack initiation. Finally, the interaction of this singularity with free edge stress singularity at the plate boundary, and the implication of such interactions (i.e., violation of St. Venant’s principle) in regards to testing of laminated composite specimens are thoroughly investigated. 相似文献
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The stationary differential systems with polynomial right sides are considered. Necessary and sufficient conditions are formulated when a given domain is a domain of asymptotic stability and the origin of coordinates is either the focus or the center. The problem of construction of a stabilizing control in a form of polynomial is studied. 相似文献
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Summary We consider the numerical treatment of second kind integral equations on the real line of the form
(abbreviatedφ =ψ +K
z
φ) in whichκ εL
1(ℝ),z εL
∞
(ℝ), andψ εBC(ℝ), the space of bounded continuous functions on ℝ, are assumed known andφ εBC(ℝ) is to be determined. We first derive sharp error estimates for the finite section approximation (reducing the range of
integration to [−A, A]) via bounds on (I − K
z
)−1 as an operator on spaces of weighted continuous functions. Numerical solution by a simple discrete collocation method on
a uniform grid on ℝ is then analysed: in the case whenz is compactly supported this leads to a coefficient matrix which allows a rapid matrix-vector multiply via the FFT. To utilise
this possibility we propose a modified two-grid iteration, a feature of which is that the coarse grid matrix is approximated
by a banded matrix, and analyse convergence and computational cost. In cases wherez is not compactly supported a combined finite section and two-grid algorithm can be applied and we extend the analysis to
this case. As an application we consider acoustic scattering in the half-plane with a Robin or impedance boundary condition
which we formulate as a boundary integral equation of the class studied. Our final result is that ifz (related to the boundary impedance in the application) takes values in an appropriate compact subsetQ of the complex plane, then the difference betweenφ(s) and its finite section approximation computed numerically using the iterative scheme proposed is ≤C
1[khlog(1/kh)+(1−θ)−1/2(kA)−1/2] in the interval [−θA, θA] (θ<1), forkh sufficiently small, wherek is the wavenumber andh the grid spacing. Moreover this numerical approximation can be computed in ≤C
2
N logN operations, whereN = 2A/h is the number of degrees of freedom. The values of the constantsC
1 andC
2 depend only on the setQ and not on the wavenumberk or the support ofz.
This work was supported by the UK Engineering and Physical Sciences Research Council and by the Radio Communications Research
Unit, Rutherford Appleton Laboratory. 相似文献