1,721,041 research outputs found
On the contact reaction in a solid circular plate simply supported along an edge arc and deflected by a central transverse concentrated force
No full textA static, purely flexural mechanical analysis is presented for a Kirchhoff solid circular plate, deflected by a transverse central force, and bilaterally supported along a single periphery arc, the remaining part of the boundary being free. The contact reaction is assumed to be formed by a distributed reaction force accompanied by a distributed moment with radial axis. This plate problem is formulated in terms of an integral equation of the Prandtl type, supplemented by a vertical and a rotational equilibrium condition. It is shown that the Prandtl equation coupled to the equilibrium condition possesses a unique solution in a proper scale of weighted Sobolev-type spaces, with certain smoothness properties, and that no solution exists if the distributed moment is absent. Finally, the behaviour of the solution at the endpoints of the support is clarified
Solid Circular Plate Clamped along Two Antipodal Edge Arcs and Deflected by a Central Transverse Concentrated Force
No full textA static, purely flexural mechanical analysis is presented for a Kirchhoff solidcircular plate, deflected by a transverse central force, and clamped along two antipodal arcs,the remaining part of the boundary being free. By adopting an integral formulation, the contactreaction is assumed to be formed by four equal concentrated forces acting at the supportextremities, accompanied by two distributed moments with radial and circumferential axis,respectively. This plate problem is rephrased in terms of a complex-valued Hilbert singularintegral equation of the second kind, whose solution is obtained in analytical, integralform. A design chart is presented that reports the plate central deflection as a function of theangular width of the plate supports
Truncated interpolation processes on unbounded intervals and their applications
No full textThe authors describe the major results they have recently obtained on the truncation of
interpolation processes on unbounded intervals, and on their applications to the numerical
evaluation of corresponding integrals and to the resolution of a class of integral equations
A note on a paper by G. Mastroianni and G. Monegato
No full textAbstract: Recently, Mastroianni and Monegato derived error estimates for a numerical approach to evaluate a double Cauchy singular integral where the density function is enough smooth (see G. Mastroianni and G. Monegato, Error estimates in the numerical evaluation of some BEM singular integrals, Math. Comp. 70, 2001, 251-267). The error bounds for the quadrature rule approximating the inner integral given in Theorems 3, 4 of that paper are not correct according to the proof. However, following a different approach, we are able to improve the pointwise error estimates given in that paper
The numerical evaluation of two integral transforms
No full textWe derive recurrence relationships for the evaluation of two integral transforms which are of interest for the numerical solutionof some integral equations and for the construction of certain quadrature rules
LGM glacial retreat in the Astico valley and mismatch with the Adige and Brenta glacial transfluences (NE Italy)
No full textValley glaciers can be fed by transfluence from major glaciers through a gap or a saddle. These glacial systems may be more sensitive to rapid climate changes, in terms of temperature and precipitation rates. Here we present a case study concerning the timing of deglaciation in a Prealpine glacial system connected to transfluences from the Adige glacier. Changes in the position of the end moraines, hosted in the terminal valley reach, are coupled with observation of the glaciofluvial sedimentation in the piedmont area, with special reference to the Astico system, providing new insights on the onset of the glacial decay at the end of LGM
On the form of the contact reaction in a solid circular plate simply supported along two antipodal edge arcs and deflected by a central transverse concentrated force
No full textA static, purely flexural mechanical analysis is presented for a Kirchhoff solid circular plate, deflected by a transverse central force, and bilaterally supported along two antipodal periphery arcs, the remaining part of the boundary being free. Two kinds of contact reactions are considered, namely the case of distributed reaction force alone, and the situation in which the distributed force is added to a distributed couple of properly selected profile. For both cases this plate problem is formulated in terms of an integral equation of the Prandtl type, coupled with two constraint conditions. The existence of solutions in an appropriate scaled weighted Sobolev space is discussed, and the behaviour of the solution at the endpoints of the support is exhibited
On the existence of a solution for a solid circular plate bilaterally supported along two antipodal boundary arcs and loaded by a central transverse concentrated force
No full textA purely flexural mechanical analysis is presented for a thin, solid, circular plate, deflected by a central transverse concentrated force, and bilaterally supported along two antipodal periphery arcs, the remaining part of the boundary being free. This problem is modeled in terms of a singular integral equation of the Prandtl type, which possesses a unique solution expressed in terms of a reaction force containing a factor exhibiting square root endpoint singularities. This solution is then shown not to respect the requested boundary constraints. It is therefore concluded that, within the framework of the purely flexural plate theory, the title problem cannot admit the weighted L-2 solution here examined. It, cannot, however, be excluded that a solution to the title problem exists, which possesses stronger endpoint singularities than those examined in this paper or is of a more general form than the one considered here
ON THE INCOMPATIBILITY BETWEEN THE EQUIVALENT SHEAR FORCE CONCEPT AND THE INTEGRAL FORMULATION OF CONTACT PROBLEMS BETWEEN KIRCHHOFF PLATES AND IRREGULAR LINEAR SUPPORTS
No full textIt is shownthat, when employing the integral formulation to describe contact problemsbetween Kirchhoff plates and irregular linear supports, the equivalent shear force concept maybe incompatible with the integral approach. In such circumstances the equivalent shear forceconcept has to be abandoned in favour of an equivalent twisting moment approach. A classicalexample of an infinite plate resting on a linear central segment is revisited in the light of theequivalent twisting moment concept, where all the computations are carried out in exact form.An additional example is developed to show that the usefulness of an integral approach basedupon the equivalent twisting moment concept remains valid even when the equivalent twistingmoment is applied at a plate border along which the twisting moment must be null, as it occursin a partially clamped border. The reaction singularity at the endpoints of a linear support isexamined with theWilliams asymptotic method. Finally, a physical interpretation is proposed forthe adoption of a distributed twisting moment among the contact reaction
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