Positive solutions of fourth order problems with clamped beam boundary conditions

n this paper we make an exhaustive study of the fourth order linear operator u((4)) + M u coupled with the clamped beam conditions u(0) = u(1) = u'(0) = u'(1) = 0. We obtain the exact values on the real parameter M for which this operator satisfies an anti-maximum principle. Such a property is equivalent to the fact that the related Green's function is nonnegative in [0, 1] x [0, 1]. When M < 0 we obtain the best estimate by means of the spectral theory and for M > 0 we attain the optimal value by studying the oscillation properties of the solutions of the homogeneous equation u((4)) + M u = 0. By using the method of lower and upper solutions we deduce the existence of solutions for nonlinear problems coupled with this boundary conditions. (C) 2011 Elsevier Ltd. All rights reserved.

The 1998 Faial earthquake, Azores: Evidence for a transform fault associated with the Nubia-Eurasia plate boundary?

With very few exceptions, M > 4 tectonic earthquakes in the Azores show normal fault solution and occur away from the islands. Exceptionally, the 1998 shock was pure strike-slip and occurred within the northern edge of the Pico-Faial Ridge. Fault plane solutions show two possible planes of rupture striking ENE-WSW (dextral) and NNW-SSE (sinistral). The former has not been recognised in the Azores, but is parallel to the transform direction related to the relative motion between the Eurasia and Nubia plates. Therefore, the main question we address in the present study is: do transform faults related to the Eurasia/Nubia plate boundary exist in the Azores? Knowing that the main source of strain is related to plate kinematics, we conclude that the sinistral strike-slip NNW-SSE fault plane solution is not consistent with either the fault dip (ca. 65, which is typical of a normal fault) or the ca. ENE-WSW direction of maximum extension; both are consistent with a normal fault, as observed in most major earthquakes on faults striking around NNW-SSE in the Azores. In contrast, the dextral strike-slip ENE-WSW fault plane solution is consistent with the transform direction related to the anticlockwise rotation of Nubia relative to Eurasia. Altogether, tectonic data, measured ground motion, observed destruction, and modelling are consistent with a dextral strike-slip source fault striking ENE-WSW. Furthermore, the bulk clockwise rotation measured by GPS is typical of bookshelf block rotations observed at the termination of such master strike-slip faults. Therefore, we suggest that the 1998 earthquake can be related to the WSW termination of a transform (ENE-WSW fault plane solution) associated with the Nubia-Eurasia diffuse plate boundary. (C) 2014 Elsevier B.V. All rights reserved.

Analysis of sandwich beam structures using kriging based higher order models

Functionally graded composite materials can provide continuously varying properties, which distribution can vary according to a specific location within the composite. More frequently, functionally graded materials consider a through thickness variation law, which can be more or less smoother, possessing however an important characteristic which is the continuous properties variation profiles, which eliminate the abrupt stresses discontinuities found on laminated composites. This study aims to analyze the transient dynamic behavior of sandwich structures, having a metallic core and functionally graded outer layers. To this purpose, the properties of the particulate composite metal-ceramic outer layers, are estimated using Mod-Tanaka scheme and the dynamic analyses considers first order and higher order shear deformation theories implemented though kriging finite element method. The transient dynamic response of these structures is carried out through Bossak-Newmark method. The illustrative cases presented in this work, consider the influence of the shape functions interpolation domain, the properties through-thickness distribution, the influence of considering different materials, aspect ratios and boundary conditions. (C) 2014 Elsevier Ltd. All rights reserved.