Thermal deformations in symmetric and antisymmetric cross-ply laminated beams subjected to partial heating are investigated. Some regions of the beam are subjected to thermal loads and the others are thermally unloaded (ΔT = 0). The thermal field is expressed in terms of Heaviside discontinuity functions. The state space approach along with Jordan canonical form is used to generate exact solutions for the thermoelastic response of beams for arbitrary boundary conditions. A first order shear deformation theory is used in the analysis. Deflections are computed for beams subjected to partial heating with various lamination schemes and boundary conditions undergoing uniform and linearly varying temperature through the thickness. Exact thermal deflection curves are presented for beams under step-wise varying temperature field. The solutions presented in this study can readily be used to investigate the thermoelastic behavior of narrow chip-substrate structure, laminated member in laser cutting, composite link in hypersonic vehicle, and etc.

We derive an analytical solution for the value of Parisian up-and-in calls by using the “moving window” technique for pricing European-style Parisian up-and-out calls. Our pricing formula can be applied to both European-style and American-style Parisian up-and-in calls, due to the fact that with an “in” barrier, the option holder cannot do or decide on anything before the option is activated, and once the option is activated it is just a plain vanilla call, which could be of American style or European style.

In this paper, we are interested in modelling the flow of the coolant (water) in anuclear reactor core. To this end, we use a monodimensional low Mach number modelsupplemented with the stiffened gas law. We take into account potential phase transitionsby a single equation of state which describes both pure and mixture phases. In someparticular cases, we give analytical steady and/or unsteady solutions which providequalitative information about the flow. In the second part of the paper, we introduce twovariants of a numerical scheme based on the method of characteristics to simulate thismodel. We study and verify numerically the properties of these schemes. We finally presentnumerical simulations of a loss of flow accident (LOFA) induced by a coolant pump tripevent.

By application of the theory of complex variable functions, asymmetrical dynamic propagation problem on the edges of mode III interface crack subjected to superimpose loads was studied. Analytical solutions of the stresses displacements and dynamic stress intensity factors are obtained by means of self- similar functions. The problems researched can be facilely transformed into Riemann-Hilbert problems and their closed solutions are attained rather simple according to this measure. After those solutions are utilized by superposition theorem, the solutions of arbitrarily complex problems can be gained.

By the approaches of the theory of complex functions, dynamic problem concerning mode I semi-infinite crack propagation was studied. Analytical solutions are very easily obtained by application of the measures of self-similar functions. The problems researched can be changed into Riemann-Hilbert problems and analytical solutions to semi-infinite crack under the condition of impulse loads and increasing loads Pt located at the origin of the coordinates, respectively, are attained.

Analytical solution is obtained for the free vibration of cross-ply laminated beams with multiple distributed extension piezoelectric actuators. The piezoelectric actuators are bonded at local position on the beam surface. The beam structure can contain one pair or two pairs or n pairs of piezoelectric actuators and it can be symmetric or unsymmetric about its mid-plane. The equations of motion and associated boundary conditions are derived for the beam model using Hamilton's principle. The state-space approach is used to find accurate natural frequencies and mode shapes for arbitrary combinations of boary conditions. The exact analytical solutions obtained are illustrated numerically in a number of figures revealing the influences of varying some parameters for the symmetric and unsymmetric cross-ply laminated beam for different type of piezoelectric actuators cases. The first order shear deformation beam theory (FOBT) is used to present the effect of actuators position and length on the nondimensional frequencies when one pair and two pairs of piezoelectric actuators are bonded at a local position on the beam surface.

Il est impératif pour l’ingénieur de s’assurer de la validité de ses outils de modélisation numérique et il lui revient de vérifier s’ils donnent la solution attendue pour un problème donné. Dans un logiciel d’éléments-finis, ceci peut être fait par l’utilisation de solutions analytiques lorsqu’elles existent, ou par la méthode des solutions manufacturées (MSM). Nous proposons dans ce travail d’étendre la MSM aux problèmes de contact unilatéral en grandes déformations pour lesquels, à notre connaissance, il n’existe pas de solutions analytiques non triviales. Nous montrerons comment l’utiliser comme un outil de vérification pour l’ingénieur. De plus, nous analyserons la précision et les taux de convergence de différents espaces d’approximation mixtes (déplacement-pression de contact), sur des éléments triangulaires et quadrangulaires.