ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik
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Recently Published Articles
- Stability results of some distributed systems involving Mindlin-Timoshenko plates in the plane
Maya Bassam, Denis Mercier, Serge Nicaise and Ali Wehbe
Article first published online: 7 OCT 2015 | DOI: 10.1002/zamm.201500172
In , Belkacem and Kasimov studied the stability of an one-dimensional Timoshenko system in with one distributed temperature or Cattaneo dissipation damping. They proved that the heat dissipation alone is sufficient to stabilize the system. But there is a difference between the Timoshenko system in and its analogous system in . For this reason, the stability results are no longer the same and of intrinsic difference. In this paper, we consider the stability of some distributed systems involving Mindlin-Timoshenko plate in the plane. If the plate is subject to two internal distributed damping then, using a direct approach based on the Fourier transform, we establish a polynomial energy decay rate for initial data in . In the case of indirect internal stability, when only one among the two equations is effectively damped while the second is indirectly damped through the coupling, we have two different situations. To be more precise, if the equation of the displacement in the vertical direction of the plate is only damped then, the system is unstable. Next, when the control is acting on the equation of the angles of rotation of a filament of the plate, no decay can be proved but our conjecture is a polynomial stability. Finally, unlike the one-dimensional case, we show that, under a heat conduction (by Fourier or Cattaneo law), the plate is unstable.
- Two-level models of polycrystalline elastoviscoplasticity: Complex loading under large deformations (pages 1067–1080)
Peter V. Trusov, Pavel S. Volegov and Anton Yu. Yanz
Article first published online: 1 OCT 2015 | DOI: 10.1002/zamm.201400153
The motion of rigid corotating frame describing quasi-rigid motion is determined by a macrolevel motion decomposition hypothesis. The following macrolevel hypotheses are considered: (1) the representative volume total motion is a deformational one; (2) the motion is decomposed into a deformational and a rigid ones with a spin being determined by an averaging of the mesolevel spins; (3) quasi-solid and deformational motions are determined by corresponding skew-symmetrical and symmetrical parts of the macrolevel displacement velocity gradient.
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- Low velocity impact analysis of composite laminated beams subjected to multiple impacts in thermal field
Mostafa Sabzikar Boroujerdy and Yasser Kiani
Article first published online: 30 SEP 2015 | DOI: 10.1002/zamm.201500132
In this research, dynamic behaviour of a composite laminated beam subjected to multiple projectiles is analysed. Temperature elevation is also taken into account. Hertz law of contact is used to model the impact phenomenon between the projectiles and the target. Beam obeys the first order shear deformation theory assumptions. Governing motion equations of the beam and projectiles are obtained using the Hamilton principle. Conventional Ritz method suitable for arbitrary in-plane and out-of-plane boundary conditions is implemented to reduce the partial differential equations into time-dependent ordinary differential equations. Time domain solution of such equations is extracted by means of the well-known fourth-order Runge-Kutta method. After validating the proposed model with the available numerical data, parametric studies are conducted to investigate the influences of multiple impactors, beam characteristics, boundary conditions and thermal environment. It is shown that, temperature elevation decreases the contact force and increases the contact time.
- Debonding fracture of bonded bimaterial semi-strips subjected to concentrated forces and couples
Norio Hasebe and Seiji Kato
Article first published online: 16 SEP 2015 | DOI: 10.1002/zamm.201500125
Debonding fracture of a bimaterial strip with two interfaces is investigated subjected to concentrated forces and couples. In the previous paper (ZAMM, see below), closed form stress functions were derived for the bonded bimaterial planes with two interfaces. As a demonstration of geometry, semi-strips bonded at two places of the ends of strips subjected to concentrated forces and couples were analyzed. Using the stress function, the stress intensities of debonding (SID) are obtained. To investigate the accuracy of SID calculated by the stress function, a comparison with the results obtained by a boundary element analysis is carried out and it is confirmed that they agree well each other. It is stated that SID is the square root of the strain energy release rate and the same as the strain energy release rate for evaluating the strength of the fracture. Then the debonding extension behaviors are investigated for some initial debonding states and three loading conditions, concentrated forces, couples and both combined loadings, using SID. Expressions to calculate SID for arbitrary loading magnitudes are derived. Fatigue growth of debonding under cyclic loading is also investigated, using Paris law regarding fatigue.