Optimization of plastic structures

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Asymmetric dynamic plastic response of stepped plates

The dynamic plastic response of circular plates to asymmetric loading is studied. An approximate theoretical procedure is developed for the evaluation of asymmetrical residual de ections. The solution technique is based on the equality of the internal dissipation and the external work, respectively. Maximal residual de ections are defined for plates of piece-wise constant thickness

Asymmetric response of inelastic circular plates to blast loading

The dynamic behaviour of clamped circular plates subjected to the concentrated blast loading is studied. The load is applied at a non-central point of the plate, non-axisymmetric deflections are taken into account. An approximate theoretical procedure developed earlier is applied for the evaluation of residual maximal deflections. The solution technique is based on the idea of equality of the power of the internal and external work, respectively. As it was shown earlier this concept leads to results which are close to exact ones in the case of axisymmetric loading of circular plates, also in the case of circular cylindrical shells

Plastic response of conical shells with stiffeners to blast loading

The inelastic response of circular conical shells to the blast loading is studied. The impact loading is applied at the initial time moment and it is removed at a certain instant of time. The load intensity depends of the coordinate of the shell. The material of the shell is a perfect plastic one obeying the Johansen yield condition and the associated flow law. It is assumed that the frustum of the cone is furnished with ring stiffeners made of the same material. A theoretical method for the evaluation of the stress strain state of the shell and for determination of maximal residual deflections is developed

Natural vibrations of circular nanoarches of piecewise constant thickness

The free vibrations of elastic circular arches made of a nano-material are considered. A method of determination of eigenfrequencies of nanoarches weakened with stable cracks is developed making use of the concept of the massless spring and Eringen's nonlocal theory of elasticity. The aim of the paper is to evaluate the sensitivity of eigenfrequencies on the geometrical and physical parameters of the nanoarch

Stability of nanobeams and nanoplates with defects

The sensitivity of critical buckling load and critical stress concerning different geometrical and physical parameters of Euler-Bernoulli nanobeams with defects is studied. Eringen’s nonlocal theory of elasticity is used for the determination of critical buckling load for stepped nanobeams subjected to axial loads for different support conditions. An analytical approach to study the impact of discontinuities and boundary conditions on the critical buckling load and critical stress of nanobeams has been developed. Critical buckling loads of stepped nanobeams are defined under the condition that the nanoelements are weakened with stable crack-like defects. Simply supported, clamped and cantilever nanobeams with steps and cracks are investigated in this article. The presented results are compared with the other available results and are found to be in a close agreement

Natural vibrations of curved nano-beams and nano-arches

The natural vibrations of curved nano-beams and nano-arches are studied. The nano-arches under consideration have piecewise constant thickness; these are weakened with stable cracks located at re-entrant corners of the steps. A method of determination of natural frequencies is developed making use of the method of weightless rotating spring. The aim of the paper is to assess the sensitivity of the eigenfrequencies on the geometrical and physical parameters of the nano-arch. The results of the calculations favourably compare with similar works of other researchers

Natural vibrations of stepped nanobeams with defects

Exact solutions for the transverse vibration of nanobeams based on the nonlocal theory of elasticity are presented. The nanobeams under consideration have piecewise constant dimensions of cross sections and are weakened with crack-like defects. It is assumed that the stationary cracks occur at the re-entrant corners of steps and that the mechanical behaviour of the nanomaterial can be modelled with the Eringen's nonlocal theory. The influence of cracks on the natural vibration is prescribed with the aid of additional local compliance at the weakened cross section. The local compliance is coupled with the stress intensity factor at the crack tip. A general algorithm for determination of eigenfrequencies is developed. It can be used in the case of an arbitrary finite number of steps and cracks

Linear stability analysis of purely elastic travelling wave solutions in pressure driven channel flows

Recent studies of pressure-driven flows of dilute polymer solutions in straight channels demonstrated the existence of two-dimensional coherent structures that are disconnected from the laminar state and appear through a sub-critical bifurcation from infinity. These travelling-wave solutions were suggested to organise the phase-space dynamics of purely elastic and elasto-inertial chaotic channel flows. Here, we consider a wide range of parameters, covering the purely-elastic and elasto-inertial cases, and demonstrate that the two-dimensional travelling-wave solutions are unstable when embedded in sufficiently wide three-dimensional domains. Our work demonstrates that studies of purely elastic and elasto-inertial turbulence in straight channels require three-dimensional simulations, and no reliable conclusions can be drawn from studying strictly two-dimensional channel flows.Comment: 10 pages, 5 page

Das affektbetonte Erlebnis in der Vorgeschichte der Schizophrenie : Tartu Ülikooli Waimuhaigete kliiniku assistendi Konstantin Lellep'i wäitekiri

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