Formation of toroidal plasma configurations with noncircular cross section

Translated from Chislennye Metody Resheniya Obratnykh Zadach Matematicheskoi Fiziki, pp. 179–186, 1988.     

Calculating the total resistance for a tube with a variable cross section

A study has been made on the decisive effect from the exit cone on the total resistance of a variable cross section tube composed of alternating divergent and convergent parts, whose radii vary on a cosine law. Numerical calculations have been performed for steady-state stabilized laminar flow of a viscous incompressible liquid. The frictional and pressure resistance coefficients have been calculated. The contribution from those resistances to the total resistance has been examined.Donetsk. Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 21, pp. 120–124, 1990.     

Analytical solutions in elasto-plastic bending of beams with rectangular cross section

Deflection analysis of beams with rectangular cross section is considered under specific loading conditions, resulting in at most quadratic bending moment distribution, and assuming elasto-plastic behaviour with no hardening. Within the framework of small strain and small displacement approach analytical solutions are derived, which enable elasto-plastic analyses of beams to be performed in a closed analytical form. In consequence, clear tracing of the elasto-plastic response evolution with a propagation of the plastic zone through the volume, i.e. its spreading along the beam’s longitudinal axis as well as its penetration through the cross section, is enabled as loads increase, from the appearance of a first plastic yielding in a structure till its collapse. With the derivation of the general solution, listed explicitly by Eqs. (21), (22) and (23), which was never presented in any article or book before, the presented article fills the gap in the analytical non-linear mechanics of beams.     

Finite element method for the vibration of cracked beams with varying cross section

Vibration analysis of cracked beams having linearly varying cross-sections both in thickness and width was investigated. A computer program using the finite element method has been written to find the dynamical characteristics (natural frequencies and mode shapes) of the cracked beam. The cracked section in the beam has been modeled by a massless spring whose flexibility depens on the local flexibility induced by the crack. The stiffness of spring has been derived from the linear elastic fracture mechanics theory as the inverse of the compliance matrix calculated using stress intensity factors and strain energy release rate expression. Some examples have been given to explain the proposed method and investigate the effects of the depth and location of cracks on the natural frequencies and mode shapes. The results of current study and those in the literature are compared and good agreements have been found. Consequently it is showed that proposed method is reliable and simple. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Periodic solutions of the second order differential equations with Lipschitzian condition

In this paper, we prove an infinity of periodic solutions to the periodically forced nonlinear Duffing equation .

     

Effect of fiber orientation and cross section of composite tubes on their energy absorption ability in axial dynamic loading

The crushing behavior of composite tubes in axial impact loading is investigated. Tubes of circular and rectangular cross section are simulated using an LS-DYNA software. The effect of fiber orientation on the energy absorbed in laminated composite tubes is also studied. The results obtained show that rectangular tubes absorb less energy than circular ones, and their maximum crushing load is also lower. The composite tubes with a [+θ/ -θ] lay-up configuration absorb a minimum amount of energy at θ = 15°. The simulation results for a rectangular composite tube with a [+30/–30] lay-up configuration are compared with available experimental data. Cylindrical composite tubes fabricated from woven glass/polyester composites with different lay-ups were also tested using a drop-weight impact tester, and very good agreement between experimental and numerical results is achieved.     

本质下确界的最优性条件及其相对熵算法实现

为了研究带约束的本质下确界优化问题,介绍了m阶偏差积分并研究了它的性质,给出了其最优性条件和概念算法.基于极小化相对熵的技术,提出了一种实现算法,并有效地解决该优化问题.数值算例验证了算法的有效性.     

Periodic and backset solutions of differential delay systems with self-supporting condition

We prove that a planar delay differential equation subjected to a feedback condition and a self-supporting impulsive condition has periodic solutions. It also can have backset solutions, that encircle the origin opposing the orientation induced by the feedback condition.     

Elasticoplastic bending of rectangular plates reinforced with fibers of constant cross section

The problem on the elastoplastic transverse bending of Kirchhoff plates of variable thickness reinforced with fibers of constant cross section is formulated and its qualitative analysis is performed. An analytical solution to the problem is constructed in the case of cylindrical bending, and, by using the Bubnov-Galerkin method, an approximate solution for a rectangular plate is obtained. Based on calculations of plates reinforced with boron fibers and steel wire, it is shown that the load-carrying capacity of the structural member in elastoplastic bending is several times (or even by an order of magnitude) higher than in purely elastic one.Translated from Mekhanika Kompozitnykh Materialov, Vol. 41, No. 1, pp. 17–36, January–February, 2005.