Two types of limit cycles of a resonant converter modelled by a three-dimensional system

In this paper, the long-run dynamics of a resonant converter is studied. The modelling of the resonant converter can be done using various approximations and the long-run dynamics of the two dimensional cases were earlier analysed. In this paper, we discuss results that can be extended to the three dimensional case. It seems that limit cycles describe the long-run dynamics in important situations in the three dimensional case, too. Our objective is to relate the limit cycles found previously in the two-dimensional case to those found now in the three dimensional approximation.     

Coexistent Fluid-Phase Equilibria in Biomembranes with Bending Elasticity

The theory of fluid surfaces with elastic resistance to bending is applied to coexistent phase equilibria in biomembranes composed of lipid bilayers. A simplified version of the model is used to simulate the necking and budding of closed vesicles.      

Shear viscosity of polymer and surfactant monolayers

The surface shear viscosity of monolayers formed at the surface of water by adsorbed polyethyl- eneoxyde and by stearic acid is measured as a function of the surface pressure of the monolayer using a new surface viscometer. The principle of the viscometer is the measurement of the drag force on a circular disk undergoing a uniform translation at the water surface: a hydrodynamic model based on the lubrication approximation allows a calculation of the surface viscosities from the absolute measurement of the drag forces. Received: 26 August 1999     

Nuclear‐relaxed elastic and piezoelectric constants of materials: Computational aspects of two quantum‐mechanical approaches

Two alternative approaches for the quantum‐mechanical calculation of the nuclear‐relaxation term of elastic and piezoelectric tensors of crystalline materials are illustrated and their computational aspects discussed: (i) a numerical approach based on the geometry optimization of atomic positions at strained lattice configurations and (ii) a quasi‐analytical approach based on the evaluation of the force‐ and displacement‐response internal‐strain tensors as combined with the interatomic force‐constant matrix. The two schemes are compared both as regards their computational accuracy and performance. The latter approach, not being affected by the many numerical parameters and procedures of a typical quasi‐Newton geometry optimizer, constitutes a more reliable and robust mean to the evaluation of such properties, at a reduced computational cost for most crystalline systems. © 2016 Wiley Periodicals, Inc.     

Geometry dependence of the viscosity of a thermotropic LC-polymer measured by slit dies

This paper reports on geometry dependent viscosity curves of the biaxial thermotropic LC-Polymer Vectra B 950 measured with rectangular slit dies. The geometry dependence of the flow behaviour originates from the flow of two layers. The layer near the wall is highly flow oriented and free from defects. The layer in the bulk has an ordered texture. The thickness of the wall layer decreases with wall shear stress. Based on the Frank theory and the assumption that the core of a moving disclination is the smallest radius of distortion, the wall layer thickness is predicted and compared with experimental data.     

旋转压电纳米梁的振动分析

本文基于非局部弹性理论，对旋转压电纳米梁模型的振动进行了分析．首先由哈密顿原理导出旋转压电纳米梁的动力学控制方程及相应的边界条件；再通过微分求积法对控制方程和两类边界条件进行离散；最后通过数值计算分析振动特性．通过改变旋转角速度、轮毂半径、非局部参数以及外部电压分析它们对压电纳米梁振动频率的影响关系．数值结果表明这些参数对压电纳米梁固有频率有不可忽略的影响，本文进一步讨论了旋转角速度对结构模态的影响．     

Rolling of a Rigid Cylinder over a Half-Plane with Initial Stresses (Harmonic and Bartenev–Khazanovich Potentials)

An asymmetric quasistationary problem for a prestressed half-plane with harmonic and Bartenev–Khazanovich potentials is solved based of the linearized theory of elasticity. The Mehler–Fock integral transform is used to solve the differential equations that describe the stress–strain state of the half-plane. The dependences of the normal and tangential stresses and stress intensity factors on the elongation are plotted     

Force-Free States, Relative Strain, and Soft Elasticity in Nematic Elastomers

The remarkable ability of nematic elastomers to exhibit large deformations under small applied forces is known as soft elasticity. The recently proposed neo-classical free-energy density for nematic elastomers, derived by molecular-statistical arguments, has been used to model soft elasticity. In particular, the neo-classical free-energy density allows for a continuous spectrum of equilibria, which implies that deformations may occur in the complete absence of force and energy cost. Here we study the notion of force-free states in the context of a continuum theory of nematic elastomers that allows for isotropy, uniaxiality, and biaxiality of the polymer microstructure. Within that theory, the neo-classical free-energy density is an example of a free-energy density function that depends on the deformation gradient only through a nonlinear strain measure associated with the deformation of the polymer microstructure relative to the macroscopic continuum. Among the force-free states for a nematic elastomer described by the neo-classical free energy density, there is, in particular, a continuous spectrum of states parameterized by a pair of tensors that allows for soft deformations. In these force-free states the polymer microstructure is material in the sense that it stretches and rotates with the macroscopic continuum. Limitations of and possible improvements upon the neo-classical model are also discussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

Constitutive branching analysis of cylindrical bodies under in-plane equibiaxial dead-load tractions

Finite homogeneous deformations of hyperelastic cylindrical bodies subjected to in-plane equibiaxial dead-load tractions are analyzed. Four basic equilibrium problems are formulated considering incompressible and compressible isotropic bodies under plane stress and plane deformation condition. Depending on the form of the stored energy function, these plane problems, in addition to the obvious symmetric solutions, may admit asymmetric solutions. In other words, the body may assume an equilibrium configuration characterized by two unequal in-plane principal stretches corresponding to equal external forces. In this paper, a mathematical condition, in terms of the principal invariants, governing the global development of the asymmetric deformation branches is obtained and examined in detail with regard to different choices of the stored energy function. Moreover, explicit expressions for evaluating critical loads and bifurcation points are derived. With reference to neo-Hookean, Mooney-Rivlin and Ogden-Ball materials, a broad numerical analysis is performed and the qualitatively more interesting asymmetric equilibrium branches are shown. Finally, using the energy criterion, a number of considerations are put forward about the stability of the computed solutions.     

Elastoplastic Axisymmetric Stress-Strain State of Laminated Shells Made of Isotropic and Transversely Isotropic Materials with Different Moduli

A method is developed for analysis of the elastoplastic stress-strain state of laminated shells of revolution under axisymmetric loading. The shells are made of isotropic and transversally isotropic materials with different moduli. The method is based on the Kirchhoff-Love hypotheses for the whole laminate, the theory of deformation along paths of small curvature (for isotropic materials), and the theory of elasticity with different tensile and compressive moduli (transversely isotropic materials). The problem is solved by the method of successive approximations. Numerical examples are given __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 8, pp. 88–96, August 2005.