Sensitivity analysis of an optimized bar-spring model with hill-top branching

Summary Characteristics of optimal solutions under nonlinear buckling constraints are investigated by using a bar-spring model. It is demonstrated that optimization under buckling constraints of a symmetric system often leads to a structure with hill-top branching, where a limit point and bifurcation points coincide. A general formulation is derived for imperfection sensitivity of the critical load factor corresponding to a hill-top branching point. It is shown that the critical load is not imperfection-sensitive even for the case where an asymmetric bifurcation point exists at the limit point.     

Closed-form solutions for a rectangular layer with central crack under anti-plane shear stress

We consider the problem of determining the stress distributionin a finite rectangular elastic layer containing a Griffithcrack which is opened by internal shear stress acting alongthe length of the crack. The mode III crack is assumed to belocated in the middle plane of the rectangular layer. The followingtwo problems are considered: (A) the central crack is perpendicularto the two fixed lateral surfaces and parallel to the othertwo stress-free surfaces; (B) all the lateral surfaces of therectangular layer are clamped and the central crack is parallelto the two lateral surfaces. By using Fourier transformations,we reduce the solution of each problem to the solution of dualintegral equations with sine kernels and a weight function whichare solved exactly. Finally, we derive closed-form expressionsfor the stress intensity factor at the tip of the crack andthe numerical values for the stress intensity factor at theedges of the cracks are presented in the form of tables.     

A test problem for molecular dynamics integrators

We derive a test problem for evaluating the ability of time-steppingmethods to preserve the statistical properties of systems inmolecular dynamics. We consider a family of deterministic systemsconsisting of a finite number of particles interacting on acompact interval. The particles are given random initial conditionsand interact through instantaneous energy- and momentum-conservingcollisions. As the number of particles, the particle density,and the mean particle speed go to infinity, the trajectory ofa tracer particle is shown to converge to a stationary Gaussianstochastic process. We approximate this system by one describedby a system of ordinary differential equations and provide numericalevidence that it converges to the same stochastic process. Wesimulate the latter system with a variety of numerical integrators,including the symplectic Euler method, a fourth-order Runge-Kuttamethod, and an energyconserving step-and-project method. Weassess the methods' ability to recapture the system's limitingstatistics and observe that symplectic Euler performs significantlybetter than the others for comparable computational expense.     

Detecting instabilities in flows of viscoelastic fluids

There is a growing interest in developing numerical tools to investigate the onset of physical instabilities observed in experiments involving viscoelastic flows, which is a difficult and challenging task as the simulations are very sensitive to numerical instabilities. Following a recent linear stability analysis carried out in order to better understand qualitatively the origin of numerical instabilities occurring in the simulation of flows viscoelastic fluids, the present paper considers a possible extension for more complex flows. This promising method could be applied to track instabilities in complex (i.e. essentially non‐parallel) flows. In addition, results related to transient growth mechanism indicate that it might be responsible for the development of numerical instabilities in the simulation of viscoelastic fluids. Copyright © 2003 John Wiley & Sons, Ltd.     

Computations of two passing‐by high‐speed trains by a relaxation overset‐grid algorithm

This paper presents a relaxation algorithm, which is based on the overset grid technology, an unsteady three‐dimensional Navier–Stokes flow solver, and an inner‐ and outer‐relaxation method, for simulation of the unsteady flows of moving high‐speed trains. The flow solutions on the overlapped grids can be accurately updated by introducing a grid tracking technique and the inner‐ and outer‐relaxation method. To evaluate the capability and solution accuracy of the present algorithm, the computational static pressure distribution of a single stationary TGV high‐speed train inside a long tunnel is investigated numerically, and is compared with the experimental data from low‐speed wind tunnel test. Further, the unsteady flows of two TGV high‐speed trains passing by each other inside a long tunnel and at the tunnel entrance are simulated. A series of time histories of pressure distributions and aerodynamic loads acting on the train and tunnel surfaces are depicted for detailed discussions. Copyright © 2004 John Wiley & Sons, Ltd.     

Free boundary viscous flows at micro and mesolevel during liquid composites moulding process

Numerical simulation aspects, related to low Reynolds number free boundary viscous flows at micro and mesolevel during the resin impregnation stage of the liquid composite moulding process (LCM), are presented in this article. A free boundary program (FBP), developed by the authors, is used to track the movement of the resin front accurately by accounting for the surface tension effects at the boundary. Issues related to the global and local mass conservation (GMC and LMC) are identified and discussed. Unsuitable conditions for LMC and consequently GMC are uncovered at low capillary numbers, and hence a strategy for the numerical simulation of such flows is suggested. FBP encompasses a set of subroutines that are linked to modules in ANSYS. FBP can capture the void formation dynamics based on the analysis developed. We present resin impregnation dynamics in two dimensions. Extension to three dimensions is a subject for further research. Several examples are shown and efficiency of different stabilization techniques are compared. Copyright © 2004 John Wiley & Sons, Ltd.     

Sulfonated poly(aryl ether ketone)s containing naphthalene moieties obtained by direct copolymerization as novel polymers for proton exchange membranes

A series of sulfonated poly(aryl ether ketone)s (SPAEKs) were prepared by aromatic nucleophilic polycondensation of 2,6‐dihydroxynaphthalene with 5,5′‐carbonyl‐bis(2‐fluorobenzenesulfonate) and 4,4′‐difluorobenzophenone. The structure and degree of sulfonation (DS) of the SPAEKs were characterized using ¹H NMR spectroscopy. The experimentally observed DS values were close to the expected values derived from the starting material ratios. The thermal stabilities of the SPAEKs were characterized by thermogravimetric analysis, which showed that in acid and sodium salt forms they were thermally stable in air up to about 240 and 380 °C, respectively. Transparent membranes cast from the directly polymerized SPAEKs exhibited good mechanical properties in both dry and hydrated states. The dependence of water uptake and of membrane swelling on the DS at different temperatures was studied. SPAEK membranes with a DS from 0.72 to 1.60 maintained adequate mechanical properties after immersion in water at 80 °C for 24 h. The proton conductivity of SPAEK membranes with different degrees of sulfonation was measured as a function of temperature. The proton conductivity of the SPAEK films increased with increased DS, and the highest room temperature conductivity (4.2 × 10^?2 S/cm) was recorded for a SPAEK membrane with a DS of 1.60, which further increased to 1.1 × 10^?1 S/cm at 80 °C. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 2866–2876, 2004     

UV‐ignited frontal polymerization of an epoxy resin

By combining frontal polymerization and radical‐induced cationic polymerization, it was possible to cure thick samples of an epoxy monomer bleached by UV light. The effect of the relative amounts of cationic photoinitiator and radical initiator was thoroughly investigated and was related to the front's velocity and its maximum temperature. The materials obtained were characterized by quantitative conversion also in the deeper layers, not reached by UV light. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 2066–2072, 2004     

Functionalization of polyethylene/silane copolymers in posttreatment reactions

7‐Octenyldimethylphenylsilane was copolymerized with ethylene via Et(Ind)₂ZrCl₂ methylaluminoxane catalyst system without loss of catalyst activity or decrease in molar mass. The comonomer contents in the polymer samples were at a level of 0.15–1.0 mol % and the reactive phenylsilane groups were posttreated to different alcoxy‐ and halosilane groups, for example, Si? F, Si? Cl, Si? OCH₃, and Si? OCH₂CH₃. The posttreatment reactions had no major effect on the molar masses or on the thermal properties (measured with differential scanning calorimetry) of the copolymers. The reaction pathways were nearly independent of the comonomer contents and the reactions reached 70–100% conversions. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 1461–1467, 2004     

Synthesis and characterization of new segmented polyurethanes with side‐chain,liquid‐crystalline chain extenders

Liquid‐crystalline, segmented polyurethanes with methoxy–biphenyl mesogens pendant on the chain extender were synthesized by the conventional prepolymer technique and esterification reaction. Two, side‐chain, liquid‐crystalline (SCLC) polyurethanes with mesogens having spacers of six and eight methylene units were prepared. The structures of the mesogenic units and SCLC polyurethanes were confirmed by Fourier transform infrared spectroscopy and ¹H NMR. Polymer properties were also examined by solubility tests, water uptakes, and inherent viscosity measurements. Differential scanning calorimetry studies indicated that the transition temperature of the isotropic to the liquid‐crystalline phase decreased with increasing spacer length. Wide‐angle X‐ray diffraction (WAXD) studies revealed the existence of liquid‐crystalline phases for both SCLC polyurethanes. Polarized optical microscopic investigations further confirmed the thermotropic liquid‐crystalline behaviors and nematic mesophases of both samples. Thermogravimetric analysis displayed better thermal stabilities for both SCLC polymers and indicated that the presence of mesogenic side chains may increase the thermal stability of segmented polyurethanes. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 290–302, 2004