Parameter identification for coupled finite element–boundary element models

To solve problems involving semi-infinite domains, one efficient approach is to use finite elements (FE) to model the regions where detailed information about materials with complicated properties is needed and to use boundary elements (BE) to simulate the semi-infinite parts. In this paper, a parameter identification algorithm is developed for coupled FE–BE models in detail. The algorithm is designed to identify all the material parameters in the FE domain and the BE domain simultaneously. Its validity is illustrated using two examples. The distribution of the observational points is also briefly tested and discussed. The numerical results reveal that this is a stable and fast-converging algorithm.     

Multi-objective robust design of energy-absorbing components using coupled process–performance simulations

The stochastic uncertainties associated with the material, process and product are represented and propagated to process and performance responses. A finite element-based sequential coupled process–performance framework is used to simulate the forming and energy absorption responses of a thin-walled tube in a manner that both material properties and component geometry can evolve from one stage to the next for better prediction of the structural performance measures. Metamodelling techniques are used to develop surrogate models for manufacturing and performance responses. One set of metamodels relates the responses to the random variables whereas the other relates the mean and standard deviation of the responses to the selected design variables. A multi-objective robust design optimization problem is formulated and solved to illustrate the methodology and the influence of uncertainties on manufacturability and energy absorption of a metallic double-hat tube. The results are compared with those of deterministic and augmented robust optimization problems.     

Sensitivity analysis and shape optimization based on FE–EFG coupled method

By use of 4-node isoparametric quadrangle interface element between finite element (FE) and meshless regions, a collocation approach is introduced to couple firstly FE and element-free Galerkin (EFG) method in this paper. By taking derivative of discreteness equilibrium equation at interface element with respect to design variable, a numerical method for discreteness-based shape design sensitivity analysis in interface element is obtained. The design sensitivity analysis (DSA) of coupled FE–EFG method is achieved by employing the DSA of nodal displacement at the interface element. The numerical method presented is testified by examples. It can be observed excellent agreement between the numerical results and the analytical solution. Finally the shape optimization of fillet is achieved by using coupled FE–EFG method. The result obtained show that imposing of the essential boundary condition is easy to implement, the computational time is reduced and the distortion of mesh is avoided.     

Modified Reynolds equation for coupled stress fluids – a porous media model

Summary. In this paper, the rheological effects of coupled stress fluids on thin film lubrication modeling are developed. Thin porous layers attached to the impermeable substrate are utilized to model the microstructure of bearing surfaces. In the fluid film region, the constitutive equations for coupled stress fluids proposed by Stokes [1] as well as the continuity and momentum equations are applied to model the flow. In the porous region, the Brinkman-extended Darcy equations are applied to model the flow. Under the usual assumption of hydrodynamic lubrication applicable to thin films, the effects of viscous shear and the stress jump boundary condition at the porous media/fluid film interface are included in deriving the modified Reynolds equation. The effects of material properties such as coupled stress parameter viscosity ratio (_i²), thickness of porous layer (_i), permeability (K_i), and stress jump parameter (_i), on the velocity distributions and load capacities of one-dimensional converging wedge problems are discussed.     

A coupled ES-FEM/BEM method for fluid–structure interaction problems

The edge-based smoothed finite element method (ES-FEM) developed recently shows some excellent features in solving solid mechanics problems using triangular mesh. In this paper, a coupled ES-FEM/BEM method is proposed to analyze acoustic fluid–structure interaction problems, where the ES-FEM is used to model the structure, while the acoustic fluid is represented by boundary element method (BEM). Three-node triangular elements are used to discretize the structural and acoustic fluid domains for the important adaptability to complicated geometries. The smoothed Galerkin weak form is adopted to formulate the discretized equations for the structure, and the gradient smoothing operation is applied over the edge-based smoothing domains. The global equations of acoustic fluid–structure interaction problems are then established by coupling the ES-FEM for the structure and the BEM for the fluid. The gradient smoothing technique applied in the structural domain can provide the important and right amount of softening effects to the “overly-stiff” FEM model and thus improve the accuracy of the solutions of coupled system. Numerical examples of acoustic fluid–structure interaction problems have been used to assess the present formulation, and the results show that the accuracy of present method is very good and even higher than those obtained using the coupled FEM/BEM with quadrilateral mesh.     

Photoluminescence emission through thin metal films via coupled surface plasmon–polaritons

We present experimental results showing the variation in photoluminescence from an organic material emitted through a thin metal film as successive dielectric overlayers are added to the far side of the metal. The intensity of the emission from the structure is examined as the surface plasmon–polariton (SPP) modes associated with the two metal surfaces evolve with increasing overlayer thickness from individual to coupled SPP modes. The SPP modes are scattered to produce light by the addition to the metal film of wavelength-scale periodic microstructure. We show that the addition of a dielectric overlayer of an appropriate thickness to the metal film is accompanied by an increase in the intensity of the emission by a factor of 3 over a similar structure with no dielectric overlayer, and by a factor of 50 over a similar planar structure. We show that this increase in emission is mediated via coupled SPP modes.     

Collimation testing by use of the Lau effect coupled with moiré readout

We present an easy, simple, and inexpensive technique for checking the quality of the collimation of optical beams using the Lau effect combined with moiré readout. The experimental arrangement consists of a modified Lau-based interferometer in which a white-light incoherent source illuminates a set of two gratings. A collimating lens is placed between the two gratings such that the self-images of the second grating are formed. The third grating is positioned at one of the self-imaging planes forming moiré fringes. The type of the moiré fringe demonstrates the quality of collimation of the optical beam. The necessary theoretical background is presented and the results of our experimental investigation are reported. The technique can also be used for accurate determination of the focal length of a collimating lens using low-cost components.     

Optical solitons in a new type of coupled nonlinear Schrödinger equations

Abstract

We consider a new type of integrable coupled nonlinear Schrödinger (CNLS) equations proposed by Park and Shin [1999, Phys. Rev. E, 59, 2372]. Using the Ablowitz-Kaup-Newell-Segur method, we construct the Lax pair for simultaneous propagation of four fields in the new type of CNLS equations. The explicit form of soliton solutions are derived using the Hirota bilinear method.     

Weakly coupled highTc superconductors—An overview

A short review of the main achievements in the development of high-T _c Josephson junction investigation is given. The six years of history of high-T _c superconductivity have produced in this field a variety of interesting results providing exciting perspectives and, at the same time, raising challenging questions. We shall attempt here to give a brief sketch of this topic, suitable for a nonspecialized audience, which, although oversimplified as well as incomplete, could supply some ideas about where we stand and where we are headed in this field.     

Dynamical theoretical model and variational principles for coupled temperature–diffusion–mechanics

In this paper, firstly, the acceleration of the temperature and concentration are assumed to need the extra increment of the heat and energy. The inertial entropy and the inertial chemical potential were proposed by Kuang (Acta Mech 203:1–11, 2009, Acta Mech 214:275–289, 2010). Secondly, the expressions of dissipative energy produced by the variation of the temperature and concentration are derived by using the second law of thermodynamics. Finally, several variational principles for coupled temperature–diffusion–mechanics are established, and their corresponding governing equations and boundary conditions are naturally presented. Meanwhile, some numerical simulations are carried out to describe the coupled reciprocity, which shows concentration diffusion with a finite velocity.     

Energy coupled to matter for magnetic alignment of rare earth–doped alumina

Energy coupled to matter (ECM) concepts such as magnetic field–assisted processing were used to align rare earth–doped alumina ceramics in the presence of applied fields. The addition of gadolinium and ytterbium dopants to alumina increased the magnetic susceptibility anisotropies, and induced magnetic torques that led to significant alignment of ceramic particles under the application of magnetic fields as low as 1.8?T. In comparison, undoped alumina materials showed minimal alignment under applied field strengths as high as 9?T. Density function theory modeling indicated that the specific dopant type dictated changes in the magnetic properties of different rare earth–doped alumina systems by directly affecting the magnetic moment localization and magnetocrystalline anisotropy.     

A coupled symmetric BE–FE method for acoustic fluid–structure interaction

A coupled symmetric BE–FE method for the calculation of linear acoustic fluid–structure interaction in time and frequency domain is presented. In the coupling formulation a newly developed hybrid boundary element method (HBEM) will be used to describe the behaviour of the compressible fluid. The HBEM is based on Hamilton's principle formulated with the velocity potential. The state variables are separated into boundary variables which are approximated by piecewise polynomial functions and domain variables which are approximated by a superposition of static fundamental solutions. The domain integrals are eliminated, respectively, replaced by boundary integrals and a boundary element formulation with a symmetric mass and stiffness matrix is obtained as result. The structure is discretized by FEM. The coupling conditions fulfil C¹-continuity on the interface. The coupled formulation can also be used for eigenfrequency analyses by transforming it from time domain into frequency domain.     

Fully coupled thermal–electric-sintering simulation of electric field assisted sintering of net-shape compacts

A fully coupled thermal–electric-sintering finite element model was developed and implemented to predict heterogeneous densification in net-shape compacts using electric field assisted sintering techniques (FAST). FAST is a single-step processing operation for producing bulk materials from powders, in which the powder is heated by the application of electric current under pressure. Previous modeling efforts on FAST have mostly considered the thermal–electric aspect of the problem and have largely neglected the sintering aspect of the problem. A new model was developed by integrating a phenomenological sintering model into a previously established thermal–electric finite element framework to predict the densification kinetics of the sample. The model was used to quantify the effect of specimen geometry on the evolution of thermoelectric gradients and resulting heterogeneous sintering kinetics during FAST processing of a conductive powder. It is shown that the new model which considers sintering kinetics and density-dependent properties provides a substantial increase in accuracy compared to thermal–electric only models. It is also shown that small changes in local resistance due to densification can greatly impact the distribution of thermoelectric gradients during the process, which are exacerbated by heterogeneous stress states induced by sample geometry. Experimental characterization of sintered specimens is used to provide qualitative validation of the model predictions.     

Rogue waves for a coupled nonlinear Schrödinger system in a multi-mode fibre

In this paper, we investigate the rogue waves for an integrable coupled nonlinear Schrödinger (CNLS) system with the self-phase modulation, cross-phase modulation and four-wave mixing term, which can describe the propagation of optical waves in a multi-mode fibre. We construct a generalized Darboux transformation (GDT) for the CNLS system and find a gauge transformation which converts the Lax pair into the constant-coefficient differential equations. Solving those equations, we can obtain the vector solutions of the Lax pair. Using the GDT, we derive an iterative formula for the nth-order rogue-wave solutions for the CNLS system. We derive the first- and second-order rogue-wave solutions for the CNLS system and analyse the profiles for the rogue waves with respect to the self-phase modulation term a, cross-phase modulation term c and four-wave mixing term b, respectively. The rogue waves become thinner with the increase in the value for the real part of b and that the effect of a or c on the rogue waves is the same as the one of the real part of b.     

Optimality criteria-based topology optimization of a bi-material model for acoustic–structural coupled systems

This article investigates topology optimization of a bi-material model for acoustic–structural coupled systems. The design variables are volume fractions of inclusion material in a bi-material model constructed by the microstructure-based design domain method (MDDM). The design objective is the minimization of sound pressure level (SPL) in an interior acoustic medium. Sensitivities of SPL with respect to topological design variables are derived concretely by the adjoint method. A relaxed form of optimality criteria (OC) is developed for solving the acoustic–structural coupled optimization problem to find the optimum bi-material distribution. Based on OC and the adjoint method, a topology optimization method to deal with large calculations in acoustic–structural coupled problems is proposed. Numerical examples are given to illustrate the applications of topology optimization for a bi-material plate under a low single-frequency excitation and an aerospace structure under a low frequency-band excitation, and to prove the efficiency of the adjoint method and the relaxed form of OC.     

Non-equilibrium thermodynamics and variational principles for fully coupled thermal–mechanical–chemical processes

In this paper, the chemical Gibbs function variational principle, the Helmholtz function variational principle and the internal energy variational principle based on irreversible thermodynamics are proposed for the thermal–chemical–mechanical fully coupling problems. The complete fully coupling governing equations, including the heat conduction, mass diffusion and chemical reactions, are derived from the variational principles. The convective effect can also be derived in the diffusion and energy equations from the variational principles naturally. Moreover, the concentrations and entropy jump conditions on the moving interface between the products due to chemical reactions and the matrix can be derived from the variational principles naturally. This work provides the basis for the analyses and computations of thermochemomechanical coupling problems.     

Simulation of the pressure drop across granulated mixtures using a coupled DEM – CFD model

The sinter process converts mixtures of iron ore, iron ore fines and fluxes into a fused aggregate (sinter) that is used as burden material in the blast furnace. The rate of this process is predicted by measuring the pressure drop across the green granulated mixture before ignition. A lower pressure drop corresponds with a higher permeability resulting in a higher sinter rate. The addition of fine material, such as concentrate or concentrate agglomerated into micropellets, to the sinter mixture affects the pressure drop. This study numerically predicts the pressure drop over several granulated mixtures in order to reduce the number of experimental measurements. The pressure drop was studied both experimentally using a pot grate and by coupled DEM (Discrete Element Method) – CFD (Computational Fluid Dynamics) simulations. The validation of the model was performed by comparing the measured and numerical values of the pressure drop across glass beads 3 and 6?mm in diameter respectively. The simulation of the pressure drop was extended to granulated mixtures that contain 0–40% concentrate or micropellets. DEM was also used to numerically simulate iron ore granules and relate their mechanical behaviour to particle size distribution, shape, friction coefficient, Young’s modulus and adhesion force.     

A coupled boundary element/differential equation method formulation for plate–beam interaction analysis

In this work, a new boundary element formulation for the analysis of plate–beam interaction is presented. This formulation uses a three nodal value boundary elements and each beam element is replaced by its actions on the plate, i.e., a distributed load and end of element forces. From the solution of the differential equation of a beam with linearly distributed load the plate–beam interaction tractions can be written as a function of the nodal values of the beam. With this transformation a final system of equation in the nodal values of displacements of plate boundary and beam nodes is obtained and from it, all unknowns of the plate–beam system are obtained. Many examples are analyzed and the results show an excellent agreement with those from the analytical solution and other numerical methods.