Coupled Boundary Research Articles

Boundary element analysis of reinforced shear deformable shells

AbstractIn this paper, stiffened shear‐deformable shells are analysed using the boundary element method. Coupled boundary integral equations are presented for describing curved shells under general loading conditions. The equations are based on boundary integral equations for plane stress and plate bending, with coupling terms arising from the curvature of the shell. Domain integrals are transformed into boundary integrals using the dual reciprocity technique. Stiffeners are modelled as curved beams, continuously attached to the shell. Numerical solutions calculated using the present method are compared with finite element results in two examples. Copyright © 2002 John Wiley & Sons, Ltd.

Plane Wave Diffraction By a Thin Semi-Infinite Chiral Slab

The problem of diffraction of a plane wave incident on a thin semi-infinite chiral slab is solved in an explicit form and the effect of chirality on diffraction phenomenon is investigated for the first time. The thin layer is simulated by appropriate coupled transition boundary conditions of the first order with respect to the thickness of the slab. Application of the law of conservation of energy enables us to prove the uniqueness of the solution and to give some sufficient conditions for the parameters of the problem securing the unique solvability. The problem in question is solved by means of the Sommerfeld integrals and by some minor modification of the Maliuzhinetz technique. The asymptotics of the far field is studied and some numerical results for the diffraction coefficients are discussed.

Left-Definite Sturm–Liouville Problems

Left-definite regular self-adjoint Sturm–Liouville problems, with either separated or coupled boundary conditions, are studied. We give an elementary proof of the existence of eigenvalues for these problems. For any fixed equation, we establish a sequence of inequalities among the eigenvalues for different boundary conditions and estimate the range of each eigenvalue as a function on the space of boundary conditions. Some of our results here yield an algorithm for numerically computing the eigenvalues of a left-definite problem with an arbitrary coupled boundary condition. Our inequalities imply that the well-known asymptotic formula for the eigenvalues in the separated case also holds in the coupled case. Moreover, we study the continuous and differentiable dependence of the eigenvalues of the general left-definite problem on all the parameters in its differential equation and boundary condition.

Algorithm 810: The SLEIGN2 Sturm-Liouville Code

The SLEIGN2 code is based on the ideas and methods of the original SLEIGN code of 1979. The main purpose of the SLEIGN2 code is to compute eigenvalues and eigenfunctions of regular and singular self-adjoint Sturm-Liouville problems, with both separated and coupled boundary conditions, and to approximate the continuous spectrum in the singular case. The code uses some new algorithms, which we describe, and has a driver program that offers a user-friendly interface. In this paper the algorithms and their implementations are discussed, and the class of problems to which each algorithm applied is identified.

Analysis of Gas-Lubricated Bearings with a Coupled Boundary Effect for Micro Gas Turbine

Due to the limitation of micro-machining technology, the bearing aspect ratio for a micro gas turbine is limited to a small value. Therefore, the load-carrying capacity of such bearing is inherently small. Thus, it is desirable to predict the load-carrying capacity as accurately as possible without being unnecessarily conservative. The direct numerical analysis of bearing characteristics was performed by mass conservation at coupled boundary. Journal bearing was numerically simulated for two cases −1) an externally pressurized bearing with four feeding holes and 2) a hydrodynamic bearing. Characteristics such as pressure distribution at the bearing surface, load-carrying capacity as a function of aspect ratio with a coupled boundary effects are investigated for micro gas turbine bearings. It is shown that a model of thrust and journal bearings coupled at boundary generally predicts a greater load-carrying capacity than uncoupled models. Presented as a Society of Tribologists and Lubrication Engineers Paper at the STLE/ASME Triboiogy Conference in San Francisco, CA October 21–24, 2001

Coupled BEM/FEM approach for nonlinear soil/structure interaction

A general coupled boundary element/finite element formulation is presented for the investigation of dynamic soil/structure interaction including nonlinearities. It is applied to investigate the transient inelastic response of structures coupled with a halfspace. The structure itself and the surrounding soil in the near field are modeled with finite elements. In this part of the model inhomogeneities and an elastoplastic material behavior with hardening effects can be taken into account. The remaining soil region, i.e. the elastic halfspace, is discretized with the boundary elements. Thus wave radiation to infinity is included in the model. In representative examples it is shown that the methodology is computationally powerful and can be used efficiently for the nonlinear analyses of complex soil/structure interaction problems.

Discrete numerical solution of strongly coupled mixed diffusion problems

This paper is concerned with the discrete numerical solution of coupled partial differential mixed problems with non-Dirichlet coupled boundary value conditions. By using a discrete separation of variables method, the proposed numerical solution of the problems is the exact solution of certain coupled partial difference system, appearing from the discretization of the continuous partial differential systems. Existence, stability, and examples are considered.

Coupled boundary and finite element analysis of a special class of two-dimensional problems of the theory of elasticity

For special problems of the theory of elasticity, coupled boundary and finite element analysis may be a useful alternative to either finite element or boundary element analysis. Herein, we propose a new mode of coupled analysis which is based on combining the linear theory of elasticity with Timoshenko’s shell theory [D(imension)-adaptive model]. For the sake of simplicity, the paper is restricted to the investigation of two-dimensional (plane strain) problems. A special type of boundary conditions is proposed for linking the parts of the cross-section of a cylindrical structure, which are treated by different theories. The boundary of the part of the cross-section, which is described by the equations of the theory of elasticity, is discretized by means of boundary elements. The remaining part of the cross-section, which is described by the equations of the Timoshenko’s shell theory, is discretized by means of finite elements. The numerical investigation demonstrates the special features of the proposed hybrid model and of the respective coupling technique.

Coupled Dual Reciprocity Boundary Element/Finite Volume Method for Transient Conjugate Heat Transfer

A coupled finite volume/dual reciprocity boundary element method is developed to solve the transient conjugate heat transfer problem of convective heat transfer over and conduction heat transfer within a solid body. In this approach, the flowfield and forced convection heat transfer external to the body is resolved by numerically solving the time-dependent Navier-Stokes equations using a finite volume method, whereas the temperature field within the body is resolved by numerically solving the heat conduction equation using a dual reciprocity boundary element method. The boundary discretization utilized to generate the computational grid for the external flowfield provides the boundary discretization required for the boundary element method. Coupling of the two fields is accomplished by enforcing Interface continuity of heat flux and temperature. Transient heat transfer data needed to verify the code were obtained in a series of experiments that are reported. Details of the experimental setup and test conditions are provided

The stable discrete numerical solution of strongly coupled mixed partial differential systems

This paper is concerned with the discrete numerical solution of coupled partial differential mixed problems with non-Dirichlet coupled boundary value conditions. By application of a discrete separation of variables method, the proposed numerical solution of the problem turns out to be the exact solution of certain coupled partial difference system, appearing from the discretization of the continuous partial differential system. Our approach avoids the iterative solution of algebraic systems which appears when one uses simple discretization methods. Existence, stability and the construction of solutions are considered.

Potential transients for an electrochemical corrosion reaction under constant current conditions

Due to the electrochemical nature of almost all corrosion reactions, electrochemical methods are commonly used to measure the corrosion rate of a metal in the laboratory or in the field. In particular, steady state methods are the most widely used for corrosion rate measurements. Transient methods, which can be much more efficient, traditionally rely on an equivalent linear circuit representing the surface kinetics, with negligible mass transport effects. This has been reported to predict transients which are not observed experimentally in many practical situations. In this paper, we consider the galvanostatic method, wherein a constant current is applied across a corroding metal surface and the transient potential response is recorded. The resulting boundary value problems incorporating mixed kinetic and diffusion control involve highly nonlinear, coupled boundary conditions. We present numerical and approximate analytical solutions which can be incorporated into corrosion analysis routines in order to calculate corrosion parameters. The analytical expressions open the possibility of measuring corrosion parameters by merely fitting a class of elementary functions to experimental potential transients. This leads to a significant reduction in the number of computations required for the curve fitting, and hence increasing the overall efficiency of the measurement process compared to the conventional steady state methods.

Sturm–Liouville Problems with Coupled Boundary Conditions and Lagrange Interpolation Series

This paper is concerned with the application of the Kramer sampling theorem to Sturm–Liouville problems with coupled boundary conditions. The analysis is restricted to the case when the spectrum of the boundary value problem is simple. In all such cases, it is shown that Kramer analytic kernels can be defined and that each kernel has an associated analytic interpolation function to give the Lagrange interpolation series.

Far-Field Analysis of Coupled Bulk and Boundary Layer Diffusion Toward an Ion Channel Entrance

We present a far-field analysis of ion diffusion toward a channel embedded in a membrane with a fixed charge density. The Smoluchowski equation, which represents the 3D problem, is approximated by a system of coupled three- and two-dimensional diffusions. The 2D diffusion models the quasi-two-dimensional diffusion of ions in a boundary layer in which the electrical potential interaction with the membrane surface charge is important. The 3D diffusion models ion transport in the bulk region outside the boundary layer. Analytical expressions for concentration and flux are developed that are accurate far from the channel entrance. These provide boundary conditions for a numerical solution of the problem. Our results are used to calculate far-field ion flows corresponding to experiments of Bell and Miller (Biophys. J. 45:279, 1984).

Rotordynamics prediction in engineering (second edition)

In this paper we study the limit point and limit circle classification for symplectic systems on time scales, which depend linearly on the spectral parameter. In a broader context, we develop a unified Weyl–Titchmarsh theory for continuous and discrete linear Hamiltonian and symplectic systems. Both separated and coupled boundary conditions are allowed. Our results include the study of the Weyl disks and circles and their limiting behavior, as well as a precise analysis of the number of linearly independent square integrable solutions. We also prove an analogue of the famous Weyl alternative. We connect and unify many known results in the Weyl–Titchmarsh theory for continuous, discrete, and special time scales systems and explain the differences between them. Some of our statements, in particular those connected with coupled endpoints or the Weyl alternative, are new even in the continuous time setting.

Effect of Wave-Enhanced Bottom Friction on Storm-Driven Circulation in Massachusetts Bay

Massachusetts Bay is a shallow (35 m average depth) semienclosed embayment, roughly 100 × 50 km, which opens into the Gulf of Maine at its eastern boundary. Surface waves associated with winter storm winds from the northeast cause large sediment resuspension events, and wave and circulation fields during these events have a quasi-steady response to the wind stress. Coupled wave, circulation, and boundary layer models indicate that wave-enhanced bottom friction has a significant damping effect on storm-driven circulation in Massachusetts Bay. The simulated response exhibits significant three-dimensional structure, but still can be fundamentally understood using idealized models. The depth-integrated momentum balance is dominated by along-bay stress, pressure gradient, and bottom stress. The effective bottom drag coefficient during typical storm conditions is increased by a factor of 2–5 when wave effects are included, but the mean bottom stress is relatively unaffected by wave effects due to a reduction in...

Non-linear transient analysis of submerged circular plates subjected to underwater explosions

A new coupled finite element and boundary integral formulation is developed for non-linear transient analysis of submerged thin circular plates subjected to underwater explosions. In this new formulation, the governing equations of motion of the structure are completely decoupled from those of wave propagation by applying Kirchhoff, s integral equation on the wet surface of the structure, thereby eliminating the need for modelling the surrounding fluid. Using Kirchhoff thin plate theory, an axisymmetric ring plate element is formulated, which takes into account both geometric and material non-linearities as well as strain-rate effects. The scattered pressure field due to the fluid-structural interaction is calculated by solving the surface integral equation in the context of element discretization method. The effects of water cavitation on structural response are included by using an appropriate pressure criterion. The time-dependent solution of the coupled fluid-structure system is then solved by applying a staggered solution algorithm at each time step in a direct time-integration procedure. The proposed formulation has been tested for a number of applications and the results obtained are compared with experiments. It is observed that the new formulation can provide reasonable solutions to both near- and far-field interaction problems for underwater shock response analysis.

A unique coupled boundary element/finite element method for the elastoacoustic analysis of fluid-filled thin shells

A coupled boundary element/finite element technique originally developed for the analysis of open thin-shell problems, such as propeller blades, is used in this paper for the analysis of the fluid-filled elastic structures. For open thin-shell problems the question of nonuniqueness does not arise, however, it was thought at the time that such a formulation would prove to be nonunique for the analysis of closed fluid-filled submerged bodies. The work presented in this paper will demonstrate that, for submerged fluid-filled closed elastic bodies, this coupled formulation is unique throughout the entire frequency range. An advantage in implementing the variational form of the acoustic integral operator is that the resulting fluid matrix is symmetric. As such, the fluid/structural coupling is simplified, and the computational efficiency enhanced.

Full-wave boundary integral equation method for suspended planar transmission lines with pedestals and finite metallization thickness

A boundary integral equation method is proposed for the full-wave analysis of suspended planar transmission lines with pedestals and/or finite metallization thickness. Coupled boundary integral equations are formulated on equivalent magnetic currents only on the apertures of subregions using the Green's identity of the second kind. Because it is possible to take a large number of terms in the series expansion of Green's functions in each subregion independently from the order of resulting matrices, this approach can avoid the relative convergence problem. Numerical results for suspended coplanar waveguides are found to have a stable convergence property and to be in excellent agreement with other available theoretical results. Numerical data reveal the effects of conductor thickness and aperture width on the transmission properties of suspended planar transmission lines with pedestals. >

Coupled boundary and finite elements for dynamic structure (3D)-foundation-soil interaction

A study of the dynamic structure (3D)-foundation-soil interaction is presented in this paper, in which finite elements (FE) and boundary elements (BE) are used. The structure and foundation are represented by the FE, and the soil by the BE. The coupling of both kinds of elements is accomplished through equilibrium and compatibility considerations along the soil-structure interface. Through numerical studies, the influence of the discretization of traction-free surface of soil, and the asymmetry of the dynamic stiffness matrix K F (BEM) is discussed.

STEADY‐STATE THERMOELASTICITY BY MULTIPLE RECIPROCITY METHOD

Thermal stress problems are analysed using two coupled boundary element codes. The first code computes the temperature and heat flux distributions whereas the second one uses these results to calculate the displacements and stresses at any point. In both codes, the multiple reciprocity method is used in order to avoid the domain discretization due to the ‘body force’ terms. Examples with different geometry and different heat sources are presented to check the accuracy of the formulations.