Application of the boundary-domain element method to the pre/post-buckling problem of von Kármán plates

Based on the BEM formulations for the finite deflection problem of von-Kármán-type plates, this paper presents an incremental boundary-domain element method for the pre/post-buckling problem of thin elastic plates. As the governing equations involve the coupled in-plane and out-of-plane deformations as the nonlinear terms, the boundary integral equations are formulated in terms of the increment by using the fundamental solutions for the linear parts of the differential operators. Some of the innovations are made in order to improve the accuracy and accelerate the convergence of the solution procedure. The load-incrementation method and also the arc-length-incrementation method are employed for each incremental step. Numerical analysis is carried out and the results are compared with the available analytical solutions to demonstrate the effectiveness of the proposed method.     

Hybrid control of vibrations of a smart von Kármán plate

The suppression of large vibrations of a smart thin elastic rectangular von Kármán’s plate is considered. The plate is subjected to external disturbances and generalized control forces produced by electromechanical feedback. The considered nonlinear initial-boundary value problem is spatially discretized by means of the time spectral method. The implicit Newmark-β iterative method is employed for the time integration of the obtained system of nonlinear equations of motion. Nonlinear controllers are designed, based on a fuzzy inference system. Two numerical algorithms involving a general control of displacement/velocity and a direct control of the Fourier coefficients are proposed. The techniques have been implemented within MATLAB environment with the use of the fuzzy logic toolbox. Numerical examples are presented.     

A justification of the Marguerre-von Kármán equations

The method of asymptotic expansions, with the thickness as the small parameter, is applied to the general three-dimensional equations for the equilibrium of nonlinearly elastic shells with specific geometries, subjected to suitable loadings and boundary conditions. Then it is shown that the leading term of the expansion is the solution of a system of equations equivalent to those of Marguerre-von Karman (the case of a clamped shell is also considered). In addition, without making any a priori assumption regarding the variation of the unknowns across the thickness of the shell, it is found that the displacement field is of Kirchhoff-Love type, and that the stresses have polynomial variations with respect to the thickness.This approach clearly delineates the types of three-dimensional loadings, boundary conditions, and shallowness, for which a three-dimensional problem may be deemed asymptotically equivalent to a two-dimensional shallow shell model.Dedicated to Professor Joachim A. Nitsche on the occasion of his sixtieth birthday     

Determining wake flow parameters for two counterphase synchronized von Kármán vortex streets from configuration stability analysis

The problem of determining the parameters of near wake flow past a pair of cylindrical bluff bodies from one-point spectra of the velocity pulsation is solved in the limit of an inviscid incompressible flow. For this purpose, the stability of wake configuration with respect to infinitesimal perturbations of the equilibrium localization of the vortices is analyzed within the framework of a flow model of two counterphase synchronized von Kármán vortex streets. A necessary condition for the flow stability is determined.     

A consistent deduction of von Kármán-type plate theories from three-dimensional nonlinear continuum mechanics

Summary Classical and refined plate theories derived from linear continuum mechanics lead to correct results only if the transverse deflection of the plate is small compared to its thickness. In the case of large deflections, geometrical nonlinearities have to be incorporated. For the classical Kirchhoff plate theory, a suitable extension for moderate rotations has been presented by von Kármán in 1911.Starting from the three-dimensional equations of nonlinear continuum mechanics, a family of von Kármán-type plate theories is deduced. For the derivation, the kinematical variables are replaced by a series representation and the principle of virtual displacements is used. It can be shown that most plate theories can be obtained from this type of theory and that the kinematical assumptions must fulfill certain conditions to obtain a solvable system of equations.     

A perturbation solution of von-Kármán circular plates with different moduli in tension and compression under concentrated force

By modifying classical von-Kármán equations, we established bimodular von-Kármán equations of thin plates with different moduli in tension and compression. Adopting central deflection as a perturbation parameter, we used a perturbation method to solve the equations under various boundary conditions, including rigidly clamped, loosely clamped, simply hinged, and simply supported. The relation of load versus central deflection and stress formulas were derived via the perturbation solution obtained. The numerical simulation also shows that the perturbation solution based on central deflection is overall valid. The results indicate that when the compressive modulus of materials is greater than the tensile one, the bearing capacity of the plate will be further strengthened, which should be considered in the analysis and design of plate-like structures with obvious bimodular effect. Moreover, by comparing with the case under uniformly distributed load, the plate-membrane transition under centrally concentrated force presents discontinuity to some extent.     

Absolute instability of the von Kármán, Bödewadt and Ekman flows between a rotating disc and a stationary lid

The stability of a family of boundary-layer flows, which includes the von Kármán, B?dewadt and Ekman flows for a rotating incompressible fluid between a rotating disc and a stationary lid, is investigated. Numerical computations with the use of a spectral method are carried out to analyse absolute and convective instability. It is shown that the stability of the system is enhanced with a decrease in distance between the disc and the lid.     

A general method for analyzing moderately large deflections of a non-uniform beam: an infinite Bernoulli–Euler–von Kármán beam on a nonlinear elastic foundation

The present paper concerns a semi-analytical procedure for moderately large deflections of an infinite non-uniform static beam resting on a nonlinear elastic foundation. To construct the procedure, we first derive a nonlinear differential equation of a Bernoulli–Euler–von Kármán “non-uniform” beam on a “nonlinear” elastic foundation, where geometrical nonlinearities due to moderately large deflection and beam non-uniformity are effectively taken into account. The nonlinear differential equation is transformed into an equivalent system of nonlinear integral equations by a canonical representation. Based on the equivalent system, we propose a method for the moderately large deflection analysis as a general approach to an infinite non-uniform beam having a variable flexural rigidity and a variable axial rigidity. The method proposed here is a functional iterative procedure, not only fairly simple but straightforward to apply. Here, a parameter, called a base point of the method, is also newly introduced, which controls its convergence rate. An illustrative example is presented to investigate the validity of the method, which shows that just a few iterations are only demanded for a reasonable solution.     

A BEM formulation for analysing the coupled stretching–bending problem of plates reinforced by rectangular beams with columns defined in the domain

In this work, a boundary element formulation to analyse plates reinforced by rectangular beams, with columns defined in the domain is proposed. The model is based on Kirchhoff hypothesis and the beams are not required to be displayed over the plate surface, therefore eccentricity effects are taken into account. The presented boundary element method formulation is derived by applying the reciprocity theorem to zoned plates, where beams are treated as thin sub-regions with larger rigidities. The integral representations derived for this complex structural element consider the bending and stretching effects of both structural elements working together. The standard equilibrium and compatibility conditions along interface are naturally imposed, being the bending tractions eliminated along interfaces. The in-plane tractions and the bending and in-plane displacements are approximated along the beam width, reducing the number of degrees of freedom. The columns are introduced into the formulation by considering domain points where tractions can be prescribed. Some examples are then shown to illustrate the accuracy of the formulation, comparing the obtained results with other numerical solutions.     

A Burton–Miller formulation of the boundary element method for baffle problems in acoustics and the BEM/FEM coupling

Baffle problems, i.e. radiation problems from objects mounted behind a hole of an infinite hard reflecting wall, can be simulated as a multi domain problem consisting of a finite interior domain around the object, and two infinite half spaces in front and behind the baffle plane. A formulation of such problems is presented in the context of the Burton–Miller boundary element method. Additionally, the coupling of the acoustic boundary element method and the structural finite element method in the context of the Burton–Miller-formulation of the baffle problem is discussed.     

A combined BEM–FEM model for the velocity–vorticity formulation of the Navier–Stokes equations in three dimensions

This paper describes a combined boundary element and finite element model for the solution of velocity–vorticity formulation of the Navier–Stokes equations in three dimensions. In the velocity–vorticity formulation of the Navier–Stokes equations, the Poisson type velocity equations are solved using the boundary element method (BEM) and the vorticity transport equations are solved using the finite element method (FEM) and both are combined to form an iterative scheme. The vorticity boundary conditions for the solution of vorticity transport equations are exactly obtained directly from the BEM solution of the velocity Poisson equations. Here the results of medium Reynolds number of up to 1000, in a typical cubic cavity flow are presented and compared with other numerical models. The combined BEM–FEM model are generally in fairly close agreement with the results of other numerical models, even for a coarse mesh.     

BEM for theomoelasticity and elasticity with body force — a revisit

For thermoelasticity and elasticity with a body force, the regular boundary element method involves a domain integral. Special techniques have been devised to eliminate the domain integral by either exact treatment, or approximation using radial basis functions. This paper gives a unified presentation of these techniques. Body forces of gravity, centrifugal, gradient, harmonic, and arbitrary types are investigated. In the approximation by radial basis function, existing work is extended to include higher order basis functions of conical, spline, and polynomial types.     

A velocity-decomposition formulation for the incompressible Navier–Stokes equations

The principle of velocity decomposition is used to combine field discretization and boundary-element techniques to solve for steady, viscous, external flows around bodies. The decomposition modifies the Navier–Stokes boundary-value problem and produces a Laplace problem for a viscous potential, and a new Navier–Stokes sub-problem that can be solved on the portion of the domain where the total velocity has rotation. The key development in the decomposition is the formulation for the boundary condition on the viscous potential that couples the two components of velocity. An iterative numerical scheme is described to solve the decomposed problem. Results are shown for the steady laminar flow over a sectional airfoil, a circular cylinder with separation, and the turbulent flow around a slender body-of-revolution. The results show the viscous potential is obtainable even for massively separated flows, and the field discretization must only encompass the vortical region of the total velocity.     

Implicit yield function formulation for granular and rock-like materials

The constitutive modelling of granular, porous and quasi-brittle materials is based on yield (or damage) functions, which may exhibit features (for instance, lack of convexity, or branches where the values go to infinity, or ‘false elastic domains’) preventing the use of efficient return-mapping integration schemes. This problem is solved by proposing a general construction strategy to define an implicitly defined convex yield function starting from any convex yield surface. Based on this implicit definition of the yield function, a return-mapping integration scheme is implemented and tested for elastic–plastic (or -damaging) rate equations. The scheme is general and, although it introduces a numerical cost when compared to situations where the scheme is not needed, is demonstrated to perform correctly and accurately.     

Chevron of microchannel plates as position-sensitive detector for β-spectrometers

The detection efficiency and position resolution of a microchannel plate chevron for electron beams of 12 to 300 keV energy at 0° to 45° angles of incidence have been investigated. The chevron is shown to ensure good stability, high detection efficiency and high position resolution in the energy range under study.     

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.     

Coupling FEM and symmetric BEM for dynamic interaction of dam–reservoir systems

A numerical model coupling boundary and finite elements suitable for dynamic dam–reservoir interaction is presented herein. This model involves standard finite element idealization of the dam structure displacements and a new symmetric boundary element formulation of the unbounded reservoir domain leading to an equivalent symmetric stiffness matrix for the discretized pressure field. These two basic parts of the computation are directly coupled by imposing an equilibrium condition at the fluid–structure interface, then the resulting algebraic system is reduced by localizing the coupled terms in the global mass matrix such as usually achieved in the added-mass formulation. Finally, the performance and the accuracy of this model are examined by comparing its results to those obtained from three other numerical models.     

Genetische Modellierung von Künstlichen Neuronalen Netzen

Zusammenfassung Künstliche Neuronale Netze (KNN) haben sich für eine automatisierte Klassifikation, wie sie etwa bei der Kreditwürdigkeitsprüfung durchzuführen ist, als Alternative zu klassischen statistischen Methoden etabliert. Während die KNN-Typ-spezifischen Lernverfahren, wie etwa das Back-Propagation-Verfahren bei Multi-Layer-Perceptron-Netzen dabei anwendungsdomänenunabhängig und auch instanzunabhängig definiert sind, stellt die Konfiguration des spezifischen KNN für eine konkrete Anwendung ein Entscheidungsproblem dar, das jeweils in Abhängigkeit der Anwendungsdomäne (Kreditwürdigkeitsprüfung) und der konkreten Instanz (unternehmenspezifische Kennzahlensysteme) zu lösen ist. Für dieses Konfigurationsproblem, das in der Literatur noch nicht umfassend behandelt wurde, wird in dieser Arbeit mit dem Genetic Modeling ein Ansatz vorgestellt, bei dem eine passende Netzkonfiguration mittels eines Genetischen Algorithmus ebenfalls aus historischem Wissen gelernt wird. Wir berichten über erste empirische Ergebnisse beim Einsatz zur Kreditwürdigkeitsprüfung mittels LVQ-KNN.