Terms Of Boundary Integrals Research Articles

OS0120 重ね合わせの原理に基づく傾斜材の応力解析法の開発(弾性数理解析とその応用,オーガナイズドセッション)

Method of elastic stress analysis for general Functionally Gradient Materials (FGMs) is studied based on the principle of superposition. In the present study, the spacial variation of the elastic constants is expressed by an embedded force doublets in an elastic continuum. As a result, the stress field of an arbitrarily gradient materials is expressed by the superposition of elastic fundamental solutions of a homogeneous body as in a similar manner of the ordinary elastic problems. The relationship between local stresses and displacements, which are expressed in terms of boundary integrals, are used to determine the unknown magnitude of force doublets.

Crack Analysis in Residual Stress Field by X-FEM

The extended finite element method (X-FEM), which can model the domain without explicitly meshing the crack surface, can be used to perform stress analyses for solving fracture mechanics problems efficiently. In the present study, the principle of superposition is used to solve crack problems in conjunction with the X-FEM. In the proposed method, the surface load distributed on the crack surface, which is modeled implicitly by the interpolation functions with enrichment terms, is introduced to X-FEM analysis. Moreover, the energy release rate at the crack front is evaluated by the domain integral method with boundary integral terms for the surface load. The proposed method is verified through numerical analyses of two- and three-dimensional crack problems in linear fracture mechanics.

Crack Analysis in Residual Stress Field by X-FEM

The extended finite element method (X-FEM), which can model the domain without explicitly meshing the crack surface, can be used to perform stress analyses for solving fracture mechanics problems efficiently. In the present study, the principle of superposition is used to solve crack problems in conjunction with the X-FEM. In the proposed method, the surface load distributed on the crack surface, which is modeled implicitly by the interpolation functions with enrichment terms, is introduced to X-FEM analysis. Moreover, the energy release rate at the crack front is evaluated by the domain integral method with boundary integral terms for the surface load. The proposed method is verified through numerical analyses of two- and three-dimensional crack problems in linear fracture mechanics.

A two‐scale homogenization procedure for the meso‐macro‐modeling of electro‐mechanically coupled problems

AbstractThe challenge in the field of ferroelectric ceramics is the modeling of complicated interactions between electrical and mechanical properties of the material on the macro‐scale, caused by switching processes on the meso‐scale. This paper presents a two‐scale homogenization framework for the description of polycrystalline material behavior of ferroelectric ceramics, that takes into account the effects occurring on the meso‐scale. The macroscopic variables of the underlying field equations are expressed in terms of mesoscopic boundary integrals and appropriate boundary conditions on the meso‐scale are derived. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Formula omitted]-regularity in the Dirichlet problem for [formula omitted

We answer the much sought after question on regularity of the viscosity solution u to the Dirichlet problem for the infinity Laplacian Δ ∞ in x = ( x 1 , … , x n ) ∈ R n ( n ≥ 1 ) with Lipschitz boundary data on ∂ U of the open set U (whether u is C 1 ( U ) ), that in fact u has Hölder regularity C ( 1 , 1 / 3 ) ( U ) . Furthermore, if each of the first partials u x j never vanishes in U ̄ (a coordinate dependent condition) then u ∈ C ( 1 , 1 ) ( U ) . The methods that we employ are distinctly different from what is generally practiced in the viscosity methods of solution, and include ‘action’ of boundary distributions, Lebesgue differentiation and regularization near the boundary and a definition of product of distributions not satisfying the Hörmander condition on their wavefront sets, while representing the first partial derivatives of u purely in terms of boundary integrals involving only first order derivatives of u on the boundary.

Dependence of Friedrichs' constant on boundary integrals

This note extends the results in ‘Optimal coercivity inequalities in W1,p(Ω)’ (G. Auchmuty, Proc. R. Soc. Edinb. A 135, 915–933.) describing the dependence of the optimal constant in the p-version of Friedrichs' inequality on the boundary integral term. In particular, it is shown that this constant is continuous, increasing, concave and increases to the optimal constant for the Dirichlet problem as s → ∞.

Dependence of Friedrichs' constant on boundary integrals

This note extends the results in ‘Optimal coercivity inequalities in W1,p(Ω)’ (G. Auchmuty, Proc. R. Soc. Edinb. A 135, 915–933.) describing the dependence of the optimal constant in the p-version of Friedrichs' inequality on the boundary integral term. In particular, it is shown that this constant is continuous, increasing, concave and increases to the optimal constant for the Dirichlet problem as s → ∞.

Singular Perturbations for Boundary Value Problems Arising from Exotic Options

We study the pricing of three exotic derivative securities (barrier, lookback, and passport options) which can be characterized by boundary value PDE problems in the context of popular Markovian SV models of stock prices. By extending the fast mean-reverting asymptotic analysis in [J.-P. Fouque, G. Papanicolaou, and K. R. Sircar, Derivatives in Financial Markets with Stochastic Volatility, Cambridge University Press, London, 2000], the usual Greek correction to the Black--Scholes prices of these contracts is further corrected by a boundary integral term that is rapidly computed numerically. In the case of the passport option, the asymptotic method is effective in accounting for SV effects in a simple and robust fashion even in the presence of a highly nonlinear embedded stochastic control problem.

Numerical Solution of Elliptic Shape Optimization Problems using wavelet-based BEM

In this article we study the numerical solution of elliptic shape optimization problems with additional constraints, given by domain or boundary integral functionals. A special boundary variational approach combined with a boundary integral formulation of the state equation yields shape gradients and functionals which are expressed only in terms of boundary integrals. Hence, the efficiency of (standard) descent optimization algorithms is considerably increased, especially for the line search. We demonstrate our method for a class of problems from planar elasticity, where the stationary domains are given analytically by Banichuk and Karihaloo in [N.V. Banichuk and B.L. Karihaloo (1976). Minimum-weight design of multi-purpose cylindrical bars. International Journal of Solids and Structures, 12, 267–273.]. In particular, the boundary integral equation is solved by a wavelet Galerkin scheme which offers a powerful tool. For optimization we apply gradient and Quasi–Newton type methods for the penalty as well as for the augmented Lagrangian functional.

319 三次元異方性熱弾性問題の境界要素法による解析法

The boundary integral representation for thermoelastic problems involves a domain integral term originated from the thermal strain. In this paper, the dual reciprocity method (DRM) is utilized to convert the domain integral into boundary integral terms. In the DRM formulation, instead of using the particular solutions associated with a suitable radial basis function, particular solutions are first assumed and the corresponding basis functions are then derived. The effectiveness of the proposed method is demonstrated through some numerical examples.

On the Dirichlet problem with several volume constraints on the level sets

We consider minimization problems involving the Dirichlet integral under an arbitrary number of volume constraints on the level sets and a generalized boundary condition. More precisely, given a bounded open domain Ω ⊂ Rn with smooth boundary, we study the problem of minimizing ∫Ω |∇u|2 among all those functions u ∈ H1 that simultaneously satisfy n-dimensional measure constraints on the level sets of the kind |{u = li}| = αi, i = 1,…, k, and a generalized boundary condition u ∈ K. Here, K is a closed convex subset of H1 such that ; the invariance of K under provides that the condition u ∈ K actually depends only on the trace of u along ∂Ω.By a penalization approach, we prove the existence of minimizers and their Hölder continuity, generalizing previous results that are not applicable when a boundary condition is prescribed.Finally, in the case of just two volume constraints, we investigate the Γ-convergence of the above (rescaled) functionals when the total measure of the two prescribed level sets tends to saturate the whole domain Ω. It turns out that the resulting Γ-limit functional can be split into two distinct parts: the perimeter of the interface due to the Dirichlet energy that concentrates along the jump, and a boundary integral term due to the constraint u ∈ K. In the particular case where K = H1 (i.e. when no boundary condition is prescribed), the boundary term vanishes and we recover a previous result due to Ambrosio et al.

A fully discrete BEM–FEM method for an exterior elasticity system in the plane

We present a modified version of the usual BEM–FEM coupling for the exterior elasticity problem in the plane (cf. Costabel and Stephan, SIAM J. Numer. Anal. 27 (1990) 1212–1226). This new formulation allows us to take advantage of techniques from Hsiao et al., Computing 25 (1980) 557–566 to compute the boundary integral terms using simple quadrature formulas. We provide error estimates for the Galerkin method and prove that the corresponding fully discrete scheme preserves the optimal rates of convergence.

Buckling analysis of elastic plates by boundary element method

This study developed a more general boundary element formulation, which allowed for wide variety of boundary conditions and arbitrary planar shapes, to the investigation of the onset of instability of elastic plate. The formulation of the problem was strictly in terms of boundary integrals so as to eliminate any discretization of domain integrals. This proposed approach placed no restrictions on the nature of the distribution of the in-plane forces within the plate. In this study, the boundary integral formulation was just in terms of the three displacements of the plate's middle surface. This eliminated the need to introduce a stress function to handle the general distributive and variable nature of the in-plane forces so as to keep the introduction of loading to just in-plane known forces or displacements acting on boundaries of the plate system.

On the extraction technique in boundary integral equations

In this paper we develop and analyze a bootstrapping algorithm for the extraction of potentials and arbitrary derivatives of the Cauchy data of regular three–dimensional second order elliptic boundary value problems in connection with corresponding boundary integral equations. The method rests on the derivatives of the generalized Green’s representation formula, which are expressed in terms of singular boundary integrals as Hadamard’s finite parts. Their regularization, together with asymptotic pseudohomogeneous kernel expansions, yields a constructive method for obtaining generalized jump relations. These expansions are obtained via composition of Taylor expansions of the local surface representation, the density functions, differential operators and the fundamental solution of the original problem, together with the use of local polar coordinates in the parameter domain. For boundary integral equations obtained by the direct method, this method allows the recursive numerical extraction of potentials and their derivatives near and up to the boundary surface.

Generalized boundary integral equation for heat conduction in non-homogeneous media: recent developments on the sifting property

In this paper, we address concerns which were raised with respect to the sifting property of the forcing function D which is crucial in deriving an integral equation for heat conduction in non-homogeneous media. The error in the sifting property (which we neglected in our previous papers) is expanded in a series which leads to evaluation of the error in terms of boundary integrals. This provides a practical estimate of the approximation encountered in the analysis of particular problems, as this may be small in certain cases and significant in others. The correction can be implemented directly or iteratively. In this paper, both methods are used. The iterative approach provides a quantitative measure of the correction and is shown to rapidly converge and improve results, particularly in the case of boundary fluxes. The boundary-only feature of our original boundary integral formulation for heat conduction in non-homogeneous media is thus retained.

Thermoelastic Analysis of the Stress Distribution Near the Edge of the Interface between the Superconductive Thin Film and its Substrate. Application of a Boundary Element Method Using Fundamental Solution of Dissimilar Materials.

Devices of thin film in the high-Tc superconductor are subjected to thermoelastic loads because they are processed in high temperature and operated in cryogenic temperature. Serious problems exist in the reliability of the devices due to thermal stresses. In this study, the stress distribution and singularity near the edge of the interface between a thin film and its substrate are discussed by thermoelastic analysis. A boundary element method using fundamental solution of dissimilar materials is extended to the thermoelastic problem. The stress distribution near the edge of the interface can be calculated with high accuracy, because there is no boundary integral terms at the interface. The singular stress field near the edge of the interface is also obtained.

A Numerical Determination of Transient Antenna Impedance Via Near-Field Integration

In this paper we describe a numerical method for determining the wideband impedance of a transient antenna, based on a method of moments solution of the time-domain electric field integral equation. The impedance is estimated from the antenna's response to a short-pulse transient excitation ; the current is determined directly from the solution of the electric field integral equation and the potential difference between the antenna arms is determined from an integration of the electric near-field. Particular attention is paid to the form of the singular near-field integrals and an alternative representation is given for these in terms of non-singular boundary integrals. The approach described in this paper has several advantages over the previous numerical approach of [1] and is validated against a variety of canonical antennas, including directive and omnidirectional transient radiators. The present numerical method is shown to provide an accurate estimate of the characteristic impedance of such canonical structures (to within 3 % of the known impedance).

A new weight function approach using indirect boundary integral method

A new weight function approach to determine SIFs (stress intensity factors) using the indirect boundary integral method has been presented. The crack opening displacement field was represented by one boundary integral term in the form of a single-layer potential whose kernel was modified from the fundamental solution. The proposed method enables the calculation of SIFs using only one SIF solution, without any modification for the crack geometries symmetric in the two-dimensional plane, e.g. a center crack in a plate with or without an internal hole, double edge cracks, circumferential cracks or radial cracks in a pipe. The application procedure for this variety of crack geometries is very simple and straightforward with only one SIF solution. The necessary information in the analysis is two reference SIFs. The analysis results using several examples verified that the present closed-form solution was in good agreement with those of the literature and applicable to various crack geometries.

Hybrid finite‐element analysis of scattering and radiation by a class of waveguide‐fed structures

AbstractA hybrid finite‐element method is presented for analysis of scattering and radiation of a class of waveguide‐fed structures that are characterized by a waveguide region, an exterior region, and a transition region. The proposed method formulates the exterior field in terms of boundary integrals and the field in the transition region using the finite‐element method. The effect of the waveguide field is incorporated through an exact absorbing boundary condition, which includes all waveguide modes. Numerical results are given to demonstrate the accuracy and capability of the method. © 1994 John Wiley & Sons, Inc.

A boundary integral modification of the Galerkin least squares formulation for the Stokes problem

A new boundary integral term is added to the Galerkin least squares (GLS) formulation. The new formulation compensates for a lack of consistency noted for the traditional GLS method when bilinear interpolation is used on quadrilateral elements. Exact solutions at the nodes are obtained for Poiseuille flow and another test problem, and the pressure singularity for the driven cavity is better captured.