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Integral Method (integral + method)
Kinds of Integral Method Selected AbstractsT-stress solutions for two-dimensional crack problems in anisotropic elasticity using the boundary element methodFATIGUE & FRACTURE OF ENGINEERING MATERIALS AND STRUCTURES, Issue 5 2006P. D. SHAH ABSTRACT The importance of a two-parameter approach in the fracture mechanics analysis of many cracked components is increasingly being recognized in engineering industry. In addition to the stress intensity factor, the T stress is the second parameter considered in fracture assessments. In this paper, the path-independent mutual M - integral method to evaluate the T stress is extended to treat plane, generally anisotropic cracked bodies. It is implemented into the boundary element method for two-dimensional elasticity. Examples are presented to demonstrate the veracity of the formulations developed and its applicability. The numerical solutions obtained show that material anisotropy can have a significant effect on the T stress for a given cracked geometry. [source] Experimental and computational investigation of three-dimensional mixed-mode fatigueFATIGUE & FRACTURE OF ENGINEERING MATERIALS AND STRUCTURES, Issue 1 2002S. C. Forth Experimental and computational methods were developed to model three-dimensional (3-D) mixed-mode crack growth under fatigue loading with the objective of evaluating proposed 3-D fracture criteria. The experiments utilized 7075-T73 aluminium forgings cut into modified ASTM E740 surface crack specimens with pre-cracks orientated at angles of 30, 45 and 60° in separate tests. The progress of the evolving fatigue crack was monitored in real time using an automated visualization system. In addition, the amplitude of the loading was increased at prescribed intervals to mark the location of the 3-D crack front for post-test inspection. In order to evaluate proposed crack growth equations, computer simulations of the experiments were conducted using a 3-D fracture model based on the surface integral method. An automatic mesher advanced the crack front by adding a ring of elements consistent with local application of fracture criteria governing rate and direction of growth. Comparisons of the computational and experimental results showed that the best correlation was obtained when KII and KIII were incorporated in the growth rate equations. [source] Thermally induced conformational changes in horseradish peroxidaseFEBS JOURNAL, Issue 1 2001David G. Pina Detailed differential scanning calorimetry (DSC), steady-state tryptophan fluorescence and far-UV and visible CD studies, together with enzymatic assays, were carried out to monitor the thermal denaturation of horseradish peroxidase isoenzyme c (HRPc) at pH 3.0. The spectral parameters were complementary to the highly sensitive but integral method of DSC. Thus, changes in far-UV CD corresponded to changes in the overall secondary structure of the enzyme, while that in the Soret region, as well as changes in intrinsic tryptophan fluorescence emission, corresponded to changes in the tertiary structure of the enzyme. The results, supported by data about changes in enzymatic activity with temperature, show that thermally induced transitions for peroxidase are irreversible and strongly dependent upon the scan rate, suggesting that denaturation is under kinetic control. It is shown that the process of HRPc denaturation can be interpreted with sufficient accuracy in terms of the simple kinetic scheme where k is a first-order kinetic constant that changes with temperature, as given by the Arrhenius equation; N is the native state, and D is the denatured state. On the basis of this model, the parameters of the Arrhenius equation were calculated. [source] Effect of double stratification on mixed convection heat and mass transfer from a vertical surface in a fluid-saturated porous mediumHEAT TRANSFER - ASIAN RESEARCH (FORMERLY HEAT TRANSFER-JAPANESE RESEARCH), Issue 6 2010V.J. Bansod Abstract This paper presents the mixed convection heat and mass transfer near a vertical surface in a stratified porous medium using an integral method. The conservation equations that govern the problem are reduced to a system of coupled non-linear ordinary differential equations, which is then reduced into a single algebraic equation using exponential profiles for the temperature and concentration. The results for heat and mass transfer rates in terms of Nusselt and Sherwood number are presented for a wide range of governing parameters like the buoyancy ratio (N), Lewis number (Le), flow driving parameter (Ra/Pe), in addition to both thermal and solutal parameters (S and R). The results indicate that the stratification effects have considerable influence on both the heat and mass transfer rates. © 2010 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com). DOI 10.1002/htj.20300 [source] A novel analytical solution for constant-head test in a patchy aquiferINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 12 2006Shaw-Yang Yang Abstract A mathematical model describing the hydraulic head distribution for a constant-head test performed in a well situated at the centre of a patchy aquifer is presented. The analytical solution for the mathematical model is derived by the Laplace transforms and the Bromwich integral method. The solution for the hydraulic head has been shown to satisfy the governing equations, related boundary conditions, and continuity requirements for the hydraulic head and flow rate at the interface of the patch and outer regions. An efficient numerical approach is proposed to evaluate the solution, which has an integral covering an integration range from zero to infinity and an integrand consisting the product and square of the Bessel functions. This solution can be used to produce the curves of dimensionless hydraulic head against dimensionless time for investigating the effect of the contrast of formation properties on the dimensionless hydraulic head distribution. Define the ratio of outer-region transmissivity to patch-region transmissivity as ,. The dimensionless hydraulic head for ,=0.1 case is about 2.72 times to that for ,=10 case at dimensionless large time (e.g. ,,106) when the dimensionless distance (,) equals 10. The results indicate that the hydraulic head distribution highly depends on the hydraulic properties of two-zone formations. Copyright © 2006 John Wiley & Sons, Ltd. [source] Crack face contact, frictional sliding and mesh design flexibilityINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 5 2005Pei Gu Abstract Physical loading sometimes causes crack face contact and frictional sliding. The relative sliding of the face induces modes II and III types of stress intensities at the crack tip region. This paper discusses domain integral method of calculating the J integral when crack face contact and sliding by friction are considered for general cracked geometries. The scheme of including crack face contact and sliding is implemented in a finite element code. Numerical examples are presented to show the accuracy for J integral value in this case. In addition, we present an approach for mesh design flexibility at the crack tip region to suit complicated engineering geometries. Copyright © 2004 John Wiley & Sons, Ltd. [source] Computational modelling of the surface fatigue crack growth on gear teeth flanksINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 8 2001S. Glode Abstract The paper describes a 2-dimensional computational model for simulation of the surface initiated fatigue crack growth in the contact area of gear teeth flanks that leads to surface pitting. The discretized model of a gear tooth with the assumed initial crack is subjected to normal contact pressure, which takes into account the EHD-lubrication conditions and tangential loading due to friction between gear teeth flanks. The model accounts also for the influence of a fluid driven into the crack by hydraulic mechanism on crack propagation. The J -integral method in the framework of the finite element analysis is used for simulation of the fatigue crack propagation from the initial to the critical crack length, when the surface material layer breaks away and pit appears on the surface. The model is applied to a real pitting problem of a gear and corresponding computational results in terms of pit sizes correlate well to the development of micropits observed in experimental testing. Copyright © 2001 John Wiley & Sons, Ltd. [source] 3-D mixed-mode K -calculations with the interaction integral method and the quarter point element stress methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 5 2001G. Dhondt Abstract The K -distribution along a straight crack in a single edge notch specimen and a slant crack in a three-point bending specimen is determined using the interaction integral method (IINT) and the quarter point element stress method (QPES). The results are discussed and recommendations for the proper use of both methods are given. Copyright © 2001 John Wiley & Sons, Ltd. [source] A Galerkin boundary integral method for multiple circular elastic inclusionsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 10 2001S. G. Mogilevskaya Abstract The problem of an infinite, isotropic elastic plane containing an arbitrary number of circular elastic inclusions is considered. The analysis procedure is based on the use of a complex singular integral equation. The unknown tractions at each circular boundary are approximated by a truncated complex Fourier series. A system of linear algebraic equations is obtained by using the classical Galerkin method and the Gauss,Seidel algorithm is used to solve the system. Several numerical examples are considered to demonstrate the effectiveness of the approach. Copyright © 2001 John Wiley & Sons, Ltd. [source] An explicit formulation for the evolution of nonlinear surface waves interacting with a submerged bodyINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 11 2007Christopher P. Kent Abstract An explicit formulation to study nonlinear waves interacting with a submerged body in an ideal fluid of infinite depth is presented. The formulation allows one to decompose the nonlinear wave,body interaction problem into body and free-surface problems. After the decomposition, the body problem satisfies a modified body boundary condition in an unbounded fluid domain, while the free-surface problem satisfies modified nonlinear free-surface boundary conditions. It is then shown that the nonlinear free-surface problem can be further reduced to a closed system of two nonlinear evolution equations expanded in infinite series for the free-surface elevation and the velocity potential at the free surface. For numerical experiments, the body problem is solved using a distribution of singularities along the body surface and the system of evolution equations, truncated at third order in wave steepness, is then solved using a pseudo-spectral method based on the fast Fourier transform. A circular cylinder translating steadily near the free surface is considered and it is found that our numerical solutions show excellent agreement with the fully nonlinear solution using a boundary integral method. We further validate our solutions for a submerged circular cylinder oscillating vertically or fixed under incoming nonlinear waves with other analytical and numerical results. Copyright © 2007 John Wiley & Sons, Ltd. [source] Adaptive integral method combined with the loose GMRES algorithm for planar structures analysisINTERNATIONAL JOURNAL OF RF AND MICROWAVE COMPUTER-AIDED ENGINEERING, Issue 1 2009W. Zhuang Abstract In this article, the adaptive integral method (AIM) is used to analyze large-scale planar structures. Discretization of the corresponding integral equations by method of moment (MoM) with Rao-Wilton-Glisson (RWG) basis functions can model arbitrarily shaped planar structures, but usually leads to a fully populated matrix. AIM could map these basis functions onto a rectangular grid, where the Toeplitz property of the Green's function would be utilized, which enables the calculation of the matrix-vector multiplication by use of the fast Fourier transform (FFT) technique. It reduces the memory requirement from O(N2) to O(N) and the operation complexity from O(N2) to O(N log N), where N is the number of unknowns. The resultant equations are then solved by the loose generalized minimal residual method (LGMRES) to accelerate iteration, which converges much faster than the conventional conjugate gradient method (CG). Furthermore, several preconditioning techniques are employed to enhance the computational efficiency of the LGMRES. Some typical microstrip circuits and microstrip antenna array are analyzed and numerical results show that the preconditioned LGMRES can converge much faster than conventional LGMRES. © 2008 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2009. [source] New approximate formula for the generalized temperature integralAICHE JOURNAL, Issue 7 2009Haixiang Chen Abstract The generalized temperature integral frequently occurs in nonisothermal kinetic analysis. This article has proposed a new approximate formula for the generalized temperature integral, which is in the following form: For commonly used values of m in kinetic analysis, the deviation of the new approximation from the numerical values of the integral is within 0.4%. More importantly, the new formula represents the exponential approximation, which is not found earlier, and it can result in a new and very accurate integral method in kinetic analysis. © 2009 American Institute of Chemical Engineers AIChE J, 2009 [source] Boundary integral method for Stokes flow past a porous bodyMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 9 2008Mirela Kohr Abstract In this paper we obtain an indirect boundary integral method in order to prove existence and uniqueness of the classical solution to a boundary value problem for the Stokes,Brinkman-coupled system, which describes an unbounded Stokes flow past a porous body in terms of Brinkman's model. Therefore, one assumes that the flow inside the body is governed by the continuity and Brinkman equations. Some asymptotic results in both cases of large and, respectively, of low permeability are also obtained. Copyright © 2007 John Wiley & Sons, Ltd. [source] Electromagnetic scattering by a perfectly conducting obstacle in a homogeneous chiral environment: solvability and low-frequency theoryMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 11 2002C. Athanasiadis Abstract The scattering of plane time-harmonic electromagnetic waves propagating in a homogeneous isotropic chiral environment by a bounded perfectly conducting obstacle is studied. The unique solvability of the arising exterior boundary value problem is established by a boundary integral method. Integral representations of the total exterior field, as well as of the left and right electric far-field patterns are derived. A low-frequency theory for the approximation of the solution to the above problem, and the derivation of the far-field patterns is also presented. Copyright © 2002 John Wiley & Sons, Ltd. [source] Numerical analysis of a non-singular boundary integral method: Part II: The general caseMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 7 2002P. Dreyfuss In order to numerically solve the interior and the exterior Dirichlet problems for the Laplacian operator, we have presented in a previous paper a method which consists in inverting, on a finite element space, a non-singular integral operator for circular domains. This operator was described as a geometrical perturbation of the Steklov operator, and we have precisely defined the relation between the geometrical perturbation and the dimension of the finite element space, in order to obtain a stable and convergent scheme in which there are non-singular integrals. We have also presented another point of view under which the method can be considered as a special quadrature formula method for the standard piecewise linear Galerkin approximation of the weakly singular single-layer potential. In the present paper, we extend the results given in the previous paper to more general cases for which the Laplace problem is set on any ,,, domains. We prove that the properties of stability and convergence remain valid. Copyright © 2002 John Wiley & Sons, Ltd. [source] Gain factor of horn array feed offset parabolic cylindrical reflector antenna for spatial power combiningMICROWAVE AND OPTICAL TECHNOLOGY LETTERS, Issue 8 2010Z. M. Xie Abstract A study on the horn array feeding offset parabolic cylindrical reflector antenna for spatial power combining is presented. The calculations based on the aperture integral method are agreed well with the measurements. The relationship between the gain factor and the dimensions of the antenna is analyzed. The optimal dimensions and orientation of the feeding horn as well as the optimal spread angle of the reflector are given. It is revealed that the gain factor of the antenna with an E_plane array feed is higher than that of the antenna with an H_plane array feed. © 2010 Wiley Periodicals, Inc. Microwave Opt Technol Lett 52: 1742,1747, 2010; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.25348 [source] Numerical solution of thermal convection problems using the multidomain boundary element methodNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 4 2002W. F. Florez Abstract The multidomain dual reciprocity method (MD-DRM) has been effectively applied to the solution of two-dimensional thermal convection problems where the momentum and energy equations govern the motion of a viscous fluid. In the proposed boundary integral method the domain integrals are transformed into equivalent boundary integrals by the dual reciprocity approach applied in a subdomain basis. On each subregion or domain element the integral representation formulas for the velocity and temperature are applied and discretised using linear continuous boundary elements, and the equations from adjacent subregions are matched by additional continuity conditions. Some examples showing the accuracy, the efficiency and flexibility of the proposed method are presented. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 18: 469,489, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/num.10016 [source] Dynamical CPA theory of magnetism , harmonic approximationPHYSICA STATUS SOLIDI (B) BASIC SOLID STATE PHYSICS, Issue 2 2003Y. Kakehashi Abstract We have developed the dynamical coherent potential approximation (CPA) to the correlated electron system on the basis of the functional integral method and the harmonic approximation. The theory becomes exact in the high temperature limit, reproduces the results of the second order perturbation theory for small Coulomb interaction, and takes into account the terms to describe the strong correlation limit. The numerical calculations show that the theory describes the Curie,Weiss susceptibility, a large reduction of the Curie temperature due to the dynamical effects, and a many-body satellite peak as well as a band narrowing in the density of states. [source] Numerical simulation of non-viscous liquid pinch off using a coupled level set boundary integral methodPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2007Maria Garzon The pinch off of an inviscid fluid column is described using a potential flow model with capillary forces. The interface velocity is obtained via a Galerkin boundary integral method for the 3D axisymmetric Laplace equation, whereas the interface location and the velocity potential on the free boundary are both approximated using level set techniques on a fixed domain. The algorithm is validated computing the Raleigh-Taylor instability for liquid columns which provides an analytical solution for short times. The simulations show the time evolution of the fluid tube and the algorithm is capable of handling pinch-off and after pinch-off events. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] On closed boundary value problems for equations of mixed elliptic-hyperbolic type,COMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 9 2007Daniela Lupo For partial differential equations of mixed elliptic-hyperbolic type we prove results on existence and existence with uniqueness of weak solutions for closed boundary value problems of Dirichlet and mixed Dirichlet-conormal types. Such problems are of interest for applications to transonic flow and are overdetermined for solutions with classical regularity. The method employed consists in variants of the a , b , c integral method of Friedrichs in Sobolev spaces with suitable weights. Particular attention is paid to the problem of attaining results with a minimum of restrictions on the boundary geometry and the form of the type change function. In addition, interior regularity results are also given in the important special case of the Tricomi equation. © 2006 Wiley Periodicals, Inc. [source] | ||||||||||||||||||||||||||||