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Numerical Examples (numerical + example)
Kinds of Numerical Examples Selected AbstractsAn efficient state-space ADI-PML algorithm for truncating DNG metamaterial FDTD domainsMICROWAVE AND OPTICAL TECHNOLOGY LETTERS, Issue 2 2007Omar Ramadan Abstract Efficient and unconditionally stable formulations of the anisotropic perfectly matched layer are presented for truncating double negative (DNG) metamaterial finite difference time domain (FDTD) grids. In the proposed formulations, the state-space equations are employed in the alternating direction implicit FDTD algorithm to obtain update equations for the field equations in the DNG metamaterial domains. Numerical example carried out in one-dimensional Lorentzian type DNG metamaterial domain is included to show the validity of the proposed formulations. © 2006 Wiley Periodicals, Inc. Microwave Opt Technol Lett 49: 494,498, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.22162 [source] Optimal corrective maintenance contract planning for aging multi-state systemAPPLIED STOCHASTIC MODELS IN BUSINESS AND INDUSTRY, Issue 5 2009Yi Ding Abstract This paper considers an aging multi-state system, where the system failure rate varies with time. After any failure, maintenance is performed by an external repair team. Repair rate and cost of each repair are determined by a corresponding corrective maintenance contract with a repair team. The service market can provide different kinds of maintenance contracts to the system owner, which also can be changed after each specified time period. The owner of the system would like to determine a series of repair contracts during the system life cycle in order to minimize the total expected cost while satisfying the system availability. Operating cost, repair cost and penalty cost for system failures should be taken into account. The paper proposes a method for determining such optimal series of maintenance contracts. The method is based on the piecewise constant approximation for an increasing failure rate function in order to assess lower and upper bounds of the total expected cost and system availability by using Markov models. The genetic algorithm is used as the optimization technique. Numerical example is presented to illustrate the approach. Copyright © 2009 John Wiley & Sons, Ltd. [source] Genetic Effects of Multiple Generations of Supportive BreedingCONSERVATION BIOLOGY, Issue 6 2001Jinliang Wang This procedure is intended to increase population size without introducing exogenous genes into the managed population. Previous work examining the genetic effects of a single generation of supportive breeding has shown that although a successful program increases the census population size, it may reduce the genetically effective population size and thereby induce excessive inbreeding and loss of genetic variation. We expand and generalize previous analyses of supportive breeding and consider the effects of multiple generations of supportive breeding on rates of inbreeding and genetic drift. We derived recurrence equations for the inbreeding coefficient and coancestry, and thereby equations for inbreeding and variance effective sizes, under three models for selecting captive breeders: at random, preferentially among those born in captivity, and preferentially among those born in the wild. Numerical examples indicate that supportive breeding, when carried out successfully over multiple generations, may increase not only the census but also the effective size of the supported population as a whole. If supportive breeding does not result in a substantial and continuous increase of the census size of the breeding population, however, it might be genetically harmful because of elevated rates of inbreeding and genetic drift. Resumen: La práctica de apoyar poblaciones silvestres débiles mediante la captura de una fracción de los individuos silvestres, su cautiverio para la reproducción y la liberación a su descendencia en habitas naturales para que convivan con organismos silvestres se conoce como reproducción de apoyo y se ha empleado ampliamente en la biología de la conservación y en el manejo de pesca y vida silvestre. Este procedimiento tiene la intención de incrementar el tamaño de la población sin introducir genes exógenos en la población bajo manejo. Trabajos previos sobre los efectos genéticos de una sola generación de reproducción de apoyo muestran que, aunque un programa exitoso incrementa el tamaño poblacional, puede reducir la población genéticamente efectivae inducir así un exceso de consanguinidad y pérdida de variación genética. Expandimos y generalizamos análisis previos de la reproducción de apoyo y consideramos los efectos de múltiples generaciones de reproducción de soporte en las tasas de consanguinidad y de deriva génica. Derivamos ecuaciones de recurrencia para el coeficiente de consanguinidad y de coancestría, y por tanto ecuaciones de tamaños efectivos de consanguinidad y de varianza, para tres modelos de selección de reproductores en cautiverio : aleatoria, preferentemente entre los nacidos en cautiverio y preferentemente entre los nacidos en libertad. Los ejemplos numéricos indican que la reproducción de apoyo, cuando es exitosa en múltiples generaciones, puede ser favorable para el incremento no solo del tamaño, sino del tamaño efectivo de la población soportada en su conjunto. Sin embargo, si la reproducción de soporte no resulta en un incremento sustancial y continuo del tamaño de la población, puede ser genéticamente dañina debido a las altas tasas de consanguinidad y de deriva genética. [source] Design of multiple tuned mass dampers by using a numerical optimizerEARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 2 2005Nam Hoang Abstract A new method to design multiple tuned mass dampers (multiple TMDs) for minimizing excessive vibration of structures has been developed using a numerical optimizer. It is a very powerful method by which a large number of design variables can be effectively handled without imposing any restriction before the analysis. Its framework is highly flexible and can be easily extended to general structures with different combinations of loading conditions and target controlled quantities. The method has been used to design multiple TMDs for SDOF structures subjected to wide-band excitation. Some novel results have been obtained. To reduce displacement response of the structure, the optimally designed multiple TMDs have distributed natural frequencies and distinct damping ratios at low damping level. The obtained optimal configuration of TMDs was different from the earlier analytical solutions and was proved to be the most effective. A robustness design of multiple TMDs has also been presented. Robustness is defined as the ability of TMDs to function properly despite the presence of uncertainties in the parameters of the system. Numerical examples of minimizing acceleration structural response have been given where the system parameters are uncertain and are modeled as independent normal variates. It was found that, in case of uncertainties in the structural properties, increasing the TMD damping ratios along with expanding the TMD frequency range make the system more robust. Meanwhile, if TMD parameters themselves are uncertain, it is necessary to design TMDs for higher damping ratios and a narrower frequency range. Copyright © 2004 John Wiley & Sons, Ltd. [source] Predictive instantaneous optimal control of elastic structures during earthquakesEARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 14 2003Kevin K. F. Wong Abstract A predictive instantaneous optimal control (PIOC) algorithm is proposed for controlling the seismic responses of elastic structures. This algorithm compensates for the time delay that happens in practical control applications by predicting the structural response over a period that equals the time delay, and by substituting the predicted response in the instantaneous optimal control (IOC) algorithm. The unique feature of this proposed PIOC algorithm is that it is simple and at the same time compensates for the time delay very effectively. Numerical examples of single degree of freedom structures are presented to compare the performance of PIOC and IOC systems for various time delay magnitudes. Results show that a time delay always causes degradation of control efficiency, but PIOC can greatly reduce this degradation compared to IOC. The effects of the structure's natural periods and the choice of control gains on the degradation induced by the time delay are also analyzed. Results show that shorter natural periods and larger control gains are both more sensitive and more serious to the degradation of control efficiency. Finally, a practical application of PIOC is performed on a six-story moment-resisting steel frame. It is demonstrated that PIOC contributes significantly to maintain stability in multiple degree of freedom structures, and at the same time PIOC has a satisfactory control performance. Copyright © 2003 John Wiley & Sons, Ltd. [source] Optimization of Monte Carlo Procedures for Value at Risk EstimatesECONOMIC NOTES, Issue 1 2002Sabrina Antonelli This paper proposes a methodology which improves the computational efficiency of the Monte Carlo simulation approach of value at risk (VaR) estimates. Principal components analysis is used to reduce the number of relevant sources of risk driving the portfolio dynamics. Moreover, large deviations techniques are used to provide an estimate of the minimum number of price scenarios to be simulated to attain a given accuracy. Numerical examples are provided and show the good performance of the methodolgy proposed. (J.E.L.: C15, G1). [source] EPISTASIS AND THE TEMPORAL CHANGE IN THE ADDITIVE VARIANCE-COVARIANCE MATRIX INDUCED BY DRIFTEVOLUTION, Issue 8 2004Carlos López-Fanjul Abstract The effect of population bottlenecks on the components of the genetic covariance generated by two neutral independent epistatic loci has been studied theoretically (additive, covA; dominance, covD; additive-by-additive, covAA; additive-by-dominance, covAD; and dominance-by-dominance, covDD). The additive-by-additive model and a more general model covering all possible types of marginal gene action at the single-locus level (additive/dominance epistatic model) were considered. The covariance components in an infinitely large panmictic population (ancestral components) were compared with their expected values at equilibrium over replicates randomly derived from the base population, after t consecutive bottlenecks of equal size N (derived components). Formulae were obtained in terms of the allele frequencies and effects at each locus, the corresponding epistatic effects and the inbreeding coefficient Ft. These expressions show that the contribution of nonadditive loci to the derived additive covariance (covAt) does not linearly decrease with inbreeding, as in the pure additive case, and may initially increase or even change sign in specific situations. Numerical examples were also analyzed, restricted for simplicity to the case of all covariance components being positive. For additive-by-additive epistasis, the condition covAt > covA only holds for high frequencies of the allele decreasing the metric traits at each locus (negative allele) if epistasis is weak, or for intermediate allele frequencies if it is strong. For the additive/dominance epistatic model, however, covAt > covA applies for low frequencies of the negative alleles at one or both loci and mild epistasis, but this result can be progressively extended to intermediate frequencies as epistasis becomes stronger. Without epistasis the same qualitative results were found, indicating that marginal dominance induced by epistasis can be considered as the primary cause of an increase of the additive covariance after bottlenecks. For all models, the magnitude of the ratio covAt/covA was inversely related to N and t. [source] THE EFFECT OF EPISTASIS ON THE EXCESS OF THE ADDITIVE AND NONADDITIVE VARIANCES AFTER POPULATION BOTTLENECKSEVOLUTION, Issue 5 2002Carlos López-Fanjul Abstract The effect of population bottlenecks on the components of the genetic variance generated by two neutral independent epistatic loci has been studied theoretically (VA, additive; VD, dominant; VAA, additive × additive; VAD, additive × dominant; VDD; dominant × dominant components of variance). Nonoverdominance and overdominance models were considered, covering all possible types of marginal gene action at the single locus level. The variance components in an infinitely large panmictic population (ancestral components) were compared with their expected values at equilibrium, after t consecutive bottlenecks of equal size N (derived components). Formulae were obtained in terms of allele frequencies and effects at each locus and the corresponding epistatic value. An excess of VA after bottlenecks can be assigned to two sources: (1) the spatiotemporal changes in the marginal average effects of gene substitution ai, which are equal to zero only for additive gene action within and between loci; and (2) the covariance between a2i and the heterozygosity at the loci involved, which is generated by dominance, with or without epistasis. Numerical examples were analyzed, indicating that an increase in VA after bottlenecks will only occur if its ancestral value is minimal or very small. For the nonoverdominance model with weak reinforcing epistasis, that increase has been detected only for extreme frequencies of the negative allele at one or both loci. With strong epistasis, however, this result can be extended to a broad range of intermediate frequencies. With no epistasis, the same qualitative results were found, indicating that dominance can be considered as the primary cause of an increase in VA following bottlenecks. In parallel, the derived total nonadditive variance exceeded its ancestral value (VNA= VD+ VAA+VAD+ VDD) for a range of combinations of allele frequencies covering those for an excess of VA and for very large frequencies of the negative allele at both loci. For the overdominance model, an increase in VA and VNA was respectively observed for equilibrium (intermediate) frequencies at one or both loci or for extreme frequencies at both loci. For all models, the magnitude of the change of VA and VNA was inversely related to N and t. At low levels of inbreeding, the between-line variance was not affected by the type of gene action. For the models considered, the results indicate that it is unlikely that the rate of evolution may be accelerated after population bottlenecks, in spite of occasional increments of the derived VA over its ancestral value. [source] A predictor,corrector scheme for the optimization of 3D crack front shapesFATIGUE & FRACTURE OF ENGINEERING MATERIALS AND STRUCTURES, Issue 1-2 2005K. KOLK ABSTRACT A predictor,corrector scheme is presented to improve the shape of 3D crack fronts within the 3D simulation of fatigue crack growth. This concept is fully functional for mode-I, and an extension for mixed-mode problems is presented. The whole procedure is embedded in an automatic incremental crack growth algorithm for arbitrary 3D problems with linear elastic material behaviour. The numerical simulation is based on the 3D dual boundary element method (Dual BEM) and on an optimized evaluation of very accurate stress intensity factors (SIFs) and T-stresses. As part of the proposed predictor,corrector scheme, 3D singularities along the crack front especially in the vicinity of the intersection of the crack front and the boundary are considered. The knowledge of these singularities allows the specification of crack front shapes with bounded energy release rate. Numerical examples with complex cross-sections are presented to show the efficiency of the proposed crack growth algorithm. The obtained results are in good agreement with recent experimental results. [source] Mineral precipitation associated with vertical fault zones: the interaction of solute advection, diffusion and chemical kineticsGEOFLUIDS (ELECTRONIC), Issue 1 2007CHONGBIN ZHAO Abstract This article is concerned with chemical reactions that occur between two interacting parallel fluid flows using mixing in vertical faults as an example. Mineral precipitation associated with fluid flow in permeable fault zones results in mineralization and chemical reaction (alteration) patterns, which in turn are strongly dependent on interactions between solute advection (controlled by fluid flow rates), solute diffusion/dispersion and chemical kinetics. These interactions can be understood by simultaneously considering two dimensionless numbers, the Damköhler number and the Z -number. The Damköhler number expresses the interaction between solute advection (flow rate) and chemical kinetics, while the Z -number expresses the interaction between solute diffusion/dispersion and chemical kinetics. Based on the Damköhler and Z -numbers, two chemical equilibrium length-scales are defined, dominated by either solute advection or by solute diffusion/dispersion. For a permeable vertical fault zone and for a given solute diffusion/dispersion coefficient, there exist three possible types of chemical reaction patterns, depending on both the flow rate and the chemical reaction rate. These three types are: (i) those dominated by solute diffusion and dispersion resulting in precipitation at the lower tip of a vertical fault and as a thin sliver within the fault, (ii) those dominated by solute advection resulting in precipitation at or above the upper tip of the fault, and (iii) those in which advection and diffusion/dispersion play similar roles resulting in wide mineralization within the fault. Theoretical analysis indicates that there exists both an optimal flow rate and an optimal chemical reaction rate, such that chemical equilibrium following focusing and mixing of two fluids may be attained within the fault zone (i.e. type 3). However, for rapid and parallel flows, such as those resulting from a lithostatic pressure gradient, it is difficult for a chemical reaction to reach equilibrium within the fault zone, if the two fluids are not well mixed before entering the fault zone. Numerical examples are given to illustrate the three possible types of chemical reaction patterns. [source] Calculation of the wave propagation angle in complex media: application to turning wave simulationsGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 3 2009Xiaofeng Jia SUMMARY The wave propagation angle is one of the key factors in seismic processing methods. For the dual-domain propagators, it is sometimes necessary to acquire the wave propagation angle in the space-frequency domain instead of the wavenumber domain or the angle domain. We propose a method dealing with this problem, in which the wavefield gradient is used for the calculation of the wave propagation angle. The wavefield gradient can be directly obtained by either the finite difference approximation or the marching expression of the propagator. This method is not applicable in the case of extremely low frequency due to the comparability between the wavelength and the grid interval. Combined with the superwide-angle one-way propagator, this approach is instrumental in simulating the turning wave, which is hard to be handled by the traditional one-way propagator. Numerical examples show the good performance of the superwide-angle one-way propagator with our approach involved. The turning wave is modelled accurately; as a result, a high-quality image of the overhanging salt flank can be obtained. [source] The fundamental solution of poroelastic plate saturated by fluid and its applicationsINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 7 2010P. H. Wen Abstract In this paper, the numerical model of the transverse vibrations of a thin poroelastic plate saturated by a fluid was proposed. Two coupled dynamic equations of equilibrium related to the plate deflection and the equivalent moment were established for an isotropic porous medium with uniform porosity. The fundamental solutions for a porous plate were derived both in the Laplace transform domain and in the time domain. A meshless method was developed and demonstrated in the Laplace transform domain for solving two coupled dynamic equations. Numerical examples demonstrated the accuracy of the method of the fundamental solutions and comparisons were made with analytical solutions. The proposed meshless method was shown to be simple to implement and gave satisfactory results for a poroelastic plate dynamic analysis. Copyright © 2009 John Wiley & Sons, Ltd. [source] Non-local damage modelling of concrete: a procedure for the determination of model parametersINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 7 2007Giang D. Nguyen Abstract This paper presents a procedure for the determination of parameters of non-local damage models. This is to assure a consistent response of a non-local damage model, as choice of the internal length and other parameters of the model are varied. Correlations between the internal length and other parameters governing the local constitutive behaviour of the model are addressed and exploited. Focus is put on the relationship between the internal length of the non-local model and the width of the fracture process zone. Numerical examples are used to demonstrate the rigour of the proposed method. Copyright © 2006 John Wiley & Sons, Ltd. [source] Smeared crack approach: back to the original trackINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 12 2006M. Cervera Abstract This paper briefly reviews the formulations used over the last 40 years for the solution of problems involving tensile cracking, with both the discrete and the smeared crack approaches. The paper focuses on the smeared approach, identifying as its main drawbacks the observed mesh-size and mesh-bias spurious dependence when the method is applied ,straightly'. A simple isotropic local damage constitutive model is considered, and the (exponential) softening modulus is regularized according to the material fracture energy and the element size. The continuum and discrete mechanical problems corresponding to both the weak discontinuity (smeared cracks) and the strong discontinuity (discrete cracks) approaches are analysed and the question of propagation of the strain localization band (crack) is identified as the main difficulty to be overcome in the numerical procedure. A tracking technique is used to ensure stability of the solution, attaining the necessary convergence properties of the corresponding discrete finite element formulation. Numerical examples show that the formulation derived is stable and remarkably robust. As a consequence, the results obtained do not suffer from spurious mesh-size or mesh-bias dependence, comparing very favourably with those obtained with other fracture and continuum mechanics approaches. Copyright © 2006 John Wiley & Sons, Ltd. [source] An internally consistent integration method for critical state models,INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 3 2005Randall J. Hickman Abstract A new procedure to integrate critical state models including Cam,Clay and modified Cam,Clay is proposed here. The proposed procedure makes use of the linearity of the virgin isotropic compression curve and the parallel anisotropic consolidation lines in e,ln p space which are basic features of the formulation of critical state models. Using this algorithm, a unique final stress state may be found as a function of a single unknown for elastoplastic loading. The key equations are given in this article for the Cam,Clay and modified Cam,Clay models. The use of the Newton,Raphson iterative method to minimize residuals and obtain a converged solution is described here. This new algorithm may be applied using the assumptions of linear elasticity or non-linear elasticity within a given loading step. The new algorithm proposed here is internally consistent and has computational advantages over the current numerical integration procedures. Numerical examples are presented to show the performance of the algorithm as compared to other integration algorithms. Published in 2005 by John Wiley & Sons, Ltd. [source] Addressing volumetric locking and instabilities by selective integration in smoothed finite elementsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 1 2009Nguyen-Xuan Hung Abstract This paper promotes the development of a novel family of finite elements with smoothed strains, offering remarkable properties. In the smoothed finite element method (FEM), elements are divided into subcells. The strain at a point is defined as a weighted average of the standard strain field over a representative domain. This yields superconvergent stresses, both in regular and singular settings, as well as increased accuracy, with slightly lower computational cost than the standard FEM. The one-subcell version that does not exhibit volumetric locking yields more accurate stresses but less accurate displacements and is equivalent to a quasi-equilibrium FEM. It is also subject to instabilities. In the limit where the number of subcells goes to infinity, the standard FEM is recovered, which yields more accurate displacements and less accurate stresses. The specific contribution of this paper is to show that expressing the volumetric part of the strain field using a one-subcell formulation is sufficient to get rid of volumetric locking and increase the displacement accuracy compared with the standard FEM when the single subcell version is used to express both the volumetric and deviatoric parts of the strain. Selective integration also alleviates instabilities associated with the single subcell element, which are due to rank deficiency. Numerical examples on various compressible and incompressible linear elastic test cases show that high accuracy is retained compared with the standard FEM without increasing computational cost. Copyright © 2008 John Wiley & Sons, Ltd. [source] Variational approach to the free-discontinuity problem of inverse crack identificationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 12 2008R. TsotsovaArticle first published online: 17 DEC 200 Abstract This work presents a computational strategy for identification of planar defects (cracks) in homogenous isotropic linear elastic solids. The underlying strategy is a regularizing variational approach based on the diffuse interface model proposed by Ambrosio and Tortorelli. With the help of this model, the sharp interface problem of crack identification is split into two coupled elliptic boundary value problems solved using the finite element method. Numerical examples illustrate the application of the proposed approach for effective reconstruction of the position and the shape of a single crack using only the information collected on the surface of the analyzed body. Copyright © 2007 John Wiley & Sons, Ltd. [source] Discrete singular convolution methodology for free vibration and stability analyses of arbitrary straight-sided quadrilateral platesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 11 2008Ömer Civalek Abstract A new discrete singular convolution (DSC) method is developed for vibration, buckling and static analyses of arbitrary straight-sided quadrilateral plates. The straight-sided quadrilateral domain is mapped into a square domain in the computational space using a four-node element. By using the geometric transformation, the governing equations and boundary conditions of the plate are transformed from the physical domain into a square computational domain. Numerical examples illustrating the accuracy and convergence of the DSC method for straight-sided quadrilateral thin plates such as rectangular, skew, trapezoidal and rhombic plates are presented. The results obtained by the DSC method were compared with those obtained by the other numerical and analytical methods. Copyright © 2007 John Wiley & Sons, Ltd. [source] Static reanalysis of structures with added degrees of freedomINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 4 2006Baisheng Wu Abstract This paper deals with static reanalysis of a structure with added degrees of freedom where the nodes of the original structure form a subset of the nodes of the modified structure. A preconditioned conjugate-gradient approach is developed. The preconditioner is constructed, and the implementation of the approach involves only decomposition of the stiffness matrix corresponding to the newly added degrees of freedom. In particular, the approach can adaptively monitor the accuracy of approximate solutions. The approach is applicable to the reanalysis of the structural layout modifications for the case of addition of some nodes, deletion and addition of elements and further changes in the geometry as well as to the local mesh refinements. Numerical examples show that the condition number of the selected preconditioned matrix is largely reduced. Therefore, the fast convergence and accurate results can be achieved by the approach. Copyright © 2005 John Wiley & Sons, Ltd. [source] The control-theory-based artificial boundary conditions for time-dependent wave guide problems in unbounded domainINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 12 2005Tianyun Liu Abstract A method is proposed to obtain the high-performance artificial boundary conditions for solving the time-dependent wave guide problems in an unbounded domain. Using the variable separation method, it is possible to reduce the spatial variables of the wave equation by one. Furthermore, introducing auxiliary functions makes the reduced wave equation a linear first-order ordinary differential system with one control input. Solving the closed-loop control system, a stable and accurate artificial boundary condition is obtained in a rigorous mathematical manner. Numerical examples have demonstrated the effectiveness of the proposed artificial boundary conditions for the time-dependent wave guide problems in unbounded domain. Copyright © 2005 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] Application of radial basis meshless methods to direct and inverse biharmonic boundary value problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 4 2005Jichun Li Abstract In this paper, we develop a non-iterative way to solve biharmonic boundary value problems by using a radial basis meshless method. This is an original application of meshless method to solving inverse problems without any iteration, since traditional numerical methods for inverse boundary value problems mainly are iterative and hence very time-consuming. Numerical examples are presented for inverse biharmonic boundary value problems and corresponding direct problems, since solving direct problems is a preliminary step for inverse problems. All our examples of direct and inverse problems are solved within seconds in CPU time on a standard PC, which makes our proposed technique a great potential candidate for wide-spread applications to other inverse problems. Copyright © 2004 John Wiley & Sons, Ltd. [source] New approaches in application of differential quadrature method to fourth-order differential equationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 2 2005Xinwei Wang Abstract Various methods to apply multiple boundary conditions in the differential quadrature method are summarized and discussed. Two of them are new approaches appearing for the first time. Numerical examples demonstrate the accuracy of the new methods in applying multiple boundary conditions. Copyright © 2004 John Wiley & Sons, Ltd. [source] Hypersingular integral equation method for three-dimensional crack problem in shear modeINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 6 2004Y. Z. ChenArticle first published online: 19 APR 200 Abstract This paper presents the use of the hypersingular integral equation method for solving the flat crack problem in shear mode. In the method, the crack opening displacement (COD) functions are assumed to be polynomials with several undetermined coefficients. The involved hypersingular integral can be reduced into a repeat integral in a particular polar co-ordinate, and further integrated by a known quadrature rule. This technique considerably reduces the effort of derivation and computation to obtain the final solution. The undetermined coefficients in the COD functions are obtained from an algebraic equation. The stress intensity factors (SIF) along the boundary of the flat crack can then be easily calculated. Numerical examples are given to demonstrate the efficiency of the proposed method. Copyright 2004 John Wiley & Sons, Ltd. [source] Conjugate filter approach for shock capturing,INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 2 2003Yun Gu Abstract This paper introduces a new scheme for the numerical computation involving shock waves. The essence of the scheme is to adaptively implement a conjugate low-pass filter to effectively remove the accumulated numerical errors produced by a set of high-pass filters. The advantages of using such an adaptive algorithm are its controllable accuracy, relatively low cost and easy implementation. Numerical examples in one and two space dimensions are presented to illustrate the proposed scheme. Copyright © 2003 John Wiley & Sons, Ltd. [source] A mixed integer programming for robust truss topology optimization with stress constraintsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 13 2010Yoshihiro Kanno Abstract This paper presents a mixed integer programming (MIP) formulation for robust topology optimization of trusses subjected to the stress constraints under the uncertain load. A design-dependent uncertainty model of the external load is proposed for dealing with the variation of truss topology in the course of optimization. For a truss with the discrete member cross-sectional areas, it is shown that the robust topology optimization problem can be reduced to an MIP problem, which is solved globally. Numerical examples illustrate that the robust optimal topology of a truss depends on the magnitude of uncertainty. Copyright © 2010 John Wiley & Sons, Ltd. [source] A dual mortar approach for 3D finite deformation contact with consistent linearizationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 11 2010Alexander Popp Abstract In this paper, an approach for three-dimensional frictionless contact based on a dual mortar formulation and using a primal,dual active set strategy for direct constraint enforcement is presented. We focus on linear shape functions, but briefly address higher order interpolation as well. The study builds on previous work by the authors for two-dimensional problems. First and foremost, the ideas of a consistently linearized dual mortar scheme and of an interpretation of the active set search as a semi-smooth Newton method are extended to the 3D case. This allows for solving all types of nonlinearities (i.e. geometrical, material and contact) within one single Newton scheme. Owing to the dual Lagrange multiplier approach employed, this advantage is not accompanied by an undesirable increase in system size as the Lagrange multipliers can be condensed from the global system of equations. Moreover, it is pointed out that the presented method does not make use of any regularization of contact constraints. Numerical examples illustrate the efficiency of our method and the high quality of results in 3D finite deformation contact analysis. Copyright © 2010 John Wiley & Sons, Ltd. [source] eXtended Stochastic Finite Element Method for the numerical simulation of heterogeneous materials with random material interfacesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 10 2010A. Nouy Abstract An eXtended Stochastic Finite Element Method has been recently proposed for the numerical solution of partial differential equations defined on random domains. This method is based on a marriage between the eXtended Finite Element Method and spectral stochastic methods. In this article, we propose an extension of this method for the numerical simulation of random multi-phased materials. The random geometry of material interfaces is described implicitly by using random level set functions. A fixed deterministic finite element mesh, which is not conforming to the random interfaces, is then introduced in order to approximate the geometry and the solution. Classical spectral stochastic finite element approximation spaces are not able to capture the irregularities of the solution field with respect to spatial and stochastic variables, which leads to a deterioration of the accuracy and convergence properties of the approximate solution. In order to recover optimal convergence properties of the approximation, we propose an extension of the partition of unity method to the spectral stochastic framework. This technique allows the enrichment of approximation spaces with suitable functions based on an a priori knowledge of the irregularities in the solution. Numerical examples illustrate the efficiency of the proposed method and demonstrate the relevance of the enrichment procedure. Copyright © 2010 John Wiley & Sons, Ltd. [source] Guaranteed computable error bounds for conforming and nonconforming finite element analyses in planar elasticityINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 9 2010Mark Ainsworth Abstract We obtain fully computable a posteriori error estimators for the energy norm of the error in second-order conforming and nonconforming finite element approximations in planar elasticity. These estimators are completely free of unknown constants and give a guaranteed numerical upper bound on the norm of the error. The estimators are shown to also provide local lower bounds, up to a constant and higher-order data oscillation terms. Numerical examples are presented illustrating the theory and confirming the effectiveness of the estimator. Copyright © 2009 John Wiley & Sons, Ltd. [source] A finite element-based level set method for structural optimizationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 7 2010Xianghua Xing Abstract A finite element-based level set method is implemented for structural optimization. The streamline diffusion finite element method is used for solving both the level set equation and the reinitialization equation. The lumped scheme is addressed and the accuracy is compared with the conventional finite difference-based level set method. A Dirichlet boundary condition is enforced during the reinitialization to prevent the boundary from drifting. Numerical examples of minimum mean compliance design illustrate the reliability of the proposed optimization method. Copyright © 2009 John Wiley & Sons, Ltd. [source] | |||||||||||||||||||||||||||||||||||||