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## Boundary Value Problem (boundary + value_problem)
Kinds of Boundary Value Problem
## Selected Abstracts## Boundary value problem for the N -dimensional time periodic Vlasov,Poisson system MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 15 2006M. BostanAbstract In this work, we study the existence of time periodic weak solution for the N -dimensional Vlasov,Poisson system with boundary conditions. We start by constructing time periodic solutions with compact support in momentum and bounded electric field for a regularized system. Then, the a priori estimates follow by computations involving the conservation laws of mass, momentum and energy. One of the key point is to impose a geometric hypothesis on the domain: we suppose that its boundary is strictly star-shaped with respect to some point of the domain. These results apply for both classical or relativistic case and for systems with several species of particles. Copyright © 2006 John Wiley & Sons, Ltd. [source] ## Boundary value problems for Dirac operators and Maxwell's equations in non-smooth domains MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 16-18 2002Marius MitreaAbstract We study the well-posedness of the half-Dirichlet and Poisson problems for Dirac operators in three-dimensional Lipschitz domains, with a special emphasis on optimal Lebesgue and Sobolev-Besov estimates. As an application, an elliptization procedure for the Maxwell system is devised. Copyright © 2002 John Wiley & Sons, Ltd. [source] ## Boundary value problems with eigenvalue depending boundary conditions MATHEMATISCHE NACHRICHTEN, Issue 5 2009Jussi BehrndtAbstract We investigate some classes of eigenvalue dependent boundary value problems of the form where A , A+ is a symmetric operator or relation in a Krein space K, , is a matrix function and ,0, ,1 are abstract boundary mappings. It is assumed that A admits a self-adjoint extension in K which locally has the same spectral properties as a definitizable relation, and that , is a matrix function which locally can be represented with the resolvent of a self-adjoint definitizable relation. The strict part of , is realized as the Weyl function of a symmetric operator T in a Krein space H, a self-adjoint extension Ã of A × T in K × H with the property that the compressed resolvent PK (Ã , ,),1|Kk yields the unique solution of the boundary value problem is constructed, and the local spectral properties of this so-called linearization Ã are studied. The general results are applied to indefinite Sturm,Liouville operators with eigenvalue dependent boundary conditions (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] ## Dielectric Characteristics for Radio Frequency Waves in a Laboratory Dipole Plasma CONTRIBUTIONS TO PLASMA PHYSICS, Issue 4 2006N. I. GrishanovAbstract Transverse and parallel dielectric permittivity elements have been derived for radio frequency waves in a laboratory dipole magnetic field plasma. Vlasov equation is resolved for both the trapped and untrapped particles as a boundary value problem to define their separate contributions to the dielectric tensor components. To estimate the wave power absorbed in the plasma volume the perturbed electric field and current density components are decomposed in a Fourier series over the poloidal angle. In this case, the dielectric characteristics can be analyzed independently of the solution of the Maxwell's equations. As usual, imaginary part of the parallel permittivity elements is necessary to estimate the electron Landau damping of radio frequency waves, whereas imaginary part of the transverse permittivity elements is important to estimate the wave dissipation by the cyclotron resonances. Computations of the imaginary part of the parallel permittivity elements are carried out in a wide range of the wave frequencies. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] ## Three-dimensional thermoelastic stresses in off-axis oriented single crystals with hexagonal symmetry CRYSTAL RESEARCH AND TECHNOLOGY, Issue 3 2007K. BöttcherAbstract A three-dimensional (3D) thermoelastic stress analysis is carried out on a single crystal with axisymmetric geometry but with a hexagonal crystallographic symmetry. The crystallographic orientation is off-axis with respect to the cylindrical coordinate system. By applying a Fourier series expansion with respect to the rotational angle , of the cylindrical coordinates, the 3D boundary value problem is reduced to a sequence of 2D ones on the meridian plane, which are solved by the finite-element method. In our example, the off-axis orientation is towards a direction of high symmetry, and therefore only four of the six stress tensor components are non-zero. In the end, the stress tensor is projected onto the slip system of the crystal. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] ## Optimal Control of Rigid-Link Manipulators by Indirect Methods GAMM - MITTEILUNGEN, Issue 1 2008Rainer CalliesAbstract The present paper is a survey and research paper on the treatment of optimal control problems of rigid-link manipulators by indirect methods. Maximum Principle based approaches provide an excellent tool to calculate optimal reference trajectories for multi-link manipulators with high accuracy. Their major drawback was the need to explicitly formulate the complicated system of adjoint differential equations and to apply the full apparatus of optimal control theory. This is necessary in order to convert the optimal control problem into a piecewise defined, nonlinear multi-point boundary value problem. An accurate and efficient access to first- and higher-order derivatives is crucial. The approach described in this paper allows it to generate all the derivative information recursively and simultaneously with the recursive formulation of the equations of motion. Nonlinear state and control constraints are treated without any simplifications by transforming them into sequences of systems of linear equations. By these means, the modeling of the complete optimal control problem and the accompanying boundary value problem is automated to a great extent. The fast numerical solution is by the advanced multiple shooting method JANUS. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] ## Implicit integration of a chemo-plastic constitutive model for partially saturated soils INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 14 2008H. W. ZhangAbstract A chemo-plastic constitutive model for partially saturated soils is proposed in this paper based on the existing models developed in Hueckel (Int. J. Numer. Anal. Meth. Geomech. 1997; 21:43,72) and Gallipoli et al. (Geotechnique 2003; 53:123,135). The chemical softening effects due to the increase in contaminant mass concentration are considered based on Hueckel's chemo-plastic model. Gallipoli's model is used to simulate the effects of suction and degree of saturation on mechanical behavior of partially saturated porous materials. In order to implement the proposed model in a finite element code, a fully implicit backward-Euler integration algorithm is put forward. Numerical solutions for the tests at local level and the application of the algorithm to the real boundary value problem demonstrate the accuracy and convergence properties of the proposed integration scheme. Copyright © 2008 John Wiley & Sons, Ltd. [source] ## Implicit integration of a mixed isotropic,kinematic hardening plasticity model for structured clays INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 10 2008Angelo AmorosiAbstract In recent years, a number of constitutive models have been proposed to describe mathematically the mechanical response of natural clays. Some of these models are characterized by complex formulations, often leading to non-trivial problems in their numerical integration in finite elements codes. The paper describes a fully implicit stress-point algorithm for the numerical integration of a single-surface mixed isotropic,kinematic hardening plasticity model for structured clays. The formulation of the model stems from a compromise between its capability of reproducing the larger number of features characterizing the behaviour of structured clays and the possibility of developing a robust integration algorithm for its implementation in a finite elements code. The model is characterized by an ellipsoid-shaped yield function, inside which a stress-dependent reversible stiffness is accounted for by a non-linear hyperelastic formulation. The isotropic part of the hardening law extends the standard Cam-Clay one to include plastic strain-driven softening due to bond degradation, while the kinematic hardening part controls the evolution of the position of the yield surface in the stress space. The proposed algorithm allows the consistent linearization of the constitutive equations guaranteeing the quadratic rate of asymptotic convergence in the global-level Newton,Raphson iterative procedure. The accuracy and the convergence properties of the proposed algorithm are evaluated with reference to the numerical simulations of single element tests and the analysis of a typical geotechnical boundary value problem. Copyright © 2007 John Wiley & Sons, Ltd. [source] ## Creep of saturated materials as a chemically enhanced rate-dependent damage process INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 14 2007Liang Bo HuAbstract Material behaviour that exhibits characteristics of creep induced by a spontaneous mineral dissolution enhanced by material damage is studied. It is believed that the characteristic rates of the chemical processes involved determine the time-rate dependence of the resulting strain. A basic model of a combined chemo-plastic softening and chemically enhanced deviatoric strain hardening for saturated geomaterials is presented. Chemical softening is postulated to occur as a consequence of the net mass removal resulting from dissolution and precipitation of specific minerals occurring at the damage-generated inter-phase interfaces. Closed and open systems are discussed. In the former case, deformation at constant stress results entirely from a local compensation mechanism between the chemical softening and strain hardening. The classical three stages of creep are interpreted in terms of mechanisms of dissolution and precipitation, as well as the variation in the reaction surface areas involved in the mass exchange. In an open system, the above local mechanism is enhanced by the removal of mass via diffusion of species affecting the mass balance. Such a system is addressed via a boundary value problem as shown in an example. Copyright © 2007 John Wiley & Sons, Ltd. [source] ## Modelling strain localization in granular materials using micropolar theory: numerical implementation and verification INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 15 2006Khalid A. AlshibliAbstract Implementation and applications for a constitutive numerical model on F-75 silica sand, course silica sand and two sizes of glass beads compressed under plane strain conditions are presented in this work. The numerical model is used to predict the stress versus axial strain and volumetric strain versus axial strain relationships of those materials; moreover, comparisons between measured and predicted shear band thickness and inclination angles are discussed and the numerical results compare well with the experimental measurements. The numerical model is found to respond to the changes in confining pressure and the initial relative density of a given granular material. The mean particle size is used as an internal length scale. Increasing the confining pressure and the initial density is found to decrease the shear band thickness and increase the inclination angle. The micropolar or Cosserat theory is found to be effective in capturing strain localization in granular materials. The finite element formulations and the solution method for the boundary value problem in the updated Lagrangian frame (UP) are discussed in the companion paper. Copyright © 2006 John Wiley & Sons, Ltd. [source] ## Visualization of material stiffness in geomechanics analysis INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 1 2006Donald C. WotringAbstract This paper presents novel visualization techniques to simplify representation of the fourth-order material stiffness tensor as a set of three-dimensional geometric objects. Stiffness visualization aids in understanding the complex stiffness characteristics of highly non-linear constitutive models including modelled material anisotropy and loading path dependent stiffness variation. Stiffness visualization is relevant for understanding the relationship of material stiffness to global behaviour in the analysis of a boundary value problem. The spherical pulse stiffness visualization method, developed in the acoustics field, is extended to visualize stiffness of geomaterials using three three-dimensional objects. This method is limited to relatively simple constitutive models with symmetric stiffness matrices insensitive to loading magnitude and direction. A strain dependent stiffness visualization method is developed that allows the examination of material stiffness for a range of loading directions and is suitable for highly non-linear and path dependent material models. The proposed stiffness visualization can be represented as 3-D, 2-D and 1-D objects. The visualization technique is used to represent material stiffness and its evolution during simulated soil laboratory tests and deep excavation construction. Copyright © 2005 John Wiley & Sons, Ltd. [source] ## Application of micropolar plasticity to post failure analysis in geomechanics INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 10 2004Majid T. ManzariAbstract A micropolar elastoplastic model for soils is formulated and a series of finite element analyses are employed to demonstrate the use of a micropolar continuum in overcoming the numerical difficulties encountered in application of finite element method in standard Cauchy,Boltzmann continuum. Three examples of failure analysis involving a deep excavation, shallow foundation, and a retaining wall are presented. In all these cases, it is observed that the length scale introduced in the polar continuum regularizes the incremental boundary value problem and allows the numerical simulation to be continued until a clear collapse mechanism is achieved. The issue of grain size effect is also discussed. Copyright © 2004 John Wiley & Sons, Ltd. [source] ## Mohr,Coulomb MiniCLoE model Uniqueness and localization studies, links with normality rule INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 1 2003R. ChambonAbstract This paper is devoted to a parametric study of a plane Mohr,Coulomb CLoE model. As CLoE models are designed with a consistency condition, it is possible to define a normality condition and to study its consequences. The positiveness of the second order work which implies the uniqueness of the solution of a small strain boundary value problem is studied firstly. Then the localization criterion is also studied. It is proved that normality has consequences similar to those for classical elasto plastic models. However if induced anisotropy is introduced in the hypoplastic CLoE model, some conclusions are no longer true. Finally plane strain experimental data are used to identify the parameters of the model. Copyright © 2002 John Wiley & Sons, Ltd. [source] ## Dynamic response of soft poroelastic bed to linear water waves,a boundary layer correction approach INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 7 2001Ping-Cheng HsiehAbstract According to Chen et al. (Journal of Engineering Mechanics, ASCE 1997; 123(10):1041,1049.) a boundary layer exists within the porous bed and near the homogeneous-water/porous-bed interface when oscillatory water waves propagate over a soft poroelastic bed. This boundary layer makes the evaluation of the second kind of longitudinal wave inside the soft poroelastic bed very inaccurate. In this study, the boundary layer correction approach for the poroelastic bed is applied to the boundary value problem of linear oscillatory water waves propagating over a soft poroelastic bed. After the analyses of length scale and order of magnitude of physical variables are done, a perturbation expansion for the boundary layer correction approach based on two small parameters is proposed and solved. The solutions are carried out for the first and third kind of waves throughout the entire domain. The second kind of wave which disappears outside the boundary layer is solved systematically inside the boundary layer. The results are compared with the linear wave solutions of Huang and Song (Journal of Engineering Mechanics, ASCE 1993; 119:1003,1020.) to confirm the validity. Moreover, a simplified boundary layer correction formulation which is expected to be very useful in numerical computation is also proposed. Copyright © 2001 John Wiley & Sons, Ltd. [source] ## On integration of a cyclic soil plasticity model INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 6 2001Majid T. ManzariAbstract Performance of three classes of explicit and implicit time-stepping integrators is assessed for a cyclic plasticity constitutive model for sands. The model is representative of an important class of cyclic plasticity models for soils and includes both isotropic and nonlinear kinematic hardening. The implicit algorithm is based on the closest point projection method and the explicit algorithm follows a cutting-plane integration procedure. A sub-stepping technique was also implemented. The performance of these algorithms is assessed through a series of numerical simulations ranging from simulations of laboratory tests (such as triaxial and bi-axial compression, direct shear, and cyclic triaxial tests) to the analysis of a typical boundary value problem of geotechnical earthquake engineering. These simulations show that the closest point projection algorithm remains stable and accurate for relatively large strain increments and for cases where the mean effective stress in a soil element reaches very small values leading to a liquefaction state. It is also shown that while the cutting plane (CP) and sub-stepping (SS) algorithms provide high efficiency and good accuracy for small to medium size strain increments, their accuracy and efficiency deteriorate faster than the closest point projection method for large strain increments. The CP and SS algorithms also face convergence difficulties in the liquefaction analysis when the soil approaches very small mean effective stresses. Copyright © 2001 John Wiley & Sons, Ltd. [source] ## Theoretical investigation of the cavity expansion problem based on a hypoplasticity model INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 5 2001V. A. OsinovAbstract The problem of the symmetric quasi-static large-strain expansion of a cavity in an infinite granular body is studied. The body is assumed to be dry or fully drained so that the presence of the pore water can be disregarded. Both spherical and cylindrical cavities are considered. Numerical solutions to the boundary value problem are obtained with the use of the hypoplastic constitutive relation calibrated for a series of granular soils. As the radius of the cavity increases, the stresses and the density on the cavity surface asymptotically approach limit values corresponding to a so-called critical state. For a given soil, the limit values depend on the initial stresses and the initial density. A comparison is made between the solutions for different initial states and different soils. Applications to geotechnical problems such as cone penetration test and pressuremeter test are discussed. Copyright © 2001 John Wiley & Sons, Ltd. [source] ## Stress analyses of laminates under cylindrical bending INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 1 2008Tarun KantAbstract A semi-analytical approach for evaluation of stresses and displacements in composite and sandwich laminates under cylindrical bending subjected to transverse load has been developed in this paper. Two dimensional (2D) partial differential equations (PDEs) of such a laminate are obtained by imposing plane-strain conditions of elasticity. The fundamental dependent variables are so selected in this formulation that they satisfy the continuity of displacements and transverse interlaminar stresses at the laminate interface through the thickness. The set of governing PDEs are transformed into a set of coupled first-order ordinary differential equations (ODEs) in thickness direction by assuming suitable global orthogonal trigonometric functions for the fundamental variables satisfying the boundary conditions. These ODEs are numerically integrated by a specially formulated ODE integrator algorithm involving transformation of a two-point boundary value problem (BVP) into a set of initial value problems (IVPs). Numerical studies on both composite and sandwich laminates for various aspect ratios are performed and presented. Accuracy of the present approach is demonstrated by comparing the results with the available elasticity solution. It is seen that the present results are in excellent agreement with the elasticity solutions. Some new results for sandwich laminates and for uniform loading condition are presented for future reference. Copyright © 2006 John Wiley & Sons, Ltd. [source] ## An adaptive multigrid iterative approach for frictional contact problems INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 7 2006S. A. MohamedAbstract The objective of this paper is the construction of a robust strategy towards adaptively solving Signorini's frictional contact problems. The frictional contact problem between a linearly elastic body and rigid foundation is formulated as a classical boundary value problem of the elastic body but associated with special inequality conditions on the contact surface. A new iterative approach is presented to solve the problem on a given mesh. In the first iteration the candidate nodes are assumed to be in micro-slip contact and then proceeding to update the contact status according to the actual displacements and stresses obtained at the end of each increment. An efficient multigrid method is developed to solve the discrete problems of different iterations. The proposed iterative procedure is integrated with an error indicator and automatic grid generator to construct an adaptive multigrid method. Numerical results of the convergence rates, automatically generated grid sequence, contact stresses and strains as well as two parametric studies are presented to prove the efficiency of the proposal. Copyright © 2005 John Wiley & Sons, Ltd. [source] ## Vector Hankel transform analysis of a tunable circular microstrip patch INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 5 2005T. FortakiAbstract In this paper, a rigorous analysis of the tunable circular microstrip patch is performed using a dyadic Green's function formulation. To make the theoretical formulation more general and hence valid for various antennas structures (not only limited to tunable microstrip patch); the dyadic Green's function is derived when the patch is assumed to be embedded in a multilayered dielectric substrate. A very efficient technique to derive the dyadic Green's function in the vector Hankel transform domain is proposed. Using the vector Hankel transform, the mixed boundary value problem is reduced to a set of vector dual integral equations. Galerkin's method is then applied to solve the integral equation where two sets of disk current expansions are used. One set is based on the complete set of orthogonal modes of the magnetic cavity, and the other consists of combinations of Chebyshev polynomials with weighting factors to incorporate the edge condition. Convergent results for these two sets of disk current expansions are obtained with a small number of basis functions. The calculated resonant frequencies and quality factors are compared with experimental data and shown to be in good agreement. Finally, numerical results for the air gap tuning effect on the resonant frequency and half-power bandwidth are also presented. Copyright © 2005 John Wiley & Sons, Ltd. [source] ## Numerical simulation of the forest impact on aquifers INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 8 2004A. LeontievAbstract Here we propose a numerical method for the computer simulation of forest impact on aquifers. With this phenomenon we understand changes in the level of groundwater table beneath the areas recovered by trees. The mathematical model of the forest impact includes a boundary value problem with free and contact boundary conditions. Considering this free-contact boundary problem as a shape optimization problem we perform boundary elements discretization. Assuming the state and free boundary variables as independents, we treat the discretized problem as a non-linear mathematical program and apply interior point algorithm to solve it. Numerical results for an illustrative 2D test problem are discussed. Copyright © 2004 John Wiley & Sons, Ltd. [source] ## Transient scattering of SH waves from an inclusion with a unilateral frictional interface,a 2D time domain boundary element analysis INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 1 2003Yang-De FengAbstract This paper develops a 2D time domain boundary element method (BEM) to solve the transient SH-wave scattering from an inclusion with a unilateral frictional interface. The incident SH-wave is assumed strong enough to break friction so that localized slip takes place along the interface. The present problem is indeed a non-linear boundary value problem since the mixed boundary conditions involve unknown intervals (the slip and stick zones). In order to determine the intervals, an iterative technique is developed. As an example, we consider the scattering of a circular cylinder embedded in an infinite solid. The numerical results of the interface traction and relative slip velocity are presented. Copyright © 2003 John Wiley & Sons, Ltd. [source] ## Torsion of orthotropic bars with L -shaped or cruciform cross-section INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 3 2001Y. Z. ChenAbstract For an orthotropic torsion bar with L -shaped or cruciform cross-section, the studied torsion problem can be reduced to a boundary value problem of elliptic partial differential equation. The studied region is separated into several rectangular sub-regions, and the series solution is suggested to solve the problem for the individual sub-region. By using the continuation condition for the functions on the neighbouring sub-regions, the investigated solution is obtainable. Finally, numerical results for the torsion rigidities of bars are given to demonstrate the influence of the degree of orthotropy. Copyright © 2001 John Wiley & Sons, Ltd. [source] ## Least-square-based radial basis collocation method for solving inverse problems of Laplace equation from noisy data INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2010Xian-Zhong MaoAbstract The inverse problem of 2D Laplace equation involves an estimation of unknown boundary values or the locations of boundary shape from noisy observations on over-specified boundary or internal data points. The application of radial basis collocation method (RBCM), one of meshless and non-iterative numerical schemes, directly induces this inverse boundary value problem (IBVP) to a single-step solution of a system of linear algebraic equations in which the coefficients matrix is inherently ill-conditioned. In order to solve the unstable problem observed in the conventional RBCM, an effective procedure that builds an over-determined linear system and combines with least-square technique is proposed to restore the stability of the solution in this paper. The present work investigates three examples of IBVPs using over-specified boundary conditions or internal data with simulated noise and obtains stable and accurate results. It underlies that least-square-based radial basis collocation method (LS-RBCM) poses a significant advantage of good stability against large noise levels compared with the conventional RBCM. Copyright © 2010 John Wiley & Sons, Ltd. [source] ## On the stability and convergence of a Galerkin reduced order model (ROM) of compressible flow with solid wall and far-field boundary treatment, INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 10 2010I. KalashnikovaAbstract A reduced order model (ROM) based on the proper orthogonal decomposition (POD)/Galerkin projection method is proposed as an alternative discretization of the linearized compressible Euler equations. It is shown that the numerical stability of the ROM is intimately tied to the choice of inner product used to define the Galerkin projection. For the linearized compressible Euler equations, a symmetry transformation motivates the construction of a weighted L2 inner product that guarantees certain stability bounds satisfied by the ROM. Sufficient conditions for well-posedness and stability of the present Galerkin projection method applied to a general linear hyperbolic initial boundary value problem (IBVP) are stated and proven. Well-posed and stable far-field and solid wall boundary conditions are formulated for the linearized compressible Euler ROM using these more general results. A convergence analysis employing a stable penalty-like formulation of the boundary conditions reveals that the ROM solution converges to the exact solution with refinement of both the numerical solution used to generate the ROM and of the POD basis. An a priori error estimate for the computed ROM solution is derived, and examined using a numerical test case. Published in 2010 by John Wiley & Sons, Ltd. [source] ## Design of an FIR filter for the displacement reconstruction using measured acceleration in low-frequency dominant structures INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2010Hae Sung LeeAbstract This paper presents a new class of displacement reconstruction scheme using only acceleration measured from a structure. For a given set of acceleration data, the reconstruction problem is formulated as a boundary value problem in which the acceleration is approximated by the second-order central finite difference of displacement. The displacement is reconstructed by minimizing the least-squared errors between measured and approximated acceleration within a finite time interval. An overlapping time window is introduced to improve the accuracy of the reconstructed displacement. The displacement reconstruction problem becomes ill-posed because the boundary conditions at both ends of each time window are not known a priori. Furthermore, random noise in measured acceleration causes physically inadmissible errors in the reconstructed displacement. A Tikhonov regularization scheme is adopted to alleviate the ill-posedness. It is shown that the proposed method is equivalent to an FIR filter designed in the time domain. The fundamental characteristics of the proposed method are presented in the frequency domain using the transfer function and the accuracy function. The validity of the proposed method is demonstrated by a numerical example, a laboratory experiment and a field test. Copyright © 2009 John Wiley & Sons, Ltd. [source] ## Nonparametric probabilistic approach of uncertainties for elliptic boundary value problem INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 6-7 2009Christian SoizeArticle first published online: 2 FEB 200Abstract The paper is devoted to elliptic boundary value problems with uncertainties. Such a problem has already been analyzed in the context of the parametric probabilistic approach of system parameters uncertainties or for random media. Model uncertainties are induced by the mathematical,physical process, which allows the boundary value problem to be constructed from the design system. If experiments are not available, the Bayesian approach cannot be used to take into account model uncertainties. Recently, a nonparametric probabilistic approach of both the model uncertainties and system parameters uncertainties has been proposed by the author to analyze uncertain linear and non-linear dynamical systems. Nevertheless, the use of this concept that has to be developed for dynamical systems cannot directly be applied for elliptic boundary value problem, for instance, for a linear elastostatic problem relative to an elastic bounded domain. We then propose an extension of the nonparametric probabilistic approach in order to take into account model uncertainties for strictly elliptic boundary value problems. The theory and its validation are presented. Copyright © 2009 John Wiley & Sons, Ltd. [source] ## A finite element formulation for thermoelastic damping analysis INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 6 2009Enrico SerraAbstract We present a finite element formulation based on a weak form of the boundary value problem for fully coupled thermoelasticity. The thermoelastic damping is calculated from the irreversible flow of entropy due to the thermal fluxes that have originated from the volumetric strain variations. Within our weak formulation we define a dissipation function that can be integrated over an oscillation period to evaluate the thermoelastic damping. We show the physical meaning of this dissipation function in the framework of the well-known Biot's variational principle of thermoelasticity. The coupled finite element equations are derived by considering harmonic small variations of displacement and temperature with respect to the thermodynamic equilibrium state. In the finite element formulation two elements are considered: the first is a new 8-node thermoelastic element based on the Reissner,Mindlin plate theory, which can be used for modeling thin or moderately thick structures, while the second is a standard three-dimensional 20-node iso-parametric thermoelastic element, which is suitable to model massive structures. For the 8-node element the dissipation along the plate thickness has been taken into account by introducing a through-the-thickness dependence of the temperature shape function. With this assumption the unknowns and the computational effort are minimized. Comparisons with analytical results for thin beams are shown to illustrate the performances of those coupled-field elements. Copyright © 2008 John Wiley & Sons, Ltd. [source] ## Fatigue life prediction using 2-scale temporal asymptotic homogenization INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2004Caglar OskayAbstract In this manuscript, fatigue of structures is modelled as a multiscale phenomenon in time domain. Multiple temporal scales are introduced due to the fact that the load period is orders of magnitude smaller than the useful life span of a structural component. The problem of fatigue life prediction is studied within the framework of mathematical homogenization with two temporal co-ordinates. By this approach the original initial boundary value problem is decomposed into coupled micro-chronological (fast time-scale) and macro-chronological (slow time-scale) problems. The life prediction methodology has been implemented in ABAQUS and validated against direct cycle-by-cycle simulations. Copyright © 2004 John Wiley & Sons, Ltd. [source] ## Cohesive-zone models, higher-order continuum theories and reliability methods for computational failure analysis, INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2004René de BorstAbstract A concise overview is given of various numerical methods that can be used to analyse localization and failure in engineering materials. The importance of the cohesive-zone approach is emphasized and various ways to incorporate the cohesive-zone methodology in discretization methods are discussed. Numerical representations of cohesive-zone models suffer from a certain mesh bias. For discrete representations this is caused by the initial mesh design, while for smeared representations it is rooted in the ill-posedness of the rate boundary value problem that arises upon the introduction of decohesion. A proper representation of the discrete character of cohesive-zone formulations which avoids any mesh bias can be obtained elegantly when exploiting the partition-of-unity property of finite element shape functions. The effectiveness of the approach is demonstrated for some examples at different scales. Moreover, examples are shown how this concept can be used to obtain a proper transition from a plastifying or damaging continuum to a shear band with gross sliding or to a fully open crack (true discontinuum). When adhering to a continuum description of failure, higher-order continuum models must be used. Meshless methods are ideally suited to assess the importance of the higher-order gradient terms, as will be shown. Finally, regularized strain-softening models are used in finite element reliability analyses to quantify the probability of the emergence of various possible failure modes. Copyright © 2004 John Wiley & Sons, Ltd. [source] ## The maximum principle violations of the mixed-hybrid finite-element method applied to diffusion equations INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 12 2002H. HoteitAbstract The abundant literature of finite-element methods applied to linear parabolic problems, generally, produces numerical procedures with satisfactory properties. However, some initial,boundary value problems may cause large gradients at some points and consequently jumps in the solution that usually needs a certain period of time to become more and more smooth. This intuitive fact of the diffusion process necessitates, when applying numerical methods, varying the mesh size (in time and space) according to the smoothness of the solution. In this work, the numerical behaviour of the time-dependent solutions for such problems during small time duration obtained by using a non-conforming mixed-hybrid finite-element method (MHFEM) is investigated. Numerical comparisons with the standard Galerkin finite element (FE) as well as the finite-difference (FD) methods are checked. Owing to the fact that the mixed methods violate the discrete maximum principle, some numerical experiments showed that the MHFEM leads sometimes to non-physical peaks in the solution. A diffusivity criterion relating the mesh steps for an artificial initial,boundary value problem will be presented. One of the propositions given to avoid any non-physical oscillations is to use the mass-lumping techniques. Copyright © 2002 John Wiley & Sons, Ltd. [source] |