Showing papers in "Communications in Numerical Methods in Engineering in 2003"
TL;DR: In this paper, a path-following constraint based on the energy release during failure was developed for finite-element discretization of a solid with a continuum damage model, which is applicable to the simulation of quasi-brittle materials when no previous knowledge is available on the failure behaviour of a body and indirect displacement control methods like CMOD cannot be applied.
Abstract: A path-following constraint is developed which is based on the energy release during failure. This makes it applicable to the simulation of quasi-brittle materials when no previous knowledge is available on the failure behaviour of a body and, consequently, indirect displacement control methods like CMOD cannot be applied. The constraint is derived from the first principle of thermodynamics for a finite-element discretization of a solid with a continuum damage model. The performance of the constraint is demonstrated by means of a bending test on a single-edge-notched beam. Copyright © 2003 John Wiley & Sons, Ltd.
123 citations
TL;DR: In this article, it was shown that the discretization of a gradient-enhanced continuum damage model does not belong to the class of mixed finite element formulations (although the model has the format of a general coupled problem), and that the Babuska-Brezzi condition does not apply to this type of models.
Abstract: Some properties of a gradient-enhanced continuum damage model were discussed by means of a numerical and theoretical study. In particular, it is demonstrated that the discretization of this model does not belong to the class of mixed finite element formulations (although the model has the format of a general coupled problem). Hence, the Babuska–Brezzi condition does not apply to this type of models. Consequently, the use of linear interpolation functions for displacements as well for non-local equivalent strains yields excellent performance in terms of rate of convergence and of convergence of the numerical procedure. Copyright © 2003 John Wiley & Sons, Ltd.
73 citations
TL;DR: In this paper, the authors focus on the case where the extent of the crack approaches the support size of the nodal shape functions, and explain the limitations of the standard approximation for arbitrary discontinuities.
Abstract: For particular discretizations and crack configurations, the enhanced approximations of the eXtended finite-element method (X-FEM) cannot accurately represent the discontinuities in the near-tip displacement fields. In this note, we focus on the particular case where the extent of the crack approaches the support size of the nodal shape functions. Under these circumstances, the asymptotic ‘branch’ functions for each tip may extend beyond the length of the crack, resulting in a non-conforming approximation. We explain the limitations of the standard approximation for arbitrary discontinuities, and propose a set of adjustments to remedy the deficiencies. We also provide numerical results that demonstrate the advantages of the modified approximation. Copyright © 2003 John Wiley & Sons, Ltd.
49 citations
TL;DR: In this paper, it was shown that when the starting point of the branch is near a bifurcation, the radius of convergence of the power series is exactly the distance from the start point to the bifurlocal point.
Abstract: The asymptotic-numerical method (ANM) is a path following technique which is based on high order power series expansions. In this paper, we analyse its behaviour when it is applied to the continuation of a branch with bifurcation points. We show that when the starting point of the continuation is near a bifurcation, the radius of convergence of the power series is exactly the distance from the starting point to the bifurcation. This leads to an accumulation of small steps around the bifurcation point. This phenomenon is related to the presence of inevitable imperfections in the FE models. We also explain that, depending on the maximal tolerated residual error (out-of-balance error), the ANM continuation may continue to follow the fundamental path or it may turn onto the bifurcated path without applying any branch switching technique.
46 citations
TL;DR: In this article, exact analytical solutions of the critical Rayleigh numbers have been obtained for a hydrothermal system consisting of a horizontal porous layer with temperature-dependent viscosity.
Abstract: Exact analytical solutions of the critical Rayleigh numbers have been obtained for a hydrothermal system consisting of a horizontal porous layer with temperature-dependent viscosity. The boundary conditions considered are constant temperature and zero vertical Darcy velocity at both the top and bottom of the layer. Not only can the derived analytical solutions be readily used to examine the effect of the temperature-dependent viscosity on the temperature-gradient driven convective flow, but also they can be used to validate the numerical methods such as the finite-element method and finite-difference method for dealing with the same kind of problem. The related analytical and numerical results demonstrated that the temperature-dependent viscosity destabilizes the temperature-gradient driven convective flow and therefore, may affect the ore body formation and mineralization in the upper crust of the Earth. Copyright (C) 2003 John Wiley Sons, Ltd.
43 citations
TL;DR: In this paper, corrected smooth particle hydrodynamics (CSPH) is used to simulate fluid flow in the high pressure die casting cavity, and the fundamental governing equations are derived based on a variational formulation.
Abstract: Mould filling simulation in high pressure die casting has been an attractive area of research for many years. Several numerical methodologies have been attempted in the past to study the flow behaviour of the molten metal into the die cavities. However, many of these methods require a stationary mesh or grid which limits their ability in simulating highly dynamic and transient flows encountered in high pressure die casting processes. In recent years, the advent of meshfree methods have expanded the capabilities of numerical techniques. Hence, these methods have emerged as an attractive alternative for modelling mould filling simulation in pressure die casting processes. In the present work, a Lagrangian particle method called corrected smooth particle hydrodynamics (CSPH) is used to simulate fluid flow in the high pressure die casting cavity. This paper mainly focuses on deriving the fundamental governing equations based on a variational formulation and presents a number of mould filling examples to demonstrate the capabilities of the CSPH numerical model.
43 citations
TL;DR: In this paper, an efficient numerical method is developed for the numerical solution of non-linear wave equations typified by the regularized long wave equation (RLW) and its generalization (GRLW).
Abstract: An efficient numerical method is developed for the numerical solution of non-linear wave equations typified by the regularized long wave equation (RLW) and its generalization (GRLW). The method developed uses a pseudo-spectral (Fourier transform) treatment of the space dependence together with a linearized implicit scheme in time. An important advantage to be gained from the use of this method, is the ability to vary the mesh length, thereby reducing the computational time. Using a linearized stability analysis, it is shown that the proposed method is unconditionally stable. The method is second order in time and all-order in space. The method presented here is for the RLW equation and its generalized form, but it can be implemented to a broad class of non-linear long wave equations, with obvious changes in the various formulae. Test problems, including the simulation of a single soliton and interaction of solitary waves, are used to validate the method, which is found to be accurate and efficient. The three invariants of the motion are evaluated to determine the conservation properties of the algorithm.
42 citations
TL;DR: In this article, the authors used both the static and kinematic approaches and an interior point optimizer code to give new precise bounds for the height limit of a Tresca or von Mises vertical slope of height h subjected to the action of gravity.
Abstract: The well-known problem of the height limit of a Tresca or von Mises vertical slope of height h, subjected to the action of gravity stems naturally from Limit Analysis theory under the plane strain condition. Although the exact solution to this problem remains unknown, this paper aims to give new precise bounds using both the static and kinematic approaches and an Interior Point optimizer code. The constituent material is a homogeneous isotropic soil of weight per unit volume γ. It obeys the Tresca or von Mises criterion characterized by C cohesion. We show that the loading parameter to be optimized, γh/C, is found to be between 3.767 and 3.782, and finally, using a recent result of Lyamin and Sloan (Int. J. Numer. Meth. Engng. 2002; 55: 573), between 3.772 and 3.782. The proposed methods, combined with an Interior Point optimization code, prove that linearizing the problem remains efficient, and both rigorous and global: this point is the main objective of the present paper. Copyright © 2003 John Wiley & Sons, Ltd.
42 citations
TL;DR: In this article, a three-dimensional finite element model for the solution of Helmholtz problems is presented, which is based on the Melenk and Babuska technique which uses a plane wave basis in combination with conventional polynomial shape functions.
Abstract: A three-dimensional finite-element model for the solution of Helmholtz problems is presented. The element is based on the Melenk and Babuska technique which uses a plane wave basis in combination with conventional polynomial shape functions. This element offers the possibility to compute many wavelengths per nodal spacing. It is constructed by multiplying the shape functions by plane waves propagating in different directions in space. A standard Galerkin-Bubnov weighting is used. The problem of a plane wave scattered by a sphere is presented and the numerical results are compared to the analytical results obtained from the closed-form series solution. This paper represents the first application of this approach to three dimensions.
41 citations
TL;DR: In this paper, an efficient and robust method of solving Laplace inverse ransform is proposed based on the wavelet theory, where the inverse function is expressed as a wavelet expansion with rapid convergence.
Abstract: An efficient and robust method of solving Laplace inverse ransform is proposed based on the wavelet theory. The inverse function is expressed as a wavelet expansion with rapid convergence. Several examples are provided to demonstrate the methodology. As an example of application, the proposed inversion method is applied to the dynamic analysis of a single-degree-of-freedom spring–mass–damper system whose damping is described by a stress–strain relation containing fractional derivatives. The results are compared with previous studies. Copyright © 2003 John Wiley Sons, Ltd
39 citations
TL;DR: In this article, a new inflatable beam finite element is proposed to predict the behavior of inflatable structures made of beam elements at high pressure, where the stiffness matrix takes into account the inflation pressure.
Abstract: Inflatable structures made of modern textile materials with important mechanical characteristics can be inflated at high pressure (up to several hundreds kPa). For such values of the pressure they have a strong mechanical strength. The aim of the paper is to construct a new inflatable beam finite element able to predict the behaviour of inflatable structures made of beam elements. Experiments and analytical studies on inflatable fabric beams at high pressure have shown that their compliance is the sum of the beam compliance and of the yarn compliance. This new finite element is therefore obtained by the equilibrium finite element method and is modified into a displacement finite element. The stiffness matrix takes into account the inflation pressure. Comparisons between experimental and numerical results are shown and prove the accuracy of this new finite element for solving problems of inflatable beams at high pressure.
TL;DR: In this paper, the method developed for eigensolution for matrices of special structures in Kaveh and Sayarinejad (Commun. Numer. Meth. Engng 2003; 19: 125-136) is extended to a more general special form known as Form III.
Abstract: The method developed for eigensolution for matrices of special structures in Kaveh and Sayarinejad (Commun. Numer. Meth. Engng 2003; 19: 125–136) is extended to a more general special form known as Form III. Efficient methods are presented for evaluating the eigenvalues and eigenvectors of these matrices. Copyright © 2004 John Wiley & Sons, Ltd.
TL;DR: In this paper, a non-iterative numerical method for solving inverse boundary value problems for linear elliptic equations of second order was developed, where the Dirichlet and Neumann boundary conditions are given only on part of the domain.
Abstract: In this paper, we develop a new non-iterative numerical method for solving inverse boundary value problems for linear elliptic equations of second order. Here we assume that the Dirichlet and Neumann boundary conditions are given only on part of the domain, we have to reconstruct the solution and its normal derivative on the unaccessible part of the domain, which is the well-known ill-posed Cauchy problem. We propose to solve such inverse problems directly by using the recently developed radial basis meshless method. Several numerical experiments are given to demonstrate the effectiveness and efficiency of the proposed method. Copyright © 2003 John Wiley & Sons, Ltd.
TL;DR: In this article, the authors present a consistent computational approach to one-, two-, and three-field variational formulations of non-linear Bernoulli-Euler beam theory, including the effects of nonlinear geometry and inelasticity.
Abstract: Bernoulli–Euler beam theory has long been the standard for the analysis of reticulated structures. The need to accurately compute the non-linear (material and geometric) response of structures has renewed interest in the application of mixed variational approaches to this venerable beam theory. Recent contributions in the literature on mixed methods and the so-called (but quite related) non-linear flexibility methods have left open the question of what is the best approach to the analysis of beams. In this paper we present a consistent computational approach to one-, two-, and three-field variational formulations of non-linear Bernoulli–Euler beam theory, including the effects of non-linear geometry and inelasticity. We examine the question of superiority of methods through a set of benchmark problems with features typical of those encountered in the structural analysis of frames. We conclude that there is no clear winner among the various approaches, even though each has predictable computational strengths. Copyright © 2003 John Wiley & Sons, Ltd.
TL;DR: In this paper, a hypersingular integral equation for curved cracks in plane elasticity is formulated and presented, where the curved crack configuration maps on the real axis with interval (-a,a), where 2a is the arc length of the crack.
Abstract: In this paper, a hypersingular integral equation for curved cracks in plane elasticity is formulated and presented. This paper describes a new numerical technique for solution of deep curved cracks in plane elasticity. In this method, the crack curve length is taken as the co-ordinate in the hypersingular integral equation of the curved crack problems. The curved crack configuration maps on the real axis with interval (-a,a), where ‘2a’ is the arc length of the crack. The original hypersingular integral equation is converted into other hypersingular integral equation which is formulated on the curve length co-ordinate, or on (-a,a). The hypersingular integral equation is solved numerically. Numerical examples prove that higher efficiency has been achieved in the suggested method. Copyright © 2003 John Wiley & Sons, Ltd.
TL;DR: In this paper, a solution procedure is presented based on the stabilized equal order mixed velocity-pressure finite element formulation of the incompressible Navier-Stokes equations, which is adapted to a moving domain by means of an arbitrary Lagrangian-Eulerian (ALE) technique.
Abstract: This work is concerned with the numerical modelling of incompressible Newtonian fluid flows on moving domains in the presence of surface tension. The solution procedure presented is based on the stabilized equal order mixed velocity-pressure finite element formulation of the incompressible Navier-Stokes equations, which is adapted to a moving domain by means of an arbitrary Lagrangian-Eulerian (ALE) technique. The accurate and very robust integration in time is achieved by employing the generalized-a method. The surface tension boundary condition is rephrased appropriately within the framework of linear finite elements. The solution procedure is verified by comparing numerical solutions with the corresponding analytical solutions and experimental data. The overall solution procedure proves to be accurate, robust and efficient. It allows the simulation of extensive deformation of the fluid domain without remeshing.
TL;DR: In this paper, an improved unstructured vertex-centred edge-based finite volume algorithm is employed for the modelling of the coupled heat and mass transfer processes prevalent in drying non-hygroscopic capillary particulate materials.
Abstract: The modelling of the coupled heat and mass transfer processes prevalent in drying non-hygroscopic capillary particulate materials is dealt with. An improved unstructured vertex-centred edge-based finite volume algorithm is employed for this purpose. Enhancements include reformulation of boundary integral flux-averaging as well as the use of a compact stencil in the computation of diffusive terms. A notable increase in accuracy is demonstrated. The developed algorithm is further validated against experimental data.
TL;DR: In this article, a numerical procedure is outlined to achieve the least squares projection of a finite dimensional representation from one surface to another in 3D. But the specific problem considered is the mortar tying of dissimilarly meshed grids in large deformation solid mechanics.
Abstract: A numerical procedure is outlined to achieve the least squares projection of a finite dimensional representation from one surface to another in three dimensions. Although the applications of such an algorithm are many, the specific problem considered is the mortar tying of dissimilarly meshed grids in large deformation solid mechanics. The algorithm includes a nearest neighbour search, a systematic subdivision of the surface of intersection into smooth subdomains (termed segments), and a robust numerical quadrature scheme for evaluation of the spatial integrals defining the mortar projection. The procedure outlined, while discussed for the mesh tying problem, is directly applicable to the study of contact-impact. Published in 2003 by John Wiley & Sons, Ltd.
TL;DR: The implementation of a 3-D parallel CFD code using the meshless method and the Total Arbitrary Lagrangian Eulerian formulations using Finite Element Method are developed and implemented in the parallel code.
Abstract: In this paper, the implementation of a 3-D parallel CFD code using the meshless method. Reproducing Kernel Particle Method (RKPM) is described. A novel procedure for implementing the essential boundary condition using the hierarchical enrichment method is presented. The Total Arbitrary Lagrangian Eulerian (ALE) formulations using Finite Element Method are developed and implemented in the parallel code. The flow past a cylinder problem served as examples throughout the paper. Both methods have shown promising results compared with analytical solution. Copyright © 2003 John Wiley & Sons, Ltd.
TL;DR: In this article, both Sibson and non-Sibson interpolants ability to exactly reproduce essential boundary conditions is investigated and a new analytical condition ensuring linear precision along explicitly described (i.e. CAD) boundaries in both two and three dimensions is presented.
Abstract: In this paper issues related to the imposition of essential boundary conditions in Natural Neighbour Galerkin methods are addressed. Both Sibson and non-Sibson interpolants ability to exactly reproduce essential boundary conditions is investigated and a new analytical condition ensuring linear precision along explicitly described (i.e. CAD) boundaries in both two and three dimensions is presented. The paper is completed with some benchmark numerical examples. Copyright © 2003 John Wiley & Sons, Ltd.
TL;DR: In this article, the authors investigated the use of radial basis functions for solving Poisson problems with a near-singular inhomogeneous source term and proposed a method for evaluating the particular solution and a homogeneous solution.
Abstract: In this paper, we investigate the use of radial basis functions for solving Poisson problems with a near-singular inhomogeneous source term. The solution of the Poisson problem is first split into two parts: near-singular solution and smooth solution. A method for evaluating the near-singular particular solution is examined. The smooth solution is further split into a particular solution and a homogeneous solution. The MPS-DRM approach is adopted to evaluate the smooth solution. Copyright © 2003 John Wiley & Sons, Ltd.
TL;DR: In this article, a simple finite element formulation for two-dimensional frictional contact problems undergoing large deformations is presented, which is equivalent to the standard node-to-segment interpolation but it leads to a less complicated matrix formulation and hence is on one hand more efficient and on the other hand easier to implement.
Abstract: In this paper a simple finite element formulation for two-dimensional frictional contact problems undergoing large deformations is presented. It is equivalent to the standard node-to-segment interpolation but it leads to a less complicated matrix formulation and hence is on one hand more efficient and on the other hand easier to implement. Copyright © 2003 John Wiley & Sons, Ltd.
TL;DR: In this paper, an improved formulation of the Element Free Galerkin (EFG) method is proposed in order to alleviate volumetric locking, and it is proved that diffuse divergence converges to the exact divergence.
Abstract: SUMMARY Locking in finite elements has been a major concern since its early developments. It appears because poor numerical interpolation leads to an over-constrained system. This paper proposes a new formulation that asymptotically suppresses locking for the Element Free Galerkin (EFG) method in incompressible limit, i.e. the so-called volumetric locking. Originally it was claimed that EFG did not present volumetric locking. However, recently, performing a modal analysis, the senior author has shown that EFG presents volumetric locking. In fact, it is concluded that an increase of the dilation parameter attenuates, but never suppresses, the volumetric locking and that, as in standard finite elements, an increase in the order of reproducibility (interpolation degree) reduces the relative number of locking modes. Here an improved formulation of the Element Free Galerkin method is proposed in order to alleviate volumetric locking. Diffuse derivatives are defined in the thesis of the second author and their convergence to the derivatives of the exact solution, when the radius of the support goes to zero (for a fixed dilation parameter), it’s proved. Therefore diffuse divergence converges to the exact divergence. Since the diffuse divergence-free condition can be imposed a priori, new interpolation functions are defined that asymptotically verify the incompressibility condition. Modal analysis and numerical results for classical benchmark tests in solids corroborate this issue. Copyright c 2002 John Wiley & Sons, Ltd.
TL;DR: A new approach to mesh smoothing is suggested, based on a combination of Laplacian smoothing and Winslow's method, which can avoid mesh folding and maintain/produce element stretch.
Abstract: In this note we suggest a new approach to mesh smoothing, based on a combination of Laplacian smoothing and Winslow's method. Using our approach, we can avoid mesh folding and maintain/produce element stretch. We also make a comparison with a method due to Giuliani and show that the latter method cannot ensure that folding is avoided.
TL;DR: The present study outlines an innovative eigenanalysis-free idea to extract the buckling mode for bifurcation instability from the LDLT-decomposed stiffness matrix and applies it to eigenvector-free procedures for identifying and pinpointing the stability point and branch-switching for post-bIfurcation analysis.
Abstract: The authors have already proposed in their previous papers an innovative eigenanalysis-free idea to extract the buckling mode for bifurcation instability from the LDLT-decomposed stiffness matrix. The present study first outlines this basic idea very briefly for a review purpose. The idea will then be applied to eigenvector-free procedures for identifying and pinpointing the stability point and branch-switching for post-bifurcation analysis. Numerical examples will examine the versatility and robustness of the proposed eigenvector-free procedures in computational bifurcation theory. It is illustrated that the proposed procedures are robust enough for multiple as well as simple bifurcation. Copyright © 2003 John Wiley & Sons, Ltd.
TL;DR: In this paper, the authors describe the extension of the method to problems of scattering of elastic waves, and demonstrate the same features as those previously obtained for the Helmholtz equation, namely that for a given level of error far fewer degrees of freedom are required in the system matrix.
Abstract: The method of plane wave basis functions, a subset of the method of Partition of Unity, has previously been applied successfully to finite element and boundary element models for the Helmholtz equation. In this paper we describe the extension of the method to problems of scattering of elastic waves. This problem is more complicated for two reasons. First, the governing equation is now a vector equation and second multiple wave speeds are present, for any given frequency. The formulation has therefore a number of novel features. A full development of the necessary theory is given. Results are presented for some classical problems in the scattering of elastic waves. They demonstrate the same features as those previously obtained for the Helmholtz equation, namely that for a given level of error far fewer degrees of freedom are required in the system matrix. The use of the plane wave basis promises to yield a considerable increase in efficiency over conventional boundary element formulations in elastodynamics. Copyright © 2003 John Wiley & Sons, Ltd.
TL;DR: In this paper, the material properties for sheet metals subjected to loading and reverse loading were estimated by using an inverse method, where the Modified Levenberg-Marquardt method was used in the optimization procedure.
Abstract: The main objective of this paper is to estimate the material properties for sheet metals subjected to loading and reverse loading by using an inverse method. Cyclic three-point bending tests are conducted. Bending moments are computed from the measured data, namely, punch stroke, punch load, bending strain and bending angle. Bending moments are also calculated based on the selected constitutive model. Normal anisotropy and non-linear isotropic/kinematic hardening are considered. Material parameters are estimated by minimizing the difference between these two bending moments. Modified Levenberg–Marquardt method is used in the optimization procedure. Stress–strain curves are generated with the material parameters found in this way. Copyright © 2004 John Wiley & Sons, Ltd.
TL;DR: This poster presents a probabilistic procedure to characterize the response of the immune system to laser-spot assisted, 3D image analysis of EMMARM, and its applications in medicine and dentistry.
Abstract: Reference GEOLEP-ARTICLE-2003-004doi:10.1002/cnm.621View record in Web of Science Record created on 2008-02-13, modified on 2016-08-08
TL;DR: In this article, the weak form of the Navier-Stokes equations is obtained using a generalized streamline operator in order to stabilize its numerical response while a temperature-based algorithm is applied to describe the latent heat release.
Abstract: In this work, a twin-roll strip casting industrial process is analysed using a fixed-mesh finite element formulation able to deal with unsteady incompressible thermally coupled flows including phase-change and non-Newtonian effects assumed to account for the flow behaviour during the whole cooling conditions. The weak form of the full Navier–Stokes equations is obtained using a generalized streamline operator in order to stabilize its numerical response while a temperature-based algorithm is applied to describe the latent heat release. This proposed methodology is tested in a two-dimensional analysis of a twin-roll casting problem where an evaluation of different thermal and flow patterns is performed. Copyright © 2003 John Wiley & Sons, Ltd.
TL;DR: In this paper, a new procedure to represent the quality measure for triangles is proposed, where triangles are identified by their three angles and are represented in a bounded domain, called angle representation region, according to the area coordinates.
Abstract: SUMMARY In this note a new procedure to represent the quality measure for triangles is proposed. The triangles are identified by their three angles and are represented in a bounded domain, called angle representation region, according to the area coordinates,which are common and well-known by finite element users. The developed representation can also be used in order to visualize the characteristics of any quality measure. This new procedure is extended to graphically represent triangular meshes in the angle representation region.