Showing papers in "Cmes-computer Modeling in Engineering & Sciences in 2000"
206 citations
TL;DR: In this paper, several upwinding schemes are proposed, and applied to solve steady convectiondiffusion problems, in one and two dimensions, in the meshless local Petrov-Galerkin (MLPG) method.
Abstract: Due to the very general nature of the Meshless Local Petrov-Galerkin (MLPG) method, it is very easy and natural to introduce the upwinding concept (even in multidimensional cases) in the MLPG method, in order to deal with convection-dominated flows. In this paper, several upwinding schemes are proposed, and applied to solve steady convectiondiffusion problems, in one and two dimensions. Even for very high Peclet number flows, the MLPG method, with upwinding, gives very good results. It shows that the MLPG method is very promising to solve the convection-dominated flow problems, and fluid mechanics problems. keyword: MLPG, MLS, convection-dominated flow, upwinding.
200 citations
TL;DR: In this paper, a truly meshless local Petrov-Galerkin (MLPG) method is proposed to solve boundary value problems, using a local symmetric weak form as a natural approach.
Abstract: The truly meshless local Petrov-Galerkin (MLPG) method holds a great promise in solving boundary value problems, using a local symmetric weak form as a natural approach. In the present paper, in the context of MLPG and the meshless interpolation of a moving least squares (MLS) type, a method which uses primary and secondary nodes in the domain and on the global boundary is introduced, in order to improve the accuracy of solution. The secondary nodes can be placed at any location where one needs to obtain a better resolution. The sub-domains for the shape functions in the MLS approximation are defined only from the primary nodes, and the secondary nodes use the same sub-domains. The shape functions based on the MLS approximation, in an integration domain, have a single type of a rational function, which reduces the difficulty of numerical integration to evaluate the weak form. The present method is very useful in an adaptive calculation, because the secondary nodes can be easily added and/or moved without an additional mesh. The essential boundary conditions can be imposed exactly, and non-convex boundaries can be treated without special techniques. Several numerical examples are presented to illustrate the performance of the present method. keyword: meshless method, MLPG method, local symmetric weak form, MLS, primary node, secondary node.
78 citations
76 citations
38 citations
TL;DR: In this paper, the synchronous resonance between the wall and the free surface is investigated for corrugations with wavelength 0.002 m, which lead to strongest interaction, and conditions leading to flow reversal are established.
Abstract: Laminar, gravity-driven flow of a liquid down an inclined wall with large-amplitude sinusoidal corrugations is studied numerically by a spectral spatial discretization method. The synchronous resonance between the wall and the free surface is investigated for corrugations with wavelength 0.002 m, which – according to linear theory – lead to strongest interaction. Free surface profile and flow structure are studied as a function of the film Reynolds number and the wall amplitude. Streamline patterns are computed and conditions leading to flow reversal are established. The distribution of the shear stress along the wall and of the normal velocity gradient close to the free surface are computed and related to heat/mass transport. keyword: wavy wall, film flow, resonance
38 citations
TL;DR: In this paper, a constitutive model for a porous metal subjected to general three-dimensional finite deformations is presented, which takes into account the evolution of porosity and the development of anisotropy due to changes in the shape and the orientation of the voids during deformation.
Abstract: A constitutive model for a porous metal subjected to general three-dimensional finite deformations is presented. The model takes into account the evolution of porosity and the development of anisotropy due to changes in the shape and the orientation of the voids during deformation. A methodology for the numerical integration of the elastoplastic constitutive model is developed. Finally, some sample applications to plane strain extrusion and compaction of a porous disk are considered using the finite element method.
35 citations
25 citations
24 citations
TL;DR: In this article, the iterative algorithm proposed by [Kozlov and Maz'ya (1990) for the backward heat conduction problem is extended in order to solve the Cauchy steady state problem and the accuracy, convergence and stability of the numerical algorithm are investigated.
Abstract: In this paper the iterative algorithm proposed by [Kozlov and Maz’ya (1990)] for the backward heat conduction problem is extended in order to solve the Cauchy steady state heat conduction problem and the accuracy, convergence and stability of the numerical algorithm are investigated. The numerical results which are obtained confirm that this new iterative BEM procedure is accurate, convergent and stable with respect to increasing the number of boundary elements and decreasing the amount of noise which is added into the input data. keyword: BEM, heat conduction, Cauchy problem, iterative algorithm
22 citations
TL;DR: In this article, a volume integral arises in the resulting integral equation if thermal effects are present and the steps to transform this volume integral into boundary ones in an exact analytical manner are reviewed for twodimensional anisotropic thermoelasticity.
Abstract: In the direct formulation of the boundary element method (BEM), a volume integral arises in the resulting integral equation if thermal effects are present. The steps to transform this volume integral into boundary ones in an exact analytical manner are reviewed in this paper for twodimensional anisotropic thermoelasticity. The general applicability of the BEM algorithm for fracture mechanics applications is demonstrated by three crack problems with slanted cracks. The numerical results of the stress intensity factors are presented and compared with those obtained using superposition. keyword: BEM, anisotropy, thermoelasticity, fracture mechanics
TL;DR: In this paper, the authors discuss further applications of the hyper-singular boundary integral equation to obtain the Green's function solution to general geometry fracture mechanics problems, such as curved multifracture crack simulation, static and transient dynamic in 2-D, 3-D and plate bending problems.
Abstract: The paper discusses further applications of the hyper-singular boundary integral equation to obtain the Green’s function solution to general geometry fracture mechanics problems, such as curved multifracture crack simulation, static and transient dynamic in 2-D, 3-D and plate bending problems. This numerical Green’s function (NGF) is implemented into alternative boundary element computer programs, as the fundamental solution, to enhance the scope of alternative applications of the NGF procedure. The results to some typical linear fracture mechanics problems are presented. keyword: HBEM, Crack, Green’s Function
TL;DR: In this paper, the terminal solid solubility of hydrogen in solution is defined on the basis of the total elastoplastic work done on the system by the forming hydride and the external loads.
Abstract: Transient hydrogen diffusion and hydride formation coupled with material deformation are studied in Zr2.5Nb alloys used in the pressure tubes of CANDU nuclear generating stations. The energetics of the hydride formation is revisited and the terminal solid solubility of hydrogen in solution is defined on the basis of the total elastoplastic work done on the system by the forming hydride and the external loads. Probabilistic precipitation of hydride is modeled in the neighborhood of a crack tip under mode I plane strain loading and a uniform initial hydrogen concentration below the stress free terminal solid solubility. Finite element analysis is used to monitor the local distribution and time evolution of hydrogen concentration, hydride volume fraction, stress, and strain as the externally applied loads increase. The mechanistic effects of the solute hydrogen and hydride formation on the stresses at the crack tip are analyzed and their consequence on the fracture toughness resistance of the material is determined. keyword: plasticity, embrittlement, hydride, diffusion, hydrogen, fracture
TL;DR: In this article, the authors describe the application of the meshless Finite Point (FP) method to the solution of the nonlinear semiconductor Poisson equation, which is a true meshless method which uses a weighted least squares fit and point collocation.
Abstract: This paper describes the application of the meshless Finite Point (FP) method to the solution of the nonlinear semiconductor Poisson equation. The FP method is a true meshless method which uses a weighted least-squares fit and point collocation. The nonlinearity of the semiconductor Poisson equation is treated by Newton-Raphson iteration, and sparse matrices are employed to store the shape function and coefficient matrices. Using examples in twoand threedimensions (2and 3-D) for a prototypical n-channel MOSFET, the FP method demonstrates promise both as a means of mesh enhancement and for treating problems where arbitrary point placement is advantageous, such as for the simulation of carrier wave packet and dopant cloud effects in the ensemble Monte Carlo method. The validity of the solutions and the capability of the method to treat arbitrary boundary conditions is shown by comparison with finite difference results. keyword: finite point methods, meshless methods, mesh generation, monte carlo methods.
TL;DR: IZoptimality, coupled with BLUP fitting, provides a highly efficient means of non-parametric metamodel generation and new options of the I-OPTTM program that is available on the World-Wide Web.
Abstract: We present a new and unique software capability for finding statistical optimal designs of deterministic experiments on continuous cuboidal regions. The objective function for the design optimization is the minimization of the expected integrated mean squared error of prediction of the metamodel that will be found, subsequent to the running of the computer simulations, using the best linear unbiased predictor (BLUP). The assumed response-model function includes an unknown, stochastic term, Z. We prove that this criterion, which we name IZ-optimality, is equivalent to I-optimality for non-deterministic experiments, in the limit of zero correlations among the Z’s for different inputs. An example is presented of metamodel generation for a micromachined-silicon flow sensor. The IZ-optimal set of inputs is found, finite-element (FE) simulations run, and the metamodel generated using a BLUP fit. The method is compared to other approaches. IZoptimality, coupled with BLUP fitting, provides a highly efficient means of non-parametric metamodel generation. IZoptimal design searching and BLUP fitting are new options of the I-OPTTM program that is available on the World-Wide Web at URL http://www-personal.engin.umich.edu/ crary/iopt. keyword: design of computer experiments, I-optimality, microelectromechanical systems, MEMS, silicon flow sensor.
TL;DR: In this paper, a vectorized model solver is developed for large-scale simulation to simulate the dynamic failure evolution without using nonlocal terms in the strain-stress space, a damage diffusion equation is formulated with the use of a combined damage/plasticity model that was primarily applied to the case of rock fragmentation.
Abstract: To simulate the dynamic failure evolution without using nonlocal terms in the strain-stress space, a damage diffusion equation is formulated with the use of a combined damage/plasticity model that was primarily applied to the case of rock fragmentation. A vectorized model solver is developed for large-scale simulation. Two-dimensional sample problems are considered to illustrate the features of the proposed solution procedure. It appears that the proposed approach is effective in simulating the evolution of localization, with parallel computing, in a single computational domain involving different lower-order governing differential equations. keyword: Brittle failure, damage diffusion, multi-physics, parallel computing
TL;DR: In this paper, a boundary element formulation for two-dimensional acoustic wave propagation in shallow water is presented, where the velocity of sound in water is constant, the free surface is horizontal, and the seabed is irregular.
Abstract: This work presents a boundary element formulation for two-dimensional acoustic wave propagation in shallow water. It is assumed that the velocity of sound in water is constant, the free surface is horizontal, and the seabed is irregular. The boundary conditions of the problem are that the sea bottom is rigid and the free surface pressure is atmospheric. For regions of constant depth, fundamental solutions in the form of infinite series can be employed in order to avoid the discretisation of both the free surface and bottom boundaries. When the seabed topography is irregular, it is necessary to divide the fluid region using the subregions technique. In this case, only irregular bottom boundaries and interfaces between regions of different depth need to be discretised. Numerical simulations of several problems are included, ranging from smooth to abrupt variations of the seabed. The results are verified by comparison with a more standard BEM formulation in which the complete seabed is discretised and truncated at a large distance. keyword: Boundary element method, subregions, underwater acoustics, shallow water, waveguides
TL;DR: In this paper, a variable gap comb drive with linear, quadratic and cubic driving force profiles was designed using numerical simulation and the electrode shapes were obtained using the indirect boundary element method.
Abstract: Polynomial driving-force comb drives are designed using numerical simulation. The electrode shapes are obtained using the indirect boundary element method. Variable gap comb drives that produce combinations of linear, quadratic, and cubic driving-force profiles are synthesized. This inverse problem is solved by an optimization procedure. Sensitivity analysis is carried out by the direct differentiation approach (DDA) in order to compute design sensitivity coefficients (DSCs) of force profiles with respect to parameters that define the shapes of the fingers of a comb drive. The DSCs are then used to drive iterative optimization procedures. Designs of variable gap comb drives with linear, quadratic and cubic driving force profiles are presented in this paper. Based on these designs, a comb drive which produces cubic polynomial driving force has been fabricated using the SCREAM I process. Test results show reasonable agreement between numerical simulations and experiments. keyword: optimal design, boundary element method, microelectro-mechanical systems, comb drive
TL;DR: In this article, a high-speed high-accuracy 3D field solver for the solution of coupled multi-physics encountered in MEMS is presented, which enables automatic model generation from layout, automatic meshing, adaptive mesh refinement of large complex geometries encountered with realistic MEMS devices.
Abstract: A high-speed high-accuracy 3D field solver for the solution of coupled multi-physics encountered in MEMS is presented. The software AutoMEMS enables automatic model generation from layout, automatic meshing, adaptive mesh refinement of large complex geometries encountered with realistic MEMS devices. Arbitrary types of materials, general geometries, and all types of boundary conditions are supported to solve coupled electro-mechanical 3D fields.
TL;DR: In this paper, the authors have spanned the length scales in a concerted simulation comprising the finite element method, classical molecular dynamics, quantum tight-binding dynamics and seamless bridges between these different physical descriptions.
Abstract: A challenging paradigm in the computational sciences is the coupling of the continuum, the atomistic and the quantum descriptions of matter for a unified dynamic treatment of a single physical problem. We described the achievement of such a goal. We have spanned the length scales in a concerted simulation comprising the finite-element method, classical molecular dynamics, quantum tight-binding dynamics and seamless bridges between these different physical descriptions. We illustrate and validate the methodology for crack propagation in silicon.
TL;DR: In this article, an inverse boundary element method is developed to characterise the components of the hydraulic conductivity tensor K of anisotropic materials, where surface measurements at exposed boundaries serve as additional input to a GA using a modified least squares functional that minimises the difference between observed and BEM-predicted boundary pressure and/or hydraulic flux measurements under current hydraulic conductivities tensor component estimates.
Abstract: An inverse boundary element method is developed to characterise the components of the hydraulic conductivity tensor K of anisotropic materials. Surface measurements at exposed boundaries serve as additional input to a Genetic Algorithm (GA) using a modified least squares functional that minimises the difference between observed and BEM-predicted boundary pressure and/or hydraulic flux measurements under current hydraulic conductivity tensor component estimates. keyword: Boundary Element Method, Genetic Algorithms, inverse problems, anisotropy, hydraulic conductivity.
TL;DR: In this paper, the authors present the formulation and numerical implementation of a spectral scheme specially developed to simulate dynamic fracture events in unidirectional and crossply fiber-reinforced composites.
Abstract: This paper presents the formulation and numerical implementation of a spectral scheme specially developed to simulate dynamic fracture events in unidirectional and crossply fiber-reinforced composites. The formulation is based on the spectral representation of the transversely isotropic elastodynamic relations between the traction stresses along the fracture plane and the resulting displacements. Example problems involving stationary or dynamically propagating cracks in fiber-reinforced composites are investigated and compared with reference solutions available in the literature and/or experimental observations. keyword: Spectral method, transversely isotropic solid, fiber-reinforced composites, dynamic fracture.
TL;DR: In this article, a direct Trefftz method with domain decomposition is applied to the two-dimensional elasticity problem and linear elements are used for modelling of the boundary geometry and approximation of boundary quantities.
Abstract: This paper presents an application of a direct Trefftz method with domain decomposition to the twodimensional elasticity problem. Trefftz functions are substituted into Betti’s reciprocity theorem to derive the boundary integral equations for each subdomain. The values of displacements and tractions on subdomain interfaces are tailored by continuity and equilibrium conditions, respectively. Since Trefftz functions are regular, much less requirements are put on numerical integration than in the traditional boundary integral method. Then, the method can be utilized to analyse also very narrow domains. Linear elements are used for modelling of the boundary geometry and approximation of boundary quantities. Numerical results for a rectangular plate with varying aspect ratio and cantilever beam are presented. keyword: plynomial Trefftz functions, direct formulation, linear approximation, boundary integral equation
TL;DR: In this article, a variational approach is proposed to predict the wake geometry and the three-dimensional vortex flow streaming back from the propeller in forward flight of a four-bladed propeller.
Abstract: Advanced propellers are being developed to improve the performance and fuel economy of future transport aircraft. To study them, various aerodynamic prediction models and systems (from theory to experiment) have been developed via several approaches (Free Wake Analysis, helicoidal source methods, scale model tests). This study focuses on the development of an efficient numerical method to predict the behaviour of rotor or propeller in forward flight. Based on a variational approach, the present numerical technique allows a significant reduction of computer resources used in the calculation of instantaneous velocities to determine the wake geometry and the three-dimensional vortex flow streaming back from the propeller. Wind tunnel test data are presented to substantiate the theory and to show its limitations. The analytical structure of the model is described and its capability is analyzed by a numerical simulation checked against available with experimental data obtained on a scale model of a fourbladed propeller. Assuming the hypothesis of incompressible flow, the simulation results show a very good agreement with experiments for a wide range of operating parameters. keyword: variational numerical scheme, propeller wake
TL;DR: Model reference adaptive control formulations are presented that rigorously impose the dynamical structure of the state space descriptions of several distinct large classes of dynamical systems, providing new insights and providing a basis for optimism regarding practical adoption of adaptive control methodology in advanced implementations.
Abstract: Model reference adaptive control formulations are presented that rigorously impose the dynamical structure of the state space descriptions of several distinct large classes of dynamical systems. Of particular interest, the formulations enable the imposition of exact kinematic differential equation constraints upon the adaptation process that compensates for model errors and disturbances at the acceleration level. Other adaptive control formulations are tailored for redundantly actuated and constrained dynamical systems. The utility of the resulting structured adaptive control formulations is studied by considering examples from nonlinear oscillations, aircraft control, spacecraft control, and cooperative robotic system control. The theoretical and computational results provide new insights and provide a basis for optimism regarding practical adoption of adaptive control methodology in advanced implementations.