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Example Problems (example + problem)
Selected AbstractsDevelopment of a genetic algorithm-based lookup table approach for efficient numerical integration in the method of finite spheres with application to the solution of thin beam and plate problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 12 2006Suleiman BaniHani Abstract It is observed that for the solution of thin beam and plate problems using the meshfree method of finite spheres, Gaussian and adaptive quadrature schemes are computationally inefficient. In this paper, we develop a novel technique in which the integration points and weights are generated using genetic algorithms and stored in a lookup table using normalized coordinates as part of an offline computational step. During online computations, this lookup table is used much like a table of Gaussian integration points and weights in the finite element computations. This technique offers significant reduction of computational time without sacrificing accuracy. Example problems are solved which demonstrate the effectiveness of the procedure. Copyright © 2006 John Wiley & Sons, Ltd. [source] A 3D mortar method for solid mechanics,INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2004Michael A. Puso Abstract A version of the mortar method is developed for tying arbitrary dissimilar 3D meshes with a focus on issues related to large deformation solid mechanics. Issues regarding momentum conservation, large deformations, computational efficiency and bending are considered. In particular, a mortar method formulation that is invariant to rigid body rotations is introduced. A scheme is presented for the numerical integration of the mortar surface projection integrals applicable to arbitrary 3D curved dissimilar interfaces. Here, integration need only be performed at problem initialization such that coefficients can be stored and used throughout a quasi-static time stepping process even for large deformation problems. A degree of freedom reduction scheme exploiting the dual space interpolation method such that direct linear solution techniques can be applied without Lagrange multipliers is proposed. This provided a significant reduction in factorization times. Example problems which touch on the aforementioned solid mechanics related issues are presented. Published in 2003 by John Wiley & Sons, Ltd. [source] Particulate flow simulations using lubrication theory solution enrichmentINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 9 2003G. J. Wagner Abstract A technique for the numerical simulation of suspensions of particles in fluid based on the extended finite element method (X-FEM) is developed. In this method, the particle surfaces need not conform to the finite element boundaries, so that moving particles can be simulated without remeshing. The finite element basis is enriched with the Stokes flow solution for flow past a single particle and the lubrication theory solution for flow between particles. The latter enrichment allows the simulation of particles that come arbitrarily close together without refining the mesh in the gap between them. Example problems illustrating both types of enrichment are shown, along with a study of a 50% solution in channel flow. Copyright © 2003 John Wiley & Sons, Ltd. [source] Efficiency of boundary element methods for time-dependent convective heat diffusion at high Peclet numbersINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 4 2005M. M. Grigoriev Abstract A higher-order boundary element method (BEM) recently developed by the current authors (Comput Methods Appl Mech Eng 2003; 192: 4281,4298; 4299,4312; 4313,4335) for time-dependent convective heat diffusion in two-dimensions appears to be a very attractive tool for efficient simulations of transient linear flows. However, the previous BEM formulation is restricted to relatively small time step sizes (i.e. ,t,4,/V2) owing to the convergence issues of the time series for the kernel representation within a time interval. This paper extends the boundary element formulation in a way to allow time step sizes several orders of magnitude larger than in the previous approach. We consider an example problem of thermal propagation, and investigate the accuracy and efficiency of BEM formulations for Peclet numbers in the range from 103 to 105. Copyright © 2005 John Wiley & Sons, Ltd. [source] Face recognition based on face-specific subspaceINTERNATIONAL JOURNAL OF IMAGING SYSTEMS AND TECHNOLOGY, Issue 1 2003Shiguang Shan Abstract In this article, we present an individual appearance model based method, named face-specific subspace (FSS), for recognizing human faces under variation in lighting, expression, and viewpoint. This method derives from the traditional Eigenface but differs from it in essence. In Eigenface, each face image is represented as a point in a low-dimensional face subspace shared by all faces; however, the experiments conducted show one of the demerits of such a strategy: it fails to accurately represent the most discriminanting features of a specific face. Therefore, we propose to model each face with one individual face subspace, named Face-Specific Subspace. Distance from the face-specific subspace, that is, the reconstruction error, is then exploited as the similarity measurement for identification. Furthermore, to enable the proposed approach to solve the single example problem, a technique to derive multisamples from one single example is further developed. Extensive experiments on several academic databases show that our method significantly outperforms Eigenface and template matching, which intensively indicates its robustness under variation in illumination, expression, and viewpoint. © 2003 Wiley Periodicals, Inc. Int J Imaging Syst Technol 13: 23,32, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ima.10047 [source] A property-based optimization of direct recycle networks and wastewater treatment processesAICHE JOURNAL, Issue 9 2009José María Ponce-Ortega Abstract This article presents a mathematical programming approach to optimize direct recycle-reuse networks together with wastewater treatment processes in order to satisfy a given set of environmental regulations. A disjunctive programming formulation is developed to optimize the recycle/reuse of process streams to units and the performance of wastewater treatment units. In addition to composition-based constraints, the formulation also incorporates in-plant property constraints as well as properties impacting the environment toxicity, ThOD, pH, color, and odor. The MINLP model is used to minimize the total annual cost of the system, which includes the cost for the fresh sources, the piping cost for the process integration and the waste stream treatment cost. An example problem is used to show the application of the proposed model. The results show that the simultaneous optimization of a recycle network and waste treatment process yields significant savings with respect to a commonly-used sequential optimization strategy. © 2009 American Institute of Chemical Engineers AIChE J, 2009 [source] A numerical method for computing the response of composites with periodic microstructurePROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2003Sven Kassbohm Dipl.-Ing. The stress-strain response of a periodic structure due to an applied eigenstrain field is investigated. The periodic structure allows reduction of the problem to a representative volume element (RVE) problem. A review of Fourier series as a particular method of solving the set of differential equations is given, and an example problem is studied. Results of the latter method are compared to results obtained using discrete Fourier transforms in a different way. [source] Visualization of aligned genomic open reading frame data,BIOCHEMISTRY AND MOLECULAR BIOLOGY EDUCATION, Issue 1 2003Alan P. Boyle Abstract Students can better appreciate the value of genomic data if they are asked to use the data themselves. However, in general the enormous volume of data involved makes detailed examination difficult. Here we present a web site that allows students to study one particular aspect of sequenced genomes. They are able to align the open reading frames (ORFs) of any available genome that is of reasonable size. The ORFs may be aligned using either the start codon or the stop codon as the starting points. Results will readily show the presence of common ribosome binding sites as well as reveal interesting order within the ORFs that is nonexistent outside of them. Students will be able to ask various questions involving comparisons of genomes and see the results presented in both a tabular and graphic format. An example problem is presented under "Results." [source] Animated instructional software for mechanics of materials: Implementation and assessmentCOMPUTER APPLICATIONS IN ENGINEERING EDUCATION, Issue 1 2006Timothy A. Philpot Abstract During the past 3 years, the Basic Engineering Department at the University of Missouri, Rolla has been developing a second-generation suite of instructional software called MecMovies for the Mechanics of Materials course. The MecMovies suite consists of over 110 animated example problems, drill-and-practice games, and interactive exercises. Students generally respond favorably to software of this type; however, much of the data that has been gathered to assess the effectiveness of similar software has been anecdotal. The method by which instructional software is incorporated into the engineering class is partly responsible for this lack of systematic evaluation. Often, software packages have been implemented in the classroom as supplemental material,recommended but not required. In the Fall 2003 semester, MecMovies was integrated thoroughly into the course assignments for one of the six UMR Mechanics of Materials sections. Four professors were involved in the study, and student performance in the experimental MecMovies section was compared to performance in the five control sections through a common final exam. At the end of the semester, students who used the MecMovies software also completed a survey questionnaire consisting of a number of subjective rating items. This paper presents a comparison of student performance in the experimental and control sections along with discussion of student qualitative ratings and comments. © 2006 Wiley Periodicals, Inc. Comput Appl Eng Educ 14: 31,43, 2006; Published online in Wiley InterScience (www.interscience.wiley.com); DOI 10.1002/cae.20065 [source] Practical causal hysteretic dampingEARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 5 2007Naohiro Nakamura Abstract A number of experiments indicate that the internal damping corresponding to the energy dissipation of many materials is essentially frequency independent. Accordingly, an analysis model that can express such characteristics (called a hysteretic damping model) in the time domain is needed. Although a great number of investigations into this subject have been carried out, there are a few practical methods. In this paper, a simple hysteretic damping model which satisfies the causality condition is presented using an extension of the complex stiffness transfer method that the author has proposed. Compared with the energy proportional damping model and the Biot model, the applicability and the efficiency of this model to time history response analyses were confirmed well by example problems. Copyright © 2006 John Wiley & Sons, Ltd. [source] Solution of non-linear dispersive wave problems using a moving finite element methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 4 2007Abigail Wacher Abstract The solution of the fully non-linear time-dependent two-dimensional shallow water equations is considered. Dispersive effects due to the Coriolis forces are taken into account. Such effects are of major importance in geophysical fluid dynamics applications. The recently proposed string gradient weighted moving finite element method is extended for this class of problems. This method simultaneously determines, at each time step, the solution of the governing partial differential equations and an optimal location of the finite element nodes. It has previously been applied to non-dispersive wave problems; here its performance under the demanding conditions of large Coriolis forces, inducing large mesh and field rotation, is studied. Optimal rates of convergence are obtained. Results for some example problems of water hump release are presented. Non-linear and linearized solutions are compared. Copyright © 2006 John Wiley & Sons, Ltd. [source] Treatment of Neumann boundaries in the complex variable boundary element methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 2 2004Kozo Sato Abstract For potential flow, the complex variable boundary element method (CVBEM) is formulated in terms of the velocity potential , and the stream function ,. In actual flow problems, , and ,,/,n are given along Dirichlet and Neumann boundaries, respectively. In the CVBEM, the Neumann-type condition ,,/,n is not directly handled, and, instead, , is used to define Neumann boundaries. Owing to this discrepancy, numerical difficulties are raised along Neumann boundaries. The current study addresses two such difficulties: (1) multiple Neumann boundaries and (2) branch cuts across Neumann boundaries. The first problem is due to the fact that , along multiple boundaries cannot be specified a priori, and the second problem is due to the discontinuous jump inherent in , for sink/source singularities. To overcome these difficulties, a new formulation of the CVBEM to solve for the unknown , values and a proper way of branch-cut placement are proposed, and these techniques are verified against example problems. Copyright © 2004 John Wiley & Sons, Ltd. [source] Multiscale modeling of impact on heterogeneous viscoelastic solids containing evolving microcracksINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2010Flavio V. Souza Abstract Multiscale computational techniques play a major role in solving problems related to viscoelastic composites due to the complexities inherent to these materials. In this paper, a numerical procedure for multiscale modeling of impact on heterogeneous viscoelastic solids containing evolving microcracks is proposed in which the (global scale) homogenized viscoelastic incremental constitutive equations have the same form as the local-scale viscoelastic incremental constitutive equations, but the homogenized tangent constitutive tensor and the homogenized incremental history-dependent stress tensor at the global scale depend on the amount of damage accumulated at the local scale. Furthermore, the developed technique allows the computation of the full anisotropic incremental constitutive tensor of viscoelastic solids containing evolving cracks (and other kinds of heterogeneities) by solving the micromechanical problem only once at each material point and each time step. The procedure is basically developed by relating the local-scale displacement field to the global-scale strain tensor and using first-order homogenization techniques. The finite element formulation is developed and some example problems are presented in order to verify the approach and demonstrate the model capabilities. Copyright © 2009 John Wiley & Sons, Ltd. [source] The extended finite element method for rigid particles in Stokes flowINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2001G. J. Wagner Abstract A new method for the simulation of particulate flows, based on the extended finite element method (X-FEM), is described. In this method, the particle surfaces need not conform to the finite element boundaries, so that moving particles can be simulated without remeshing. The near field form of the fluid flow about each particle is built into the finite element basis using a partition of unity enrichment, allowing the simple enforcement of boundary conditions and improved accuracy over other methods on a coarse mesh. We present a weak form of the equations of motion useful for the simulation of freely moving particles, and solve example problems for particles with prescribed and unknown velocities. Copyright © 2001 John Wiley & Sons, Ltd. [source] Large eddy simulation of turbulent flows in complex and moving rigid geometries using the immersed boundary methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 7 2005Mayank Tyagi Abstract A large eddy simulation (LES) methodology for turbulent flows in complex rigid geometries is developed using the immersed boundary method (IBM). In the IBM body force terms are added to the momentum equations to represent a complex rigid geometry on a fixed Cartesian mesh. IBM combines the efficiency inherent in using a fixed Cartesian grid and the ease of tracking the immersed boundary at a set of moving Lagrangian points. Specific implementation strategies for the IBM are described in this paper. A two-sided forcing scheme is presented and shown to work well for moving rigid boundary problems. Turbulence and flow unsteadiness are addressed by LES using higher order numerical schemes with an accurate and robust subgrid scale (SGS) stress model. The combined LES,IBM methodology is computationally cost-effective for turbulent flows in moving geometries with prescribed surface trajectories. Several example problems are solved to illustrate the capability of the IBM and LES methodologies. The IBM is validated for the laminar flow past a heated cylinder in a channel and the combined LES,IBM methodology is validated for turbulent film-cooling flows involving heat transfer. In both cases predictions are in good agreement with measurements. LES,IBM is then used to study turbulent fluid mixing inside the complex geometry of a trapped vortex combustor. Finally, to demonstrate the full potential of LES,IBM, a complex moving geometry problem of stator,rotor interaction is solved. Copyright © 2005 John Wiley & Sons, Ltd. [source] Scheduling multistage batch plants with sequence-dependent changeoversAICHE JOURNAL, Issue 8 2009Pedro M. Castro Abstract This article deals with the optimal short-term scheduling of multistage batch plants with parallel units and sequence-dependent changeovers, together with the optimal selection of the number and size of batches to be produced. A new resource-task network-based, multiple time-grid continuous-time formulation is proposed that explicitly considers a virtual, shared, intermediate storage unit per stage to keep track of material transfer between processing units belonging to consecutive stages of production. Adequate material transfer is implicitly ensured through mass balances and timing constraints relating the times of event points of dissimilar grids. The new formulation is compared with a conceptually different approach from another research group. The results for several example problems show that the new formulation is tighter, typically requiring fewer event points to find the global optimal solution, and is significantly more efficient computationally. The results also show that for single batch problems other approaches are preferable. © 2009 American Institute of Chemical Engineers AIChE J, 2009 [source] Reliable computation of mixture critical pointsAICHE JOURNAL, Issue 1 2001Benito A. Stradi The determination of critical points of mixtures is important for both practical and theoretical reasons in modeling phase behavior, especially at high pressure. This article presents the first completely reliable method for locating all the critical points of a given mixture. The method also verifies the nonexistence of a critical point if a mixture of a given composition does not have one. The methodology used is based on interval analysis, in particular an interval Newton/generalized bisection algorithm providing a mathematical and computational guarantee that all mixture critical points are located. The procedure is initialization-independent and thus requires no a priori knowledge of the number of mixture critical points or their approximate locations. The technique is illustrated using several example problems involving cubic equation-of-state models; however, the technique is for general purpose and can be applied in connection with other thermodynamic models. [source] | ||||||||||