Transactions on Information and Communications Technologies vol 15, 1997 WIT Press, ISSN
|
|
- Gregory Malone
- 6 years ago
- Views:
Transcription
1 Optimization of time dependent adaptive finite element methods K.-H. Elmer Curt-Risch-Institut, Universitat Hannover Appelstr. 9a, D Hannover, Germany Abstract To obtain reliable numerical solutions of transient dynamic problems and wave propagation problems with high accuracy it is necessary to use models with many degrees of freedom and many time steps. New algorithms and methods are developed to optimize the finite element model and to minimize the computational time on high-performance computers. The moving wave front is used for a broad time dependent mesh refinement, based on intensity vectors and the speed of wave propagation (intensity indicator), several time steps in advance. The a-posteriori Zienkiewicz-Zhu error indicator controls the adaptive mesh refinement. The implicit-explicit algorithm for direct time integration is based upon operator splitting and mesh partitions. The algorithm avoids subcycling on vector- and parallel-computers and uses the same time step for a coarse mesh and the local mesh refinement. 1 Introduction Numerical simulations use idealized models like analytical methods but allow the investigation of realistic systems with complex behaviour. Among other things the advantage of numerical simulation in computational dynamics is the investigation and visualization of complex time dependent processes and interactions in dynamic systems with complicated initial and boundary conditions. Better understanding of the mechanical behaviour is of special interest in many fields of application like earthquake engineering, soil dynamics, nondestructive testing and acoustics, where it is not possible or too expensive to obtain all the desired information by measurements: stresses and strain within a continuous system or the energy flow and intensity within a structure. However, the complexity of many realistic
2 2 1 4 High Performance Computing problems in transient dynamics requires very large systems. To obtain reliable numerical solutions of transient dynamic problems with high accuracy it is necessary to use models with many degrees of freedom and many time steps. So new algorithms and methods are developed to optimize time dependent finite element models and minimize the computational time on highperformance computers. The idea is to use the Zienkiewicz-Zhu error estimator [6] for wave propagation problems with h-adaptive time dependent FE-methods. As local mesh refinement and system setup after each time step is very expensive, a method is developed to estimate all regions that are to be refined several time steps in advance. Then the a-posteriori Zienkiewicz-Zhu error estimator is only used to control if the refinement has been sufficient or not. Knowing the expected direction of the energy flow from intensity vectors, the moving wave front allows a broad time dependent mesh refinement several time steps in advance. Because of the high accuracy and small demand on computational time explicit time integration is used for all elements of the coarse mesh. To avoid subcycling on vector- and parallel-computers all parts of the mesh with local mesh refinement and a Courant-number less than 1 are treated implicitly with the same time step using an implicit-explicit algorithm. 2 Implicit-Explicit Time Integration The solution of the initial value problem of the semidiscrete equation of motion Mu + Cii-f Ku = F (1) is the displacement u = u(t) that fulfills the differential equation and the initial conditions. Time integration procedures only consider the differential equation at discrete times tn with the approximations u^, v^ and a^ for the functions u(tn)<, u(tn) and u(tn) and an approximation error depending on the difference procedure [4] The integration procedures of the Newmark family use the following relations to get a solution at the new time step tn+i'- + CVn+l + KUn+1 (2) Un+1 = Un+A*Vn+ [(l-2/?)an + 2/?«In+l] (3) Vn+1 = with the Newmark parameter 7 and /?. The unknown acceleration an+i of the implicit scheme results from the solution of the equation (M + 7 AtC + /?A**K)an+i = F*+i - Cv*+i - Kiin+i (5)
3 with the predictor term: High Performance Computing and the corrector term: -2/3K (6) (7) +i (8) i (9) For (3 = 0 and 7 = the Newmark predictor-corrector scheme becomes an explicit scheme identical to the central difference method with the temporally discrete equation of motion + CVn+l + KQn+l = F*+i (10) with the diagonal matrix M. As long as M is diagonal, a^+i may be determined from this without solving equations. The implementation of the Newmark method as an implicit-explicit scheme allows part of the mesh to be treated implicitly and part to be treated explicitly [3]. This has considerable practical advantages in that 'stiff' subdomains of large finite element models can be treated economically with an implicit integrator if the Courant-number is larger than 1. When using the implicit-explicit method the elements of a finite element model are devided into two groups: the implicit elements and the explicit elements. The system matrices contain explicit and implicit groups: with the equation of motion M = M' + M^ (ii) C = C' + C^ (12) K = K' + K* (13) F = F' + F* (14) M*n+l + C'Vn+l + CfVm+i + K'll^+i + K Un+l = Fn+1 (15) where the implicit arrays multiply corrector values, whereas explicit arrays multiply predictor values. With (6) and (7) the equation to determine the acceration a^+i is: i (16) with M* = M + 7A*C' + /3A**K' (17)
4 2 1 6 High Performance Computing Starting with a coarse reference mesh and a time step based upon the maximum frequency of the spectrum, the explicit time integration procedure is used because of high accuracy and only small computational costs. The time step of the explicit procedure must be equal or less than the critical time step of the elements. Refined parts of the mesh with small elements and the Courant-number larger than 1 are treated implicitly with the same time step for the whole system. It is an advantage especially on high-performance computers like vectorand parallel-computers to use the same time step without subcycling. On vector-computers subcycling means additional calculations on a part of the whole mesh with short vector length and on parallel-computers domain decomposition with local subcycling and date dependency is not very efficient. 3 Time Dependent Adaptive FEM The local approximation errors of a FE-solution can be described with the numerical approximation u of the exact displacement vector u: or in terms of stresses: eu = u-u (18) e, = <7-<7 (19) The energy norm of the error is an integral scalar quantity of the domain H and is defined for elasticity problems in stresses as: - - )*D- V - *)<*«* (20) with the elasticity matrix D This error is related to the strain energy of the problem. The approximation errors decrease as the size of the subdivision of the FE-mesh gets smaller with the so called h-refinement. As in most cases the exact solutions of a are not known, the error estimation after Zienkiewicz-Zhu [6] uses an improved approximation a* (f.e. by averaging of discontinuous stresses <j) and the errors in stresses are estimated errors: e* = y_-& (21) In an optimal mesh the distribution of the local energy norm error e, of any element i should be equal between all elements. To achieve this each element i of the m elements is to be refined, if the local error \\e\\i is not smaller than the desired average error 6m- e, <,("*"' + "*"')* = ^ (22) with the desired relative percentage error r\ of the energy norm and the relation: m l? (23)
5 High Performance Computing In dynamic problems the total error of the problem consists of the error of the potential energy and the error of the kinetic energy. E = E, + & (24) It is obvious that the error of the total energy of the dynamic problem mainly depends on the error of the FE-discretization if the time step of the integration procedure is small enough for all frequencies of the problem and it is known that the error of the kinetic energy from spatial discretization in general is much smaller than the error of the potential energy. An error estimate for the semidiscrete hyperbolic problem is given in [3] and [5]. It shows that in the case of mesh refinements the rate of convergence of the potential energy is one order smaller than the rate of the kinetic energy. Thus the rate of convergence of the total energy is mainly dependent on the potential energy and the Zienkiewicz-Zhu [6] error estimator is also applicable to hyperbolic problems with time dependent adaptive mesh refinement. 4 Intensity Indicator As most of the computational time is wasted with mesh refinement procedures and expensive system setup a method is developed [2] to estimate all elements and regions that are to be refined, several time steps in advance. The expected direction of the energy flow and the propagation of the different kind of waves in 2- and 3-dimensional systems can be described by intensity vectors and the moving wave front can be used for a broad time dependent mesh refinement in advance. The intensity of a wavefieldshows the transport of energy per time and area. The intensity vector gives informations about the local change of energy and the direction of energy flow. The total energy E of a domain ft consists of the potential energy Ep and the kinetic energy E&: with the potential energy the kinetic energy E=Ep4-Et (25) #? = g / c,jw%^%t,;<m, (26) LJ J \i & = o / m,?wn, (27) z Vn and the elastic tensor Cijki [1] the power of the wave front is: de r -i^- = y W%6, 4- c,;wt/ij%t,f)dn (28)
6 218 High Performance Computing Together with the fundamental equation: pi/, = 0\j-,j = < (29) and Hooke's law the equation (28) yields: (30) (31) (32) With the definition [2] of the component Ij of the intensity vector I: it follows (34) 1* In the case of stationary processes it is usual to use mean values of time averages. For transient dynamic problems and wave propagation problems it is more suitable to use the instantaneous intensity vector. The intensity components /^, Iy and /^ of element k of a 3-dimensional FE-model are: (33) 'xy (7, TXZ TV (35) In x-direction this is: These intensity components describe the direction of the instantaneous energy flow of each element. The wave front propagates in this direction in the next time steps and also the zone with mesh refinements. This allows to estimate the zone with all elements that are to be refined several time steps in advance. With the maximum wave propagation velocity CL (36) CL =. (1 -i/-2i/2) (37) the propagation of the refinement zone is (38)
7 High Performance Computing The a-posteriori Zienkiewicz-Zhu error indicator is only used to control if the refinement is sufficient or not. This does not lead to optimized FE-meshes, like meshes of adaptive FE-methods for static problems, but it saves a lot of computational time, if the estimated mesh is sufficient for several time steps. A broad time dependent mesh refinement for several time steps is more efficient than several steps of mesh refinement. 5 Example The example of Fig. 1 shows a cantilever beam of steel of W / H / L 10 / 250 / 1000 mrn with the free right hand end subjected to a vertical pulse load of P = 2.0/cTV and TS = 0.040ms duration with a broad frequency range. The material constants are: i/ = 0,3 The initial 2-dimensional FE-mesh from automatic mesh generation of Fig. 1 shows 142 nodes and 232 isoparametric elements. With regard to the frequency range the time step is set to 0.001ms with explicit time integration for all elements. The aim of the time dependent FE-mesh refinement is to limit the relative energy norm error 77 to about 15 % in each element for all time steps. The mesh refinement procedure is only activated every 5 time steps. After this the a-posteriori Zienkiewicz-Zhu error estimator ist used to control the last mesh refinement. If it is not sufficient, the last 5 time steps are repeated with a corrected mesh refinement. To avoid this additional costs a broad refinement is used. Figure 2 shows the adaptive FE-mesh with 260 nodes and 450 elements after 20 time steps with refined elements in the upper right corner of the system below the driving point of the load. The instantaneous intensity vectors of Fig. 3 visualize the energy flow at that time. For direct time integration the implicit-explicit algorithm is used, based upon operator splitting and mesh partitions. Domains with the original coarse mesh are treated explicitly whereas all refined elements are treated implicitly with the same original time step. This avoids expensive subcycling on vector- and parallel-computers. The simulation in Fig. 4 shows the horizontal normal stresses of the beam within the travelling waves after 50 time steps. The time dependent adaptive mesh in Fig. 5 shows 504 nodes and 919 elements. It is obvious that this adaptive FE-method with a-priori intensity indicator does not lead to optimized FE-meshes with an equal distribution of the
8 220 High Performance Computing discretization error but it is a very efficient solution method if the estimated mesh is sufficient for several time steps. The demand on CPU-time and on storage depends on the number of degrees of freedom of the system. In Fig. 6 the CPU-time of the time dependent adaptive FE-method with intensity indicator and implicit-explicit time integration of 100 time steps is related and compared to the CPU-time of a completely refined system ( = 100 %). The costs of the adaptive solution depends on the number of intermediate time steps between the steps of mesh refinement. Figure 6 shows that adaptive mesh refinement after each time step is very unefficient but leads to optimal meshes and takes even more time than the completely refined problem without adaptivity. There is a minimum of only 25 % CPUtime in this example when using about 5 to 10 intermediate time steps. In the case of large problems it is possible to reduce the computational time of transient adaptive solutions with intensity indicator and Zienkiewicz- Zhu error indicator on high-performance computers down to about 20-10% of a conventional FE-solution. Figure 1: Initial FE-mesh with 142 nodes and 232 triangle elements Figure 2: Adaptive refined mesh 20 time steps after the pulse load with 260 nodes and 450 elements
9 High Performance Computing 221 Figure 3: Instantaneous intensity vectors and energy flow after 20 time steps Figure 4: Horizontal normal stresses in N/m* after 50 time steps Figure 5: Refined mesh after 50 time steps with 504 nodes and 919 elements
10 222 High Performance Computing ReJat. CPU-Time i?n (%] S*R: iso Ref: 100. _ 80. _ i 60. _ 40. _ 20. _ \^ ^. iterat. _ intermediate time ste 2 TOTAL CPU-TIME adaptive transient FEM Figure 6: Relative costs of the adaptive solution to the conventional solution References [1] Achenbach, J.D.: Wave Propagation in Elastic Solids, North-Holland Publishing Company, Amsterdam, New York, Oxford (1980). [2] Elmer, K.-H.: Optimierung numerischer FE-Modelle zur Simulation der Wellenausbreitung mit Vektor- und Parallelrechnern (Optimization of Numerical FE-Models for Simulating Wave Propagation on Vector and Parallel Computers), DFG-Report NA 139/17-2, Curt-Risch- Institut, Hannover [3] Hughes, T.J.R.: The Finite Element Method, Prentice-Hall, Englewood Cliffs, N.J., (1989). [4] Natke, H.G.: Baudynamik, B.C. Teubner, Stuttgart, (1989). [5] Strang, G. and G.J.Fix: An Analysis of the Finite Element Methods, Prentice-Hall, Englewood Cliffs, N.J., (1973). [6] Zienkiewicz, O.C. and J.Z.Zhu: A Simple Error Estimator and Adaptive Procedure for Practical Engineering Analysis, Int. J. Numer. Methods Eng., 24, (1987).
Finite Element Method. Chapter 7. Practical considerations in FEM modeling
Finite Element Method Chapter 7 Practical considerations in FEM modeling Finite Element Modeling General Consideration The following are some of the difficult tasks (or decisions) that face the engineer
More informationcourse outline basic principles of numerical analysis, intro FEM
idealization, equilibrium, solutions, interpretation of results types of numerical engineering problems continuous vs discrete systems direct stiffness approach differential & variational formulation introduction
More informationComparison of implicit and explicit nite element methods for dynamic problems
Journal of Materials Processing Technology 105 (2000) 110±118 Comparison of implicit and explicit nite element methods for dynamic problems J.S. Sun, K.H. Lee, H.P. Lee * Department of Mechanical and Production
More informationChapter 7 Practical Considerations in Modeling. Chapter 7 Practical Considerations in Modeling
CIVL 7/8117 1/43 Chapter 7 Learning Objectives To present concepts that should be considered when modeling for a situation by the finite element method, such as aspect ratio, symmetry, natural subdivisions,
More informationExplicit\Implicit time Integration in MPM\GIMP. Abilash Nair and Samit Roy University of Alabama, Tuscaloosa
Explicit\Implicit time Integration in MPM\GIMP Abilash Nair and Samit Roy University of Alabama, Tuscaloosa Objectives Develop a Implicit algorithm for GIMP based on Implicit MPM* Benchmark the algorithm
More informationCHAPTER 1. Introduction
ME 475: Computer-Aided Design of Structures 1-1 CHAPTER 1 Introduction 1.1 Analysis versus Design 1.2 Basic Steps in Analysis 1.3 What is the Finite Element Method? 1.4 Geometrical Representation, Discretization
More informationFinite Element Analysis Prof. Dr. B. N. Rao Department of Civil Engineering Indian Institute of Technology, Madras. Lecture - 36
Finite Element Analysis Prof. Dr. B. N. Rao Department of Civil Engineering Indian Institute of Technology, Madras Lecture - 36 In last class, we have derived element equations for two d elasticity problems
More informationAdaptive numerical methods
METRO MEtallurgical TRaining On-line Adaptive numerical methods Arkadiusz Nagórka CzUT Education and Culture Introduction Common steps of finite element computations consists of preprocessing - definition
More informationME 345: Modeling & Simulation. Introduction to Finite Element Method
ME 345: Modeling & Simulation Introduction to Finite Element Method Examples Aircraft 2D plate Crashworthiness 2 Human Heart Gears Structure Human Spine 3 F.T. Fisher, PhD Dissertation, 2002 Fluid Flow
More informationRevised Sheet Metal Simulation, J.E. Akin, Rice University
Revised Sheet Metal Simulation, J.E. Akin, Rice University A SolidWorks simulation tutorial is just intended to illustrate where to find various icons that you would need in a real engineering analysis.
More informationVisualization of errors of finite element solutions P. Beckers, H.G. Zhong, Ph. Andry Aerospace Department, University of Liege, B-4000 Liege, Belgium
Visualization of errors of finite element solutions P. Beckers, H.G. Zhong, Ph. Andry Aerospace Department, University of Liege, B-4000 Liege, Belgium Abstract The aim of this paper is to show how to use
More informationThe Finite Element Method for the Analysis of Non-Linear and Dynamic Systems. Prof. Dr. Eleni Chatzi, J.P. Escallo n Lecture December, 2013
The Finite Element Method for the Analysis of Non-Linear and Dynamic Systems Prof. Dr. Eleni Chatzi, J.P. Escallo n Lecture 11-17 December, 2013 Institute of Structural Engineering Method of Finite Elements
More informationNon-Linear Finite Element Methods in Solid Mechanics Attilio Frangi, Politecnico di Milano, February 3, 2017, Lesson 1
Non-Linear Finite Element Methods in Solid Mechanics Attilio Frangi, attilio.frangi@polimi.it Politecnico di Milano, February 3, 2017, Lesson 1 1 Politecnico di Milano, February 3, 2017, Lesson 1 2 Outline
More informationModeling Strategies for Dynamic Finite Element Cask Analyses
Session A Package Analysis: Structural Analysis - Modeling Modeling Strategies for Dynamic Finite Element Cask Analyses Uwe Zencker, Günter Wieser, Linan Qiao, Christian Protz BAM Federal Institute for
More informationLoad Balancing for Problems with Good Bisectors, and Applications in Finite Element Simulations
Load Balancing for Problems with Good Bisectors, and Applications in Finite Element Simulations Stefan Bischof, Ralf Ebner, and Thomas Erlebach Institut für Informatik Technische Universität München D-80290
More informationPartial Differential Equations
Simulation in Computer Graphics Partial Differential Equations Matthias Teschner Computer Science Department University of Freiburg Motivation various dynamic effects and physical processes are described
More informationApplication of Finite Volume Method for Structural Analysis
Application of Finite Volume Method for Structural Analysis Saeed-Reza Sabbagh-Yazdi and Milad Bayatlou Associate Professor, Civil Engineering Department of KNToosi University of Technology, PostGraduate
More informationAdaptive Isogeometric Analysis by Local h-refinement with T-splines
Adaptive Isogeometric Analysis by Local h-refinement with T-splines Michael Dörfel 1, Bert Jüttler 2, Bernd Simeon 1 1 TU Munich, Germany 2 JKU Linz, Austria SIMAI, Minisymposium M13 Outline Preliminaries:
More informationINTEGRATION SCHEMES FOR THE TRANSIENT DYNAMICS OF NONLINEAR CABLE STRUCTURES
6th European Conference on Computational Mechanics (ECCM 6) 7th European Conference on Computational Fluid Dynamics (ECFD 7) 1115 June 2018, Glasgow, UK INTEGRATION SCHEMES FOR THE TRANSIENT DYNAMICS OF
More informationTransactions on Modelling and Simulation vol 20, 1998 WIT Press, ISSN X
r-adaptive boundary element method Eisuke Kita, Kenichi Higuchi & Norio Kamiya Department of Mechano-Informatics and Systems, Nagoya University, Nagoya 464-01, Japan Email: kita@mech.nagoya-u.ac.jp Abstract
More information13.472J/1.128J/2.158J/16.940J COMPUTATIONAL GEOMETRY
13.472J/1.128J/2.158J/16.940J COMPUTATIONAL GEOMETRY Lecture 23 Dr. W. Cho Prof. N. M. Patrikalakis Copyright c 2003 Massachusetts Institute of Technology Contents 23 F.E. and B.E. Meshing Algorithms 2
More informationOverview of the High-Order ADER-DG Method for Numerical Seismology
CIG/SPICE/IRIS/USAF WORKSHOP JACKSON, NH October 8-11, 2007 Overview of the High-Order ADER-DG Method for Numerical Seismology 1, Michael Dumbser2, Josep de la Puente1, Verena Hermann1, Cristobal Castro1
More informationACCURACY OF NUMERICAL SOLUTION OF HEAT DIFFUSION EQUATION
Scientific Research of the Institute of Mathematics and Computer Science ACCURACY OF NUMERICAL SOLUTION OF HEAT DIFFUSION EQUATION Ewa Węgrzyn-Skrzypczak, Tomasz Skrzypczak Institute of Mathematics, Czestochowa
More informationA Finite Element Method for Deformable Models
A Finite Element Method for Deformable Models Persephoni Karaolani, G.D. Sullivan, K.D. Baker & M.J. Baines Intelligent Systems Group, Department of Computer Science University of Reading, RG6 2AX, UK,
More informationFinite element method - tutorial no. 1
Martin NESLÁDEK Faculty of mechanical engineering, CTU in Prague 11th October 2017 1 / 22 Introduction to the tutorials E-mail: martin.nesladek@fs.cvut.cz Room no. 622 (6th floor - Dept. of mechanics,
More informationCS205b/CME306. Lecture 9
CS205b/CME306 Lecture 9 1 Convection Supplementary Reading: Osher and Fedkiw, Sections 3.3 and 3.5; Leveque, Sections 6.7, 8.3, 10.2, 10.4. For a reference on Newton polynomial interpolation via divided
More informationContinued Fraction Absorbing Boundary Conditions for Transient Elastic Wave Propagation Modeling
Continued Fraction Absorbing Boundary Conditions for Transient Elastic Wave Propagation Modeling Md Anwar Zahid and Murthy N. Guddati 1 Summary This paper presents a novel absorbing boundary condition
More informationSeven Techniques For Finding FEA Errors
Seven Techniques For Finding FEA Errors by Hanson Chang, Engineering Manager, MSC.Software Corporation Design engineers today routinely perform preliminary first-pass finite element analysis (FEA) on new
More informationA substructure based parallel dynamic solution of large systems on homogeneous PC clusters
CHALLENGE JOURNAL OF STRUCTURAL MECHANICS 1 (4) (2015) 156 160 A substructure based parallel dynamic solution of large systems on homogeneous PC clusters Semih Özmen, Tunç Bahçecioğlu, Özgür Kurç * Department
More informationADAPTIVE APPROACH IN NONLINEAR CURVE DESIGN PROBLEM. Simo Virtanen Rakenteiden Mekaniikka, Vol. 30 Nro 1, 1997, s
ADAPTIVE APPROACH IN NONLINEAR CURVE DESIGN PROBLEM Simo Virtanen Rakenteiden Mekaniikka, Vol. 30 Nro 1, 1997, s. 14-24 ABSTRACT In recent years considerable interest has been shown in the development
More informationNUMERICAL COUPLING BETWEEN DEM (DISCRETE ELEMENT METHOD) AND FEA (FINITE ELEMENTS ANALYSIS).
NUMERICAL COUPLING BETWEEN DEM (DISCRETE ELEMENT METHOD) AND FEA (FINITE ELEMENTS ANALYSIS). Daniel Schiochet Nasato - ESSS Prof. Dr. José Roberto Nunhez Unicamp Dr. Nicolas Spogis - ESSS Fabiano Nunes
More informationEffectiveness of Element Free Galerkin Method over FEM
Effectiveness of Element Free Galerkin Method over FEM Remya C R 1, Suji P 2 1 M Tech Student, Dept. of Civil Engineering, Sri Vellappaly Natesan College of Engineering, Pallickal P O, Mavelikara, Kerala,
More informationSHAPE SENSITIVITY ANALYSIS INCLUDING QUALITY CONTROL WITH CARTESIAN FINITE ELEMENT MESHES
VI International Conference on Adaptive Modeling and Simulation ADMOS 2013 J. P. Moitinho de Almeida, P. Díez, C. Tiago and N. Parés (Eds) SHAPE SENSITIVITY ANALYSIS INCLUDING QUALITY CONTROL WITH CARTESIAN
More informationLETTERS TO THE EDITOR
INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, VOL. 7, 135-141 (1983) LETTERS TO THE EDITOR NUMERICAL PREDICTION OF COLLAPSE LOADS USING FINITE ELEMENT METHODS by S. W. Sloan
More informationAircraft Impact Analysis of New York World Trade Center Tower by Using the ASI-Gauss Technique
Proceeding of ICCES 05, 1-10 December 2005, INDIA 1212 Aircraft Impact Analysis of New York World Trade Center Tower by Using the ASI-Gauss Technique D. Isobe 1 and K. M. Lynn 2 Summary In this paper,
More informationAnalysis of Pile Behaviour due to Damped Vibration by Finite Element Method (FEM)
ISSN 2395-1621 Analysis of Pile Behaviour due to Damped Vibration by Finite Element Method (FEM) #1 L.M.Sardesai, #2 G.A.Kadam 1 sardesaileena@rediffmail.com.com 2 ganeshkadam07@gmail.com #1 Mechanical
More informationAvailable online at ScienceDirect. Procedia Engineering 90 (2014 )
Available online at www.sciencedirect.com ScienceDirect Procedia Engineering 90 (2014 ) 288 293 10th International Conference on Mechanical Engineering, ICME 2013 Parallelization of enriched free mesh
More informationCoupled analysis of material flow and die deflection in direct aluminum extrusion
Coupled analysis of material flow and die deflection in direct aluminum extrusion W. Assaad and H.J.M.Geijselaers Materials innovation institute, The Netherlands w.assaad@m2i.nl Faculty of Engineering
More informationContents. I The Basic Framework for Stationary Problems 1
page v Preface xiii I The Basic Framework for Stationary Problems 1 1 Some model PDEs 3 1.1 Laplace s equation; elliptic BVPs... 3 1.1.1 Physical experiments modeled by Laplace s equation... 5 1.2 Other
More informationStatic and Dynamic Analysis Of Reed Valves Using a Minicomputer Based Finite Element Systems
Purdue University Purdue e-pubs International Compressor Engineering Conference School of Mechanical Engineering 1980 Static and Dynamic Analysis Of Reed Valves Using a Minicomputer Based Finite Element
More informationNUMERICAL MODELING OF DISPERSION PHENOMENA IN THICK PLATE
NUMERICAL MODELING OF DISPERSION PHENOMENA IN THICK PLATE Petr Hora, Jiří Michálek Abstract This paper report on a technique for the analysis of propagating multimode signals. The method involves a -D
More informationIntroduction to Finite Element Method
Guest Lecture in Prodi Teknik Sipil Introduction to Finite Element Method Wong Foek Tjong, Ph.D. Petra Christian University Surabaya Lecture Outline 1. Overview of the FEM 2. Computational steps of the
More informationCorrected/Updated References
K. Kashiyama, H. Ito, M. Behr and T. Tezduyar, "Massively Parallel Finite Element Strategies for Large-Scale Computation of Shallow Water Flows and Contaminant Transport", Extended Abstracts of the Second
More informationA Multiple Constraint Approach for Finite Element Analysis of Moment Frames with Radius-cut RBS Connections
A Multiple Constraint Approach for Finite Element Analysis of Moment Frames with Radius-cut RBS Connections Dawit Hailu +, Adil Zekaria ++, Samuel Kinde +++ ABSTRACT After the 1994 Northridge earthquake
More informationExample 24 Spring-back
Example 24 Spring-back Summary The spring-back simulation of sheet metal bent into a hat-shape is studied. The problem is one of the famous tests from the Numisheet 93. As spring-back is generally a quasi-static
More informationThe numerical simulation of complex PDE problems. A numerical simulation project The finite element method for solving a boundary-value problem in R 2
Universidad de Chile The numerical simulation of complex PDE problems Facultad de Ciencias Físicas y Matemáticas P. Frey, M. De Buhan Year 2008 MA691 & CC60X A numerical simulation project The finite element
More informationScientific Manual FEM-Design 17.0
Scientific Manual FEM-Design 17. 1.4.6 Calculations considering diaphragms All of the available calculation in FEM-Design can be performed with diaphragms or without diaphragms if the diaphragms were defined
More informationLagrangian and Eulerian Representations of Fluid Flow: Kinematics and the Equations of Motion
Lagrangian and Eulerian Representations of Fluid Flow: Kinematics and the Equations of Motion James F. Price Woods Hole Oceanographic Institution Woods Hole, MA, 02543 July 31, 2006 Summary: This essay
More informationThe Dynamic Response of an Euler-Bernoulli Beam on an Elastic Foundation by Finite Element Analysis using the Exact Stiffness Matrix
Journal of Physics: Conference Series The Dynamic Response of an Euler-Bernoulli Beam on an Elastic Foundation by Finite Element Analysis using the Exact Stiffness Matrix To cite this article: Jeong Soo
More informationFinite Element Analysis of Dynamic Flapper Valve Stresses
Purdue University Purdue e-pubs International Compressor Engineering Conference School of Mechanical Engineering 2000 Finite Element Analysis of Dynamic Flapper Valve Stresses J. R. Lenz Tecumseh Products
More informationLASer Cavity Analysis and Design
The unique combination of simulation tools for LASer Cavity Analysis and Design During the last 15 years LASCAD has become industry-leading so ware for LASer Cavity Analysis and Design. The feedback from
More informationIntroduction to the Finite Element Method (3)
Introduction to the Finite Element Method (3) Petr Kabele Czech Technical University in Prague Faculty of Civil Engineering Czech Republic petr.kabele@fsv.cvut.cz people.fsv.cvut.cz/~pkabele 1 Outline
More informationEuropean Hyperworks Technology Conference 2010 Mesh and orientation dependance of FE models for dynamic simulations.
European Hyperworks Technology Conference 2010 Mesh and orientation dependance of FE models for dynamic simulations. Sébastien ROTH Jennifer OUDRY Hossein SHAKOURZADEH Influence of mesh density on a finite
More informationRevision of the SolidWorks Variable Pressure Simulation Tutorial J.E. Akin, Rice University, Mechanical Engineering. Introduction
Revision of the SolidWorks Variable Pressure Simulation Tutorial J.E. Akin, Rice University, Mechanical Engineering Introduction A SolidWorks simulation tutorial is just intended to illustrate where to
More informationEFFICIENCY OF HIGHER ORDER FINITE ELEMENTS FOR THE ANALYSIS OF SEISMIC WAVE PROPAGATION
EFFICIENCY OF HIGHER ORDER FINITE ELEMENTS FOR THE ANALYSIS OF SEISMIC WAVE PROPAGATION Jean-François Semblat, J. J. Brioist To cite this version: Jean-François Semblat, J. J. Brioist. EFFICIENCY OF HIGHER
More informationBackward facing step Homework. Department of Fluid Mechanics. For Personal Use. Budapest University of Technology and Economics. Budapest, 2010 autumn
Backward facing step Homework Department of Fluid Mechanics Budapest University of Technology and Economics Budapest, 2010 autumn Updated: October 26, 2010 CONTENTS i Contents 1 Introduction 1 2 The problem
More informationSeismic Soil-Structure Interaction Analysis of the Kealakaha Stream Bridge on Parallel Computers
Seismic Soil-Structure Interaction Analysis of the Kealakaha Stream Bridge on Parallel Computers Seung Ha Lee and Si-Hwan Park Department of Civil and Environmental Engineering University of Hawaii at
More informationFederal Institute for Materials Research and Testing (BAM), Unter den Eichen 87, Berlin, Germany
Jannis Bulling 1, Jens Prager 1, Fabian Krome 1 1 Federal Institute for Materials Research and Testing (BAM), Unter den Eichen 87, 12205 Berlin, Germany Abstract: This paper addresses the computation of
More informationThe Level Set Method applied to Structural Topology Optimization
The Level Set Method applied to Structural Topology Optimization Dr Peter Dunning 22-Jan-2013 Structural Optimization Sizing Optimization Shape Optimization Increasing: No. design variables Opportunity
More informationChallenge Problem 5 - The Solution Dynamic Characteristics of a Truss Structure
Challenge Problem 5 - The Solution Dynamic Characteristics of a Truss Structure In the final year of his engineering degree course a student was introduced to finite element analysis and conducted an assessment
More informationComputational methods - modelling and simulation
Computational methods - modelling and simulation J. Pamin With thanks to: Authors of presented simulations C.A. Felippa (Univ. of Colorado at Boulder) www.colorado.edu/engineering/cas/courses.d/ifem.d
More informationRecent Developments in Isogeometric Analysis with Solid Elements in LS-DYNA
Recent Developments in Isogeometric Analysis with Solid Elements in LS-DYNA Liping Li David Benson Attila Nagy Livermore Software Technology Corporation, Livermore, CA, USA Mattia Montanari Nik Petrinic
More informationINTERNATIONAL JOURNAL OF CIVIL AND STRUCTURAL ENGINEERING Volume 2, No 3, 2012
INTERNATIONAL JOURNAL OF CIVIL AND STRUCTURAL ENGINEERING Volume 2, No 3, 2012 Copyright 2010 All rights reserved Integrated Publishing services Research article ISSN 0976 4399 Efficiency and performances
More informationIndex. C m (Ω), 141 L 2 (Ω) space, 143 p-th order, 17
Bibliography [1] J. Adams, P. Swarztrauber, and R. Sweet. Fishpack: Efficient Fortran subprograms for the solution of separable elliptic partial differential equations. http://www.netlib.org/fishpack/.
More informationu = v is the Laplacian and represents the sum of the second order derivatives of the wavefield spatially.
Seismic Elastic Modelling Satinder Chopra, Arcis Corporation, Calgary, Canada Summary Seismic modeling experiments were performed to understand the seismic responses associated with a variety of subsurface
More informationDriven Cavity Example
BMAppendixI.qxd 11/14/12 6:55 PM Page I-1 I CFD Driven Cavity Example I.1 Problem One of the classic benchmarks in CFD is the driven cavity problem. Consider steady, incompressible, viscous flow in a square
More informationMEEN 3360 Engineering Design and Simulation Spring 2016 Homework #1 This homework is due Tuesday, February 2, From your book and other
MEEN 3360 Engineering Design and Simulation Spring 2016 Homework #1 This homework is due Tuesday, February 2, 2016 1.0 From your book and other sources, write a paragraph explaining CFD and finite element
More informationReduction of Finite Element Models for Explicit Car Crash Simulations
Reduction of Finite Element Models for Explicit Car Crash Simulations K. Flídrová a,b), D. Lenoir a), N. Vasseur b), L. Jézéquel a) a) Laboratory of Tribology and System Dynamics UMR-CNRS 5513, Centrale
More informationTICAM - Texas Institute for Computational and Applied Mathematics. The University of Texas at Austin. Taylor Hall Abstract
A New Cloud-Based hp Finite Element Method J. T. Oden, C. A. M. Duarte y and O. C. Zienkiewicz z TICAM - Texas Institute for Computational and Applied Mathematics The University of Texas at Austin Taylor
More informationAnalysis of Fluid-Structure Interaction Effects of Liquid-Filled Container under Drop Testing
Kasetsart J. (Nat. Sci.) 42 : 165-176 (2008) Analysis of Fluid-Structure Interaction Effects of Liquid-Filled Container under Drop Testing Chakrit Suvanjumrat*, Tumrong Puttapitukporn and Satjarthip Thusneyapan
More informationA PHYSICAL SIMULATION OF OBJECTS BEHAVIOUR BY FINITE ELEMENT METHOD, MODAL MATCHING AND DYNAMIC EQUILIBRIUM EQUATION
A PHYSICAL SIMULATION OF OBJECTS BEHAVIOUR BY FINITE ELEMENT METHOD, MODAL MATCHING AND DYNAMIC EQUILIBRIUM EQUATION Raquel Ramos Pinho, João Manuel R. S. Tavares FEUP Faculty of Engineering, University
More informationMetafor FE Software. 2. Operator split. 4. Rezoning methods 5. Contact with friction
ALE simulations ua sus using Metafor eao 1. Introduction 2. Operator split 3. Convection schemes 4. Rezoning methods 5. Contact with friction 1 Introduction EULERIAN FORMALISM Undistorted mesh Ideal for
More informationIntroduction to Finite Element Analysis using ANSYS
Introduction to Finite Element Analysis using ANSYS Sasi Kumar Tippabhotla PhD Candidate Xtreme Photovoltaics (XPV) Lab EPD, SUTD Disclaimer: The material and simulations (using Ansys student version)
More informationExperiment 6 SIMULINK
Experiment 6 SIMULINK Simulink Introduction to simulink SIMULINK is an interactive environment for modeling, analyzing, and simulating a wide variety of dynamic systems. SIMULINK provides a graphical user
More informationInfluence of mesh density on a finite element model under dynamic loading Sébastien ROTH
Influence of mesh density on a finite element model under dynamic loading Sébastien ROTH Jennifer OUDRY Influence of mesh density on a finite element model under dynamic loading 1. Introduction 2. Theoretical
More informationRecent Advances on Higher Order 27-node Hexahedral Element in LS-DYNA
14 th International LS-DYNA Users Conference Session: Simulation Recent Advances on Higher Order 27-node Hexahedral Element in LS-DYNA Hailong Teng Livermore Software Technology Corp. Abstract This paper
More informationSPH: Why and what for?
SPH: Why and what for? 4 th SPHERIC training day David Le Touzé, Fluid Mechanics Laboratory, Ecole Centrale de Nantes / CNRS SPH What for and why? How it works? Why not for everything? Duality of SPH SPH
More informationBuckling of Rigid Frames I
CIVE.5120 Structural Stability (3-0-3) 02/28/17 Buckling of Rigid Frames I Prof. Tzuyang Yu Structural Engineering Research Group (SERG) Department of Civil and Environmental Engineering University of
More information2.7 Cloth Animation. Jacobs University Visualization and Computer Graphics Lab : Advanced Graphics - Chapter 2 123
2.7 Cloth Animation 320491: Advanced Graphics - Chapter 2 123 Example: Cloth draping Image Michael Kass 320491: Advanced Graphics - Chapter 2 124 Cloth using mass-spring model Network of masses and springs
More informationEXACT BUCKLING SOLUTION OF COMPOSITE WEB/FLANGE ASSEMBLY
EXACT BUCKLING SOLUTION OF COMPOSITE WEB/FLANGE ASSEMBLY J. Sauvé 1*, M. Dubé 1, F. Dervault 2, G. Corriveau 2 1 Ecole de technologie superieure, Montreal, Canada 2 Airframe stress, Advanced Structures,
More informationCOMPUTER AIDED ENGINEERING. Part-1
COMPUTER AIDED ENGINEERING Course no. 7962 Finite Element Modelling and Simulation Finite Element Modelling and Simulation Part-1 Modeling & Simulation System A system exists and operates in time and space.
More informationX-FEM based modelling of complex mixed mode fatigue crack propagation
X-FEM based modelling of complex mixed mode fatigue crack propagation Hans Minnebo 1, Simon André 2, Marc Duflot 1, Thomas Pardoen 2, Eric Wyart 1 1 Cenaero, Rue des Frères Wright 29, 6041 Gosselies, Belgium
More informationSimulation of Overhead Crane Wire Ropes Utilizing LS-DYNA
Simulation of Overhead Crane Wire Ropes Utilizing LS-DYNA Andrew Smyth, P.E. LPI, Inc., New York, NY, USA Abstract Overhead crane wire ropes utilized within manufacturing plants are subject to extensive
More informationNOISE PROPAGATION FROM VIBRATING STRUCTURES
NOISE PROPAGATION FROM VIBRATING STRUCTURES Abstract R. Helfrich, M. Spriegel (INTES GmbH, Germany) Noise and noise exposure are becoming more important in product development due to environmental legislation.
More informationStress Analysis of thick wall bellows using Finite Element Method
Stress Analysis of thick wall bellows using Finite Element Method Digambar J. Pachpande Post Graduate Student Department of Mechanical Engineering V.J.T.I. Mumbai, India Prof. G. U. Tembhare Assistant
More informationA-posteriori Diffusion Analysis of Numerical Schemes in Wavenumber Domain
2th Annual CFD Symposium, August 9-1, 218, Bangalore A-posteriori Diffusion Analysis of Numerical Schemes in Wavenumber Domain S. M. Joshi & A. Chatterjee Department of Aerospace Engineering Indian Institute
More informationAdaptive Surface Modeling Using a Quadtree of Quadratic Finite Elements
Adaptive Surface Modeling Using a Quadtree of Quadratic Finite Elements G. P. Nikishkov University of Aizu, Aizu-Wakamatsu 965-8580, Japan niki@u-aizu.ac.jp http://www.u-aizu.ac.jp/ niki Abstract. This
More informationMedical Image Segmentation using Level Sets
Medical Image Segmentation using Level Sets Technical Report #CS-8-1 Tenn Francis Chen Abstract Segmentation is a vital aspect of medical imaging. It aids in the visualization of medical data and diagnostics
More informationTAU mesh deformation. Thomas Gerhold
TAU mesh deformation Thomas Gerhold The parallel mesh deformation of the DLR TAU-Code Introduction Mesh deformation method & Parallelization Results & Applications Conclusion & Outlook Introduction CFD
More informationDevelopment of a Maxwell Equation Solver for Application to Two Fluid Plasma Models. C. Aberle, A. Hakim, and U. Shumlak
Development of a Maxwell Equation Solver for Application to Two Fluid Plasma Models C. Aberle, A. Hakim, and U. Shumlak Aerospace and Astronautics University of Washington, Seattle American Physical Society
More informationCHAPTER-10 DYNAMIC SIMULATION USING LS-DYNA
DYNAMIC SIMULATION USING LS-DYNA CHAPTER-10 10.1 Introduction In the past few decades, the Finite Element Method (FEM) has been developed into a key indispensable technology in the modeling and simulation
More informationGEOMETRY-BASED VIRTUAL MODEL VARIANTS FOR SHAPE OPTIMIZATION AND CAD REFEED
GEOMETRY-BASED VIRTUAL MODEL VARIANTS FOR SHAPE OPTIMIZATION AND CAD REFEED *Dr. Werner Pohl, ** Prof. Dr. Klemens Rother *Fast Concept Modelling & Simulation (FCMS) GmbH, Munich, Germany, **University
More informationChapter 1 Introduction
Chapter 1 Introduction GTU Paper Analysis (New Syllabus) Sr. No. Questions 26/10/16 11/05/16 09/05/16 08/12/15 Theory 1. What is graphic standard? Explain different CAD standards. 2. Write Bresenham s
More informationAMS527: Numerical Analysis II
AMS527: Numerical Analysis II A Brief Overview of Finite Element Methods Xiangmin Jiao SUNY Stony Brook Xiangmin Jiao SUNY Stony Brook AMS527: Numerical Analysis II 1 / 25 Overview Basic concepts Mathematical
More informationOptimised corrections for finite-difference modelling in two dimensions
Optimized corrections for 2D FD modelling Optimised corrections for finite-difference modelling in two dimensions Peter M. Manning and Gary F. Margrave ABSTRACT Finite-difference two-dimensional correction
More informationAnalysis of Distortion Parameters of Eight node Serendipity Element on the Elements Performance
Analysis of Distortion Parameters of Eight node Serendipity Element on the Elements Performance Vishal Jagota & A. P. S. Sethi Department of Mechanical Engineering, Shoolini University, Solan (HP), India
More informationModule 1: Introduction to Finite Element Analysis. Lecture 4: Steps in Finite Element Analysis
25 Module 1: Introduction to Finite Element Analysis Lecture 4: Steps in Finite Element Analysis 1.4.1 Loading Conditions There are multiple loading conditions which may be applied to a system. The load
More informationADAPTIVE FINITE ELEMENT
Finite Element Methods In Linear Structural Mechanics Univ. Prof. Dr. Techn. G. MESCHKE SHORT PRESENTATION IN ADAPTIVE FINITE ELEMENT Abdullah ALSAHLY By Shorash MIRO Computational Engineering Ruhr Universität
More informationarxiv: v1 [math.na] 26 Jun 2014
for spectrally accurate wave propagation Vladimir Druskin, Alexander V. Mamonov and Mikhail Zaslavsky, Schlumberger arxiv:406.6923v [math.na] 26 Jun 204 SUMMARY We develop a method for numerical time-domain
More informationParametric Study of Engine Rigid Body Modes
Parametric Study of Engine Rigid Body Modes Basem Alzahabi and Samir Nashef C. S. Mott Engineering and Science Center Dept. Mechanical Engineering Kettering University 17 West Third Avenue Flint, Michigan,
More information