Reiner Anderl, Peter Binde Simulations with NX Reiner Anderl Peter Binde Simulations with NX Kinematics, FEA, CFD, EM and Data Management With numerous examples of NX The authors: Prof Dr.-Ing Reiner Anderl, Technische Universität Darmstadt Peter Binde, Dr Binde Ingenieure, Design & Engineering GmbH, Wiesbaden Translated by the authors with the help of Dimitri Albert, Jan Helge Bøhn, Martin Geyer and Andreas Rauschnabel Distributed in North and South America by Hanser Publications 6915 Valley Avenue, Cincinnati, Ohio 45244-3029, USA Fax: (513) 527-8801 Phone: (513) 527-8977 www.hanserpublications.com Distributed in all other countries by Carl Hanser Verlag Postfach 86 04 20, 81631 Munich, Germany Fax: +49 (89) 98 48 09 www.hanser-fachbuch.de The use of general descriptive names, trademarks, etc., in this publication, even if the former are not especially identified, is not to be taken as a sign that such names, as understood by the Trade Marks and Merchandise Marks Act, may accordingly be used freely by anyone While the advice and information in this book are believed to be true and accurate at the date of going to press, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made The publisher makes no warranty, express or implied, with respect to the material contained herein Cataloging-in-Publication Data is on file with the Library of Congress Bibliografische Information der deutschen Bibliothek: Die Deutsche Bibliothek verzeichnet diese Publikation in der Deutschen Nationalbibliografie; detaillierte bibliografische Daten sind im Internet über abrufbar All rights reserved No part of this book may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying or by any information storage and retrieval system, with out permission in writing from the publisher © Carl Hanser Verlag, Munich 2014 Copy editing: Jürgen Dubau, Jan Helge Bøhn Production Management: Andrea Reffke Coverconcept: Marc Müller-Bremer, www.rebranding.de, Munich Coverdesign: Stephan Rönigk Typeset, printed and bound by Kösel, Krugzell Printed in Germany ISBN 978-1-56990-479-4 E-Book ISBN 978-1-56990-480-0 Contents Preface 1 Introduction 1.1 Learning Tasks, Learning Objectives, and Important Prerequisites for Working with the Book 1.2 Work Environments 1.3 Working with the Book Motion-Simulation (Multibody Dynamics) 2.1 11 Introduction and Theory 2.1.1 Simulation Methods 2.1.2 Restrictions 2.1.3 Classifications of MBD Learning Tasks on Kinematics 2.2.1 Steering Gear 2.2.2 Top-down Development of the Steering Lever Kinematics 2.2.3 Collision Check on Overall Model of the Steering System Learning Tasks on Dynamics 2.3.1 Drop Test on Vehicle Wheel Learning Tasks on Co-Simulation 2.4.1 Balancing a Pendulum 11 12 14 14 15 15 33 50 59 59 68 68 Design-Simulation FEM (Nastran) 79 2.2 2.3 2.4 3.1 Introduction and Theory 80 3.1.1 Linear Statics 81 3.1.2 Nonlinear Effects 83 3.1.3 Influence of the Mesh Fineness 85 3.1.4 Singularities 86 3.1.5 Eigenfrequencies 87 3.1.6 Heat Transfer 89 3.1.7 Linear Buckling 90 VI Contents 3.2 Learning Tasks on Design Simulation 90 3.2.1 Notch Stress at the Steering Lever (Sol101) 91 3.2.2 Temperature Field in a Rocket (Sol153) 139 Advanced Simulation (FEM) 149 4.1 Introduction 150 4.1.1 4.1.2 4.1.3 4.1.4 Sol 101: Linear Static and Contact Sol 103: Natural Frequencies Sol 106: Nonlinear Static Sol 601/701: Advanced Nonlinear 4.2 Learning Tasks on Linear Analysis and Contact (Sol 101/103) 4.2.1 Stiffness of the Vehicle Frame 4.2.2 Size and Calculation of a Coil Spring 4.2.3 Natural Frequencies of the Vehicle Frame 4.2.4 Clamping Seat Analysis on the Wing Lever with Contact 4.3 Learning Tasks Basic Non-Linear Analysis (Sol 106) 4.3.1 Analysis of the Leaf Spring with Large Deformation 4.3.2 Plastic Deformation of the Brake Pedal 4.4 Learning Tasks Advanced Nonlinear (Sol 601) 4.4.1 Snap Hook with Contact and Large Deformation 151 151 152 152 154 154 185 199 207 229 229 239 249 249 Advanced Simulation (CFD) 271 5.1 5.2 Principle of Numerical Flow Analysis 272 Learning Tasks (NX-Flow) 273 5.2.1 Flow Behavior and Lift Forces at a Wing Profile 273 Advanced Simulation (EM) 6.1 6.2 Principles of Electromagnetic Analysis 6.1.1 Electromagnetic Models 6.1.2 Maxwell Equations 6.1.3 Material Equations 6.1.4 Model Selection 6.1.5 Electrostatics 6.1.6 Electrokinetics 6.1.7 Electrodynamics 6.1.8 Magnetostatics 6.1.9 Magnetodynamics 6.1.10 Full Wave (High Frequency) Installation and Licensing 297 298 299 300 302 303 306 306 306 307 307 307 308 Contents VII 6.3 Learning Tasks (EM) 310 6.3.1 Coil with Core, Axisymmetric 311 6.3.2 Coil with Core, 3D 326 6.3.3 Electric Motor 330 Management of Analysis and Simulation Data 7.1 351 Introduction and Theory 7.1.1 CAD/CAE Integration Issues 7.1.2 Solutions with Teamcenter for Simulation 7.2 Learning Tasks on Teamcenter for Simulation 7.2.1 Carrying out an NX CAE Analysis in Teamcenter 7.2.2 Which CAD Model Belongs to which FEM Model? 7.2.3 Creating Revisions 351 351 352 354 355 362 365 Manual Analysis of a FEM Example 371 8.1 Task Formulation 371 8.2 Idealization and Choice of a Theory 372 8.3 Analytical Solution 372 8.4 Space Discretization for FEM 373 8.5 Setting up and Solving the FEA System of Equations 374 8.6 Analytical Solution Compared with Solution from FEA 376 Bibliography Index 379 383 Preface Virtual product development has gained significant importance in particular through the integration of 3D solid based modeling, analysis and simulation Supported by the rapid enhancement of modern information and communication technology application integrated virtual product development has become an essential contribution in higher engineering education, continuing education as well as in industrial advanced and on-the-job training Since 2003 Technische Universität Darmstadt has been selected and approved as PACE university and has become a part of the international PACE network PACE stands for Partners for the Advancement of Collaborative Engineering Education and is a sponsoring program initiated by General Motors Corp (in Germany Adam Opel GmbH) PACE is driven by General Motors Corp., Autodesk, HP (Hewlett Packard), Siemens, Oracle, and further well acknowledged companies of the virtual product development branch (www pacepartners.org) Donations and sponsoring through the PACE partner companies has facilitated the preparation and the publishing of this book This publication has been developed based on cooperation between Dr Binde Ingenieure – Design & Engineering GmbH (www.drbinde.de) and the Division of Computer Integrated Design within the department of Mechanical Engineering of Technische Universität Darmstadt (www.dik.maschinenbau.tu-darmstadt.de) We thank very much Mr Haiko Klause for his support to chapter and Mr Andreas Rauschnabel for his contribution to the Motion and FEM examples for Version of the CAD system NXTM Furthermore we are grateful for the support of Carl Hanser Verlag, mainly Mrs Julia Stepp A very special thank you is dedicated to Prof Dr Jan Helge BØhn who supported us through his excellent cross-reading Last but not least we thank all readers who encouraged us to prepare this book also in English We wish all readers and users a successful application of the selected examples and hopefully a beneficial knowledge acquisition usable for both, the successful graduation and the successful knowledge application during the industrial career August 2014 Prof Dr.-Ing Reiner Anderl Dr.-Ing Peter Binde Introduction Engineering science has seen significant changes take place during the past two decades These changes have been driven by a powerful development of information and communication technologies and their introduction into both the product development process and the products themselves In essence, it has enabled computer integrated virtual product development, complete with integrated 3D modeling, analysis, simulation, and optimization The primary goal of virtual product development is the efficient development of innovative product solutions that satisfy the customers’ needs Consequently, the integration of computer-based methods into the digital workflow of the product development process has become critical to the success of virtual product development Engineering, designing, and detailing are all essential tasks for the development of innovative product solutions, as is the ability to accurately predict the product’s behavior subject to the multitude of potential use cases and operating conditions Fortunately, with the continuous improvement of information and communication technologies, and with the subsequent improvements in integration of computer aided design, analysis, simulation, and optimization, it has become increasingly easier to complete these essential product development tasks Information and communication technologies (ICT) are increasingly influencing the product development process, especially as the process becomes increasingly virtualized This influence results from: Rapid information acquisition from sources worldwide; Availability of new computer-based methods for product development and design – such as for product modeling (e. g., parametric, feature based, and knowledge-driven CAD); analysis, simulation and optimization (e. g., finite element analysis (FEA), multibody simulation (MBS), and computational fluid dynamics (CFD)); rapid validation and verification (e. g., digital mock-up (DMU)); rapid prototyping (e. g., virtually by using virtual and augmented reality, or physically by using generative manufacturing machines); and processing product data in successive process chains (so called CAX processes); and Mapping of the organizational and workflow structures within product data management (PDM) systems, with the aim to provide easy, intuitive, and immediate access to development status, progress, and results Impact of information and communication technologies on product development 4 1 Introduction The concept of virtual product development has clearly been shaped by the deep penetration of ICT into the product development process, to provide seamless flows of product data Virtual product development can be systematically achieved over an escalating set of levels (see next figure) These levels consist of: 3D CAD; Digital mock-ups; Virtual prototyping; Virtual product simulation; and Virtual factory Virtuality Virtual Product Development FunctionalDigital Mockup 3D-CAD 3D CAD Digital Mockup + Geometry + Assembling+ Assemblyinformation structure + Features + Parametrics Virtual Factory Virtual Prototype/ Virtual Product + Functional information + Material + (Software Logics) Integration of Information Levels of virtual product development + Production + Controlling + Logistics + Finances + Marketing Product Data Management 3D CAD is the fundamental basis 3D CAD is the fundamental basis for describing product geometry; usually modeled as solid geometry These digital product descriptions involve single-part modeling as well as assembly modeling, and generally describe a product structure This modeling is typically parametric and feature-based DMU Digital mock-ups (DMU) provide a visual representation of the product structure, including the part and assembly geometries These geometries are typically approximated using triangles When the part and assembly models are represented as solids, and complemented by material data, then mass properties, such as mass and center of gravity, can be estimated Digital mock-ups enable virtual prototyping for simulating assembly and dis assembly processes, and for investigating collision detection The most important simulation methods are FEA, MBS and CFD Virtual prototypes – often referred to as digital prototypes – include material and physical properties in addition to part geometries and product structures These prototypes can therefore be used to simulate the functional and physical behavior of a product while 1.1 Learning Tasks, Learning Objectives, and Important Prerequisites for Working with the Book 5 isualizing its behavior The functional and physical modeling within a virtual prototype v tends to be application and discipline specific Typical applications include stress analysis using finite element analysis (FEA) based on the finite element method (FEM), multi-body simulation/dynamics (MBS/MBD), or fluid dynamic simulation using computational fluid dynamics (CFD) Simulations may also integrate thermal analysis, electromagnetic analysis (EM), or kinematic analysis, or their combinations, usually based on FEA, to more fully investigate and understand the product behavior The term virtual product refers to the aggregation of a product’s physical properties together with its logical dependencies to produce a comprehensive, interoperable product model The term virtual factory refers to the digital representation of a factory, including its physical properties and manufacturing processes The objective is to facilitate simulation, analysis, and optimization of factory operations, including material flows, logistics, and order processing Product data resulting from the application of the various modeling, analysis, simulation and optimization software systems is stored as files in the product data management (PDM) system, enhanced by meta-data representing organizational and workflow information such as release status, effectivity, identification, classification, and version numbers The increasing use of 3D CAD in industry leads to an increasing need to integrate numerical analysis, simulation, and optimization methods and tools With this integration, product data, once it is described or generated, can then be used and reused in successive processes to avoid manual reentry errors, and to identify errors and mistakes early This in turn enhances product quality and increases the efficiency of the virtual product development process and successive physical product realization The PDM system manages all product data generated through virtual product development ■■1.1 Learning Tasks, Learning Objectives, and Important Prerequisites for Working with the Book Based on the objective to use 3D CAD data for analysis, simulation and optimization, the question of how 3D CAD data can be further used follows For this purpose representative example scenarios for the procedures of the finite element method, the multi-body simulation, fluid dynamics and the electromagnetic simulation have been developed in this book, by which the integration of modeling, analysis and simulation will be presented The here outlined scenarios are based on the 3D CAD system NX9 and its integral analysis and simulation modules To facilitate understanding the methodology and to shorten the training period, a single contiguous assembly was chosen for most learning tasks of this book This is the CAD model of the legendary Opel RAK2 that was created in student projects as a 3D CAD solid The training content is taught on the basis of methodology examples 372 8 Manual Analysis of a FEM Example ■■8.2 Idealization and Choice of a Theory In idealization, assumptions and simplifications are made to carry out the analysis afterwards For this task, the truss theory is assumed, since a dimension is large compared to the other two Further, it is assumed that the component is at rest, small deformations are present and the stress-strain behavior is linear, so it can be described by Hooke’s law Example task for the representation of the principle of FEM: The body is divided into two finite elements, so there are three nodes 2L = 200mm F=1000N x u1 u2 u3 F1 F2 F3 El1 Kn1 El2 Kn2 Kn3 A(x)=300mm2 - x E=210000N/mm2 ■■8.3 Analytical Solution The differential equation to be solved for the problem results from the conditions for: The analytical solution will be compared with the FEM results Statics (equilibrium condition, S: force in cutting plane normal), S ( x) = F σ ( x) = S ( x) A( x) = 1000 N 300mm − x Kinematics and ε ( x) = ∂u ∂x Material law σ ( x) = E ⋅ε ( x) 8.4 Space Discretization for FEM 373 Merged together as: ∂u F = , or ∂x E 300mm − x u ( x) = x F dx ∫ E 300mm − x Resolved to this integral calculus: dx ∫ ax + b = a ⋅ ln(ax + b) The corresponding solutions at the three locations of interest2 are found3 for the unknown function [Bronstein]: ( ln ( 300 − x ) − ln ( 300 ) ) 210 u1 = u ( x = ) = mm u2 = u ( x = 100 ) = 0, 001930786 mm u3 = u ( x = 200 ) = 0, 005231487 mm u ( x) = Results at three points from the analytical solution ■■8.4 Space Discretization for FEM For the analysis with the FEM, the body has to be separated into two elements Out of this, three nodes arise At each node, the displacement and the force are identified Elements, nodes, displacements and forces in the following are labeled as shown in the figure above For each element a shape function is chosen which still has unknown coefficients With these coefficients, each of the shape functions can be adjusted so that it approximates the real solution We choose the following linear shape functions for the elements and 2: uEL1 = aEL1 x + bEL1 uEL = aEL x + bEL Next, the shape functions have to be represented as functions of the unknown nodal quantities For the designated nodal quantities u1, u2 and u3 are incorporated The following conditions are available: u ( x = ) = u1 , u ( x = L ) = u2 , u ( x = L ) = u3 For the shape functions depending on the nodal quantities results: These locations are later the node locations at which FEA solutions will be calculated Because of the simple geometry in this case an analytic solution for the differential equation can easily be found A linear shape function means that we assume that the desired solution result behaves linear 374 8 Manual Analysis of a FEM Example These are still the same shape functions as before, they now only depend on the sought nodal displacements u2 − u1 x + u1 L u −u = x + 2u2 − u3 L uEL1 = uEL With these terms, the displacement pattern in the two elements is set up on the unknown nodal displacement magnitudes ■■8.5 Setting up and Solving the FEA System of Equations To obtain a system of equations which is suitable for calculating the unknown nodal displacements, the principle of the minimum of the potential energy should be used here We provide an energy function that includes errors and then demand that the errors become minimal small The external energy is taken into account, which can be specified accurately In contrast, the internal energy is written in the form of our approximate shape functions and will therefore be erroneous It is required that the error is minimized by taking the derivative of the total potential energy and setting it equal to zero These derivatives can be formed by every unknown Thus, a linear system of equations is obtained for which the unknowns can be calculated The internal energy or strain energy Π in a pull rod4 can for example be recognized through the elongation: ∏ = pull_rod EA dx ∫L ∂u With ε = ∂x and the function for the area A ( x ) = 300 − x , as well as the two shape functions, the internal energies for the two elements as a function of the unknown nodal displacements can be specified: ∏ = El1 ∏ = El 2 L N ∂u ⋅ ( u2 − u1 ) E A( x) El1 dx = 262500 ∫0 ∂ x mm 2L N ∂u ⋅ ( u3 − u2 ) E A( x) El dx = 472500 ∫L mm ∂x The external energy W is the applied work from the undeformed to the deformed position: Different notations for the strain energy per length in a pull rod [Schnell Gross Hauger] are: 1 N or EA 2 or N2 EA 8.5 Setting up and Solving the FEA System of Equations 375 u W = ∫Fdu For the external energy is obtained: W= ( u1F1 + u2 F2 + u3 F3 ) +∏− −W W= = 00 The result is an ∏ + Now the energy portions can be assembled according to ∏ ∏ El1 El El1 El equation for the total potential energy P, which depends on the unknown nodal displacements: P = 262500 N N 2 ( u2 − u1 ) + 472500 ( u3 − u2 ) − ( u1F1 + u2 F2 + u3 F3 ) = mm mm From the derivations ∂P = 0, ∂u1 ∂P = 0, ∂u2 ∂P =0 ∂u3 three equations arise, which can be represented in matrix form as follows: −4 ⋅ 262500 ⋅ 262500 u1 F1 − ⋅ 262500 ⋅ 262500 + 472500 − ⋅ 472500 ( ) ⋅ u2 = F2 −4 ⋅ 472500 ⋅ 472500 u3 F3 This energy function has errors because of our linear shape functions To minimize the errors, we will set up derivatives and set them equal to zero This results in e quations This system of equations can also be understood as overall stiffness matrix K, the displacement vector u and force vector F and be noted in the form kij ⋅ ui = Fj In a finite element program, this form is generated directly by composing5 the individual element stiffness matrices to the overall stiffness matrix of the system The deformation vector ui and the force vector Fi arise from boundary conditions The following conditions are known6 in this example: u1 = 0, F2 = 0, F3 = 1000 N 1000 N acting on the right node Thus, the system of linear equations can be resolved The result is: u1 = 0mm u2 = 0, 00190476mm u3 = 0, 005079mm Instead of “composing” it is also spoken of “assembling” With the numerical values of the matrix representation of the example, the influence of the two elements can be seen on the overall stiffness matrix One of the two quantities, displacement or force, is always known at a node, the other can then be calculated These are the results of the FEM 376 8 Manual Analysis of a FEM Example ■■8.6 Analytical Solution Compared with Solution from FEA The results, which are also shown in the figure below, show that the analysis at the nodes with FEM correspond relatively accurately with the analytical solution Between the nodes, the solutions coincide worse, which is due to the chosen linear shape functions Stress and strain results could now be derived from the calculated displacement magnitudes This will be omitted here Stress results differ more than displacements from the analytical result Common methods to increase the accuracy of the results are: Finer meshing, i. e smaller elements, higher element density7 Increase of the polynomial of the shape functions8 Displacement results in comparison: Analytical analysis and FEM The comparison of the analytical analysis with the FEM reveals the good compliance of the results, although they were produced with only small numbers of elements and linear shape functions because of the limited computational complexity With the use of computers to solve the computational work, a much better compliance can be expected Bibliography [Bronstein] Bronstein I. N./Semendjajew K. A.: Taschenbuch der Mathematik 24th Edition Community Edition, Verlag Nauka, Moskau und Teubner Verlag, Leipzig, 1989 [Galerkin] Galerkin, B. G.: Stäbe und Platten Reihen in gewissen Gleichgewichtsproblemen elastischer Stäbe und Platten Vestnik der Ingenieure, Vol 19, 1915, p 897–908 This is also known as h-adaptivity This is also known as p-adaptivity 8.6 Analytical Solution Compared with Solution from FEA 377 [Ritz] Ritz, W.: Über eine neue Methode zur Lösung gewisser Variationsprobleme der Mathematischen Physik In: Reine Angewendete Mathematik, Vol 135, 1908, p 1–61 [SchnellGrossHauger] Schnell, W./Gross, D Hauger, W.: Technische Mechanik 2: Elastostatik 3rd Edition Springer Verlag, Berlin/Heidelberg/New York 1989 Bibliography [adams1] Overview of ADAMS/SOLVER Online-Dokumentation zu NX [Alber-Laukant] Alber-Laukant B.: Struktur- und Prozesssimulation zur Bauteildimensionierung mit thermoplastischen Kunststoffen Validierung von Werkstoffbeschreibungen für den technischen Einsatz 1st Edition Shaker-Verlag 2008 [Anderl1] Anderl, R.: Virtuelle Produktentwicklung A (Skript zur Vorlesung 2014) Technische Universität Darmstadt 2014 [Anderl2] Anderl, R.: Virtuelle Produktentwicklung C (Skript zur Vorlesung 2014) Technische Universität Darmstadt 2014 [Anderl3] Anderl R./Grau M./Malzacher J.: SIMPDM – a harmonized approach for the strategic implementation of simulation data management NAFEMS World Congress 2009 [Anderl4] Anderl R./Malzacher J.: SimPDM – SimulationsdatenmanagementStandard nach Maß In: CAD CAM, No 1–2, 2009, p 38–41 [Anderl5] Anderl R./Rollmann T./Völz D./Nattermann R./Maltzahn S./Mosch C.: Virtuelle Produktentwicklung In: Steinhilper, R./Rieg, F (Hrsg.): Handbuch Konstruktion, Carl Hanser Verlag, München 2012, p 934– 936 [Anderl6] Anderl R./Maltzahn S./Krastel M.: Collaborative CAD/CAE Integration – Bringing SimPDM to Practice NAFEMS European Conference on Simulation Process and Data Management 2011 [Anderl7] Anderl R./Maltzahn S.: C3I – Collaborative CAD/CAE Integration NAFEMS World Congress 2011 [Bathe] Bathe, H J.: Finite-Elemente-Methoden 2nd Edition Springer Verlag, Berlin/Heidelberg/New York/Tokyo 2006 [Binde1] Binde, P.: NX Motion (MKS-Bewegungsanalyse, Kinematik, Kinetik) Schulungsunterlagen zum Training Dr Binde Ingenieure GmbH, Wiesbaden 2014 [Binde2] Binde, P.: NX Design Simulation mit NX/Nastran Solver Schulungs unterlagen zum Training Dr Binde Ingenieure GmbH, Wiesbaden 2014 380 Bibliography [Binde3] Binde, P.: NX Advanced Simulation FEM mit NX/Nastran Solver Schulungsunterlagen zum Training Dr Binde Ingenieure GmbH, Wiesbaden 2014 [Binde4] Binde, P.: NX Advanced Nonlinear FE-Analysis mit NX/Nastran Solver Schulungsunterlagen zum Training Dr Binde Ingenieure GmbH, Wiesbaden 2014 [Binde5] Binde, P.: Strömungs- und thermische Analyse mit NX/Flow & Thermal Schulungsunterlagen zum Training Dr Binde Ingenieure GmbH, Wiesbaden 2014 [Bossavit] Bossavit, A Computational Electromagnetism Variational Formulations, Complementarity, Edge Elements Academic Press, San Diego/ London/Boston/New York/Sydney/Tokyo/Toronto 1997 [Bronstein] Bronstein I. N./Semendjajew K. A.: Taschenbuch der Mathematik 24th Edition Gemeinschaftsausgabe Verlag Nauka, Moskau und Teubner Verlag, Leipzig, 1989 [Dubbel] Grote, K. H./Feldhusen, J (Hrsg.): Dubbel Taschenbuch für den Maschinenbau 21th Edition Springer Verlag, Berlin/Heidelberg/New York 2004 [Dular] Dular, P.: Modélisation du champ magnétique et des courants induits dans des systèmes tridimensionnels non linéaires Ph.D thesis 152 Université de Liège, Faculty of Applied Sciences, Liège 1994 [ESCref] I-DEAS ESC Electronic System Cooling Reference Manual [FKM] Forschungskuratorium Maschinenbau e.V (FKM): Rechnerischer Festigkeitsnachweis für Maschinenbauteile aus Stahl, Einsenguss- und Aluminiumwerkstoffen (FKM-Richtlinie) 6th, extended Edition VDMA Verlag 2012 [Galerkin] Galerkin, B. G.: Stäbe und Platten Reihen in gewissen Gleichgewichtsproblemen elastischer Stäbe und Platten Vestnik der Ingenieure, Vol 19, 1915, p 897–908 [GetDP 2014] GetDP, a general environment for the treatment of discrete problems (http://www.geuz.org/getdp/) [Geuzaine 2001] Geuzaine, C.: High order hybrid finite element schemes for Maxwell’s equations taking thin structures and global quantities into account Université de Liège, Liège 2001 [Geuzaine 2013] Geuzaine, C.: ELEC0041 Modeling and Design of Electromagnetic Systems Université de Liège, Applied & Computational Electromagnetics (ACE) [GrossHaugerSchnell] Gross, D./Hauger, W./Schnell, W.: Technische Mechanik 1: Statik 9th Edition Springer Verlag, Berlin/Heidelberg/New York 2006 [HaugerSchnellGross] Hauger, W./Schnell, W./Gross, D.: Technische Mechanik 3: Kinetik 12th Edition Springer Verlag, Berlin/Heidelberg/New York 2012 [Komzsik] Komzsik, L What every Engineer should know about Computational Techniques of Finite Element Analysis, 2nd Edition CRC Press, London/New York 2009 Bibliography [Malzacher] Malzacher J./Tabbert P.: Simulationsdatenmanagement Integration der Simulationsdaten in die PDM-Strategie Engineering Process Day, Darmstadt 2008 [Maya] Maya Heat Transfer Technologies Ltd: NX/Flow Schulungsunterlagen zum Training 2014 [nxn_advnonlinear] NX Nastran Advanced Nonlinear Theory and Modeling Guide Dokumentation zur NX Nastran Installation [nxn_dmap] NX Nastran DMAP User’s Guide Online-Dokumentation zu NX Nastran [nxflowref] NX Flow Reference Manual Dokumentation zur Installation [nxn_nonlinear106_1] NX Nastran Basic Nonlinear Analysis User’s Guide Online-Dokumentation zu NX Nastran [nxn_nonlinear106_2] NX Nastran Handbook of Nonlinear Analysis (106) Online-Dokumentation zu NX Nastran [nxn_num] NX Nastran Numerical Methods User’s Guide Online-Dokumentation zu NX Nastran [nxn_paral] NX Nastran Parallel Processing User’s Guide Online-Dokumentation zu NX Nastran [nxn_qrg] NX Nastran Quick Reference Guide Dokumentation zur NX Nastran Installation [nxn_user] NX Nastran User’s Guide Online-Dokumentation zu NX Nastran [nxn_verif] NX Nastran Verification Manual Online-Dokumentation zu NX Nastran [recurdyne1] Using Recurdyne Online-Dokumentation zur NX [RiegHackenschmidt] Rieg F./Hackenschmidt R.: Finite Elemente Analyse für Ingenieure Eine leicht verständliche Einführung 3rd Edition Carl Hanser Verlag, München 2009 [Ritz] Ritz, W.: Über eine neue Methode zur Lösung gewisser Variationsprobleme der Mathematischen Physik In: Reine Angewendete Mathematik, Vol 135, 1908, p 1–61 [RoloffMatek] Muhs D./Wittel H./Jannasch D./Voßiek J.: Roloff/Matek Maschinenelemente Normung, Berechnung, Gestaltung 21th Edition Springer Vieweg, Wiesbaden 2013 [RoloffMatekTab] Muhs D./Wittel H./Jannasch D./Voßiek J.: Roloff/Matek Maschinen elemente Tabellen 18th Edition Vieweg+Teubner Verlag, Wiesbaden 2007 [Schäfer] Schäfer, M.: Numerik im Maschinenbau Springer Verlag, Berlin/Heidelberg/New York 1999 [SchnellGrossHauger] S chnell, W./Gross, D./Hauger, W.: Technische Mechanik 2: Elasto statik 11th Edition Springer Verlag, Berlin/Heidelberg/New York 2012 381 382 Bibliography [shb1] Schumacher, A./Hierold, R./Binde, P.: Finite-Elemente-Berechnungen am Konstruktionsarbeitsplatz – Konzept und Realisierung In: VDI – Konstruktion 11/12, 2002 (see also www.drbinde.de\download\FEM_ am_Konstruktionsarbeitsplatz.pdf) [shbm] Schumacher, A./Hierold, R./Binde, P./Merkel M.: Parametrisierte CADModelle als Basis für eine CAE gesteuerte Komponentenentwicklung Kongress: Berechnung und Simulation im Fahrzeugbau Würzburg 2002 [SimPDM] ProStep iViP Recommendation “Integration of Simulation and Computation in a PDM Environment (SimPDM)” PSI 4, Version 2.0 2008 [spurk1] Spurk, H./Aksel, N.: Strömungslehre Einführung in die Theorie der Strömungen 8th Edition Springer Verlag, Berlin/Heidelberg/New York 2010 [TCSim] Schulungsunterlagen zu Teamcenter for Simulation Siemens PLM Software [Weiland] Weiland, T.: A Discretization Method for the Solution of Maxwell’s Equations for Six-Component Fields In: International Journal of Electronics and Communications (AEÜ), Vol 31, No 3, 1977 p 116–120 All screenshots are taken from NX9, Siemens PLM software Index 2D Contact 19 3D contact 63 64-Bit 10 A Adams 10 ADINA 152 Ampere’s law 300 analytical solution 372 Animation 20 approval processes 354 Articulation 15, 31 automatic time stepping 265 AUTOMPC 182 axisymmetric 311 B beam 187 beam element 187 –190 beam theory 171 bolt load 220 boundary conditions 116 boundary layer resolution 282 Bushing 19 C Cable 19 CAEAnalysis 353, 364 CAEGeometry 353 CAEManager 364 – 368 CAEModel 353, 364 cams 12 capacitance 299 capacitor 299 CFD 271 CGAP 209 checking element shapes 128 clamping element 207 clamping seat 207 clamping situation 14 clearance 14 cloning 200 coil 299, 301, 303, 311, 314, 317 – 319, 321, 324, 326 – 329, 331, 334 coil spring 185 collision check 58 collisions 16 combination 176 Component-based Simulation 25 conduction losses 318, 331, 348 – 349 conflict situations 24 connection 166 conservation equations 272 Constant driver 31 Constant Velocity 18 Constraints 116 contact 249 contact non-linearity 84 convection boundary condition 146 convergence 135 convergence control 291 convergence criterion 275, 276 convergence validation 136 Co-Simulation 17, 24 coupled systems 150 coupling elements 177 Create Sequence 20 Curve on Curve 20 cylindrical joint 18, 43 D damper 12, 19 damping 64, 206 data model 354, 363 data protection 352 default settings 10, 66 determined degrees of freedom 15 dielectric permeability 302 dielectric relationship 302 Direct Matrix Abstraction Programming 151 384 Index displacement function 371 displacement results 120 DMAP 151 DMU 3 – 4 driver 17, 30 dynamics 24, 59 E Eddy Current losses 318, 331, 348 – 349 Eddy Currents 304 edge subdivisions 233 eigenfrequencies 87, 199 electrical conductivity 302 electrical engineering components 297 electrical field theory 297 electrodynamics 299, 305 – 306 electrokinetics 299, 305 – 306 electromagnetic field analysis 150 electrostatics 299, 305 – 306 enforced displacement 194 Environment 17, 24 equilibrium condition 372 equivalent stress hypothesis 123 evaluation of accuracy 91 excitation 206 F f06 file 263 Faraday’s law 301 ferromagnetic 302 finite-volume method 272 fixed joint 18, 22, 63 Flexible Body Dynamics 17, 25 Flexible Link 19 flow analysis 272 flow boundary conditions 284 flow surfaces 284 Force 20 forced movement 338, 340 four-node tetrahedrons 127 friction 64 frictionless sliding 289 full wave 299, 305, 307 Full Wave (High Frequency) 299, 307 Function driver 31 Function Manager 19 FVM 272 G gap elements 152 gear 19, 31 General Motion 339 geometric nonlinear analysis 230 Graphing 20, 45 H Harmonic driver 31 heat flux 147 heat transfer 89 hexahedral elements 127 HEX Solid Meshing 252 high frequency 299, 307 Hooke’s law 83, 372 I induction law 301 inductivity 299, 326 inlet 286 Inline 18 installation 308 – 310 Interference 20 iron losses 348 – 349 J joint primitives 18 L large deformation 229, 249 large displacement 85, 229, 249, 261 leaf spring 229 learning tasks 5 library 61 licensing 308 lift force 293 lifting off contacts 60 linear buckling 90 linear statics 81 link 17, 25, 62 linked phase voltage 347 load transfer to FEM 20 load types 112 local mesh refinement 131 losses 318, 331, 348, 350 M machine portals 187 magnetic permeability 302 magnetic relationship 302 MAGNETICS 150 magnetodynamics 297 – 299, 305, 307 magnetostatics 297, 299, 303, 305, 307 Marker 18 mass properties 25 master model concept 21 Master Model Dimension 19 material equations 302 material law 372 material properties 109, 143, 283 MATLAB Simulink 17 Index 385 matrix form 375 maturity tracking 352 maximum distortion energy hypothesis 123 maximum principal stress 123 maximum tensile stress 196 Maxwell’s equations 298 MBD program 12 Measure 20 memory 10 mesh connections 144 mesh fineness 85 Mesh Mating Condition 144, 208 Mesh Point 189 middle node elements 127 midsurface 161 Motion Connections 28 motion-driven systems 15 Motion Joint Wizard 22 Motor Driver 24 motor libraries 17 Moving Band 332, 339 – 340 Multibody Dynamics 12 multi-processor 10 N named references 353, 362 Newton’s Method 261, 344 non-linear contact 208 – 209 non-linear effects 83 non-linear geometry 261 non-linear material 84 non-linear stress-strain behavior 256 notch factor 126 notch stress 91 NX Response Analysis 151 NX/Thermal 150 O ohm resistance 299, 303, 331, 348 – 349 Ohm’s law 302 Opel RAK2 5 opening 285 Orientation 18 outlet opening 287 over-determinations 24 over-determined degrees of freedom 24 P Parallel 18 parameterization 186 PDM 3, perfect insulation 146 Phase Shift 342 phase voltage 343, 347 piece of cake 142 pivotable constraint 113 planar joint 18 Plant Input 20 Plant Output 20 plastic deformation 240 plasticity 241 PMDC-Motor 20 point mass 201 Point on Curve 19 Point on Surface 20 Poisson’s Ratio 110 polygon body 98 polygon geometry 133, 233 Populate Spreadsheet 20 post-processor 118 presetting 10 press fit 207 pressure distribution 293 pretensioned bearings 186 principle of linear FEM 82 principle of the minimum of the potential energy 374 principles of electromagnetic analysis 298 processor 10 process orientation 352 R Rack and Pinion 19 reaction force 186, 195 RecurDyn 10 redundant degrees of freedom 24, 41 release and change processes 352 residual tolerance 344 resistance 299, 303 restrictions of MBD 14 revising 365, 367 revisions 353, 362, 365 – 368 revolute joint 18, 26 ring-element-based method 141 rivet joints 176 rotational degrees of freedom 156, 179 rotational driver 13 S screw 18 Sensor 18 shape function 371, 373 – 376 sheet 162 shell elements 157 signal chart 20, 24 simulation data 351, 369 simulation data management 352 Simulation File View 97 singularities 86, 137 skin depth 304 slider 18, 56 Smart Point 18 386 Index snap hook 249 soft spring bearing 217 – 218 Sol 101 151 Sol 103 151 Sol 106 152 Sol 601 152 space discretization 373 spherical joint 18, 55 spring 12, 19 standard meshing 108 starting behavior 340 Steinmetz formula 303 stiffness matrix 375 Stitch Edge 162 stress-strain behavior 372 structural mechanics 14 super elements 202 surface roughness 284 surface subdivisions 101 Surface to Surface Contact 209 Surface to Surface Gluing 208 symmetry 141 synchronization of the processes 352 system of differential equations 12 T TC_CAE_Defining 353, 362 TC_CAE_Source 353, 362 TC_CAE_Target 353, 362 Teamcenter 352 – 355, 357 – 359, 361, 363 – 366, 368 – 369 temperature boundary condition 145 temperature field 139 temperature gradient 147 ten-node tetrahedral elements 127 thermodynamic problem 150 time-dependent travel path 258 time step 291 time step size 275 TMG 150 tolerances 42 toolbar 16 top-down method 35 Torque 20 Trace 20 transport equations 272 traverse path 258 truss theory 372 turbulence model 276 U underdetermined 28 undetermined degrees of freedom 15 universal joint 18 V vents 285 version levels 352 virtual product development 3 – 5 von Mises 123 W wake space 296 wall thickness 165 weak springs 216 Whitney elements 314 without redundancy 24 Y Young’s Modulus 110 Correct Calculations d ok D an bo DV rora the On 8Au om Z8 s fr 8, le Z8 amp ex all Frank Rieg Reinhard Hackenschmidt Bettina Alber-Laukant Finite Element Analysis for Engineers Basics and Practical Applications with Z88Aurora Rieg/Hackenschmidt/Alber-Laukant Finite Element Analysis for Engineers Basics and Practical Applications with Z88Aurora 733 pages With DVD € 79.99 ISBN 978-1-56990-487-9 Also available as ebook € 64.99 ebook-ISBN 978-1-56990-488-6 The Finite Element Analysis today is the leading engineer‘s tool to analyze structures concerning engineering mechanics, i.e statics, heat flows, eigenvalue problems and many more Thus, this book wants to provide well-chosen aspects of this method for students of engineering sciences and engineers already established in the job in such a way, that they can apply this knowledge immediately to the solution of practical problems Over 30 examples along with all input data files on DVD allow a comprehensive practical training of engineering mechanics Two very powerful FEA programs are provided on DVD, too: Z88, the open source finite elements program for static calculations, as well as Z88Aurora, the very comfortable to use and much more powerful freeware finite elements program which can also be used for non-linear calculations, stationary heat flows and eigenproblems, i.e natural frequencies Both are full versions with which arbitrarily big structures can be computed – only limited by your computer memory and your imagination More Information on Books: www.hanser-fachbuch.de