Structural Dynamics Toolbox FEMLink For Use with MATLAB r User’s Guide Etienne Balm`es Version 5.2 Jean-Michel Lecl`ere How to Contact SDTools 33 +1 41 13 13 57 Phone 33 +6 77 17 29 99 Fax SDTools Mail 44 rue Vergniaud 75013 Paris (France) http://www.sdtools.com Web comp.soft-sys.matlab Newsgroup http://www.openfem.net An Open-Source Finite Element Toolbox [email protected] Technical support [email protected] Product enhancement suggestions [email protected] Sales, pricing, and general information Structural Dynamics Toolbox User’s Guide on May 27, 2005 c Copyright 1991-2005 by SDTools The software described in this document is furnished under a license agreement. The software may be used or copied only under the terms of the license agreement. No part of this manual in its paper, PDF and HTML versions may be copied, printed, photocopied or reproduced in any form without prior written consent from SDTools. Structural Dynamics Toolbox is a registered trademark of SDTools OpenFEM is a registered trademark of INRIA and SDTools MATLAB is a registered trademark of The MathWorks, Inc. Other products or brand names are trademarks or registered trademarks of their respective holders. Contents 1 Preface 9 1.1 Getting started . 10 1.2 Understanding the Toolbox architecture . 12 1.2.1 Layers of code . 12 1.2.2 Global variables . 13 1.3 Typesetting conventions and scientific notations . 14 1.4 Release notes for SDT 5.2 and FEMLink 3.1 . 17 1.4.1 Key features . 17 1.4.2 Detail by function . 18 1.4.3 Notes by MATLAB release . 19 1.5 Release notes for SDT 5.1 and FEMLink 3.0 . 20 1.5.1 Key features . 20 1.5.2 Detail by function . 21 1.5.3 Notes by MATLAB release . 22 2 Structural dynamic concepts 25 2.1 I/O shape matrices . 26 2.2 Normal mode models . 28 2.3 Damping . 30 2.3.1 Viscous damping in the normal mode model form . 30 2.3.2 Damping in finite element models . 31 2.4 State space models . 34 2.5 Complex mode models . 35 2.6 Pole/residue models . 37 2.7 Parametric transfer function . 39 2.8 Non-parametric transfer function . 40 3 Modal test tutorial 41 3.1 Preparing a modal test . 42 1 CONTENTS 3.1.1 Geometry declaration . 42 3.1.2 Sensor/shaker configurations . 44 3.2 Data import and visualization . 46 3.2.1 Data acquisition . 46 3.2.2 Importing FRF data ....................... 47 3.2.3 Getting started with the iiplot interface . 49 3.2.4 Operational deflection shapes . 52 3.3 Identification of modal properties . 54 3.3.1 The id rc procedure step by step . 54 3.3.2 Background theory . 61 3.3.3 When id rc fails . 62 3.3.4 Direct system parameter identification algorithm . 64 3.3.5 Orthogonal polynomial identification algorithm . 65 3.4 MIMO, Reciprocity, State-space, ... 67 3.4.1 Multiplicity (minimal state-space model) . 67 3.4.2 Reciprocal models of structures . 69 3.4.3 Normal mode form . 71 4 Test/analysis correlation tutorial 75 4.1 Topology correlation and test preparation . 77 4.1.1 Combining models . 77 4.1.2 Observation matrix for a sensor configuration . 78 4.1.3 Sensor/shaker placement . 80 4.2 Test/analysis correlation . 81 4.2.1 Shape based criteria . 81 4.2.2 Energy based criteria . 82 4.2.3 Correlation of FRFs . 83 4.3 Expansion methods . 84 4.3.1 Underlying theory for expansion methods . 84 4.3.2 Basic interpolation methods for unmeasured DOFs . 86 4.3.3 Subspace based expansion methods . 87 4.3.4 Model based expansion methods . 89 4.4 Structural dynamic modification . 89 5 FEM tutorial 93 5.1 model data structure . 94 5.1.1 GUI Access to FEM models . 94 5.1.2 Direct declaration of geometry (truss example) . 95 5.1.3 Building models with femesh . 97 5.1.4 Handling material and element properties . 98 2 5.1.5 Coordinate system handling . 99 5.2 Defining a case . 100 5.2.1 Cases GUI . 100 5.2.2 Boundary conditions and constraints . 101 5.2.3 Loads . 102 5.2.4 Sensors . 103 5.3 Computing the response . 103 5.3.1 Simulate GUI . 103 5.3.2 Static responses . 104 5.3.3 Normal modes (partial eigenvalue solution) . 105 5.3.4 State space and other modal models . 106 5.3.5 Manipulating large finite element models . 108 5.4 Post-processing with feplot ....................... 109 5.4.1 Starting the visualization interface . 110 5.4.2 Using iimouse commands . 110 5.4.3 Viewing deformations . 111 5.4.4 Superposing deformations . 112 5.4.5 Element selections . 112 5.4.6 Other information . 113 5.5 Interfacing with other FEM codes . 113 5.5.1 Importing models from other codes . 114 5.5.2 Importing model matrices from other codes . 114 6 Advanced FEM tools 117 6.1 Model reduction theory . 118 6.1.1 General framework . 118 6.1.2 Normal mode models . 119 6.1.3 Static correction to normal mode models . 121 6.1.4 Static correction with rigid body modes . 122 6.1.5 Other standard reduction bases . 123 6.1.6 Substructuring . 124 6.1.7 Reduction for parameterized problems . 126 6.2 CMS examples . 127 6.2.1 Component mode synthesis . 127 6.2.2 Substructuring using superelements . 129 6.3 Model parameterization with upcom .................. 131 6.3.1 Theoretical framework . 131 6.3.2 upcom parameterization for full order models . 132 6.3.3 Getting started with upcom ................... 133 6.3.4 Reduction for variable models . 134 3 CONTENTS 6.3.5 Predictions of the response using upcom ............ 135 6.4 Finite element model updating . 136 6.4.1 Error localization/parameter selection . 137 6.4.2 Update based on frequencies . 137 6.4.3 Update based on FRF . 138 7 Developer information 141 7.1 Nodes ................................... 142 7.2 Model description matrices . 143 7.3 Material property matrices . 144 7.4 Element property matrices . 145 7.5 DOF definition vector . 146 7.6 FEM model structure . 147 7.7 FEM case data structure . 149 7.8 FEM result data structure . 150 7.9 Curves and data sets . 151 7.10 DOF selection . 151 7.11 Node selection . 153 7.12 Element selection . 155 7.13 Constraint and fixed boundary condition handling . 157 7.14 Creating new elements (advanced tutorial) . 160 7.14.1 General information . 160 7.14.2 Writing a new element function . 160 7.14.3 Conventions . 168 7.15 Generic compiled elements . 170 7.16 Variable names and progamming rules . 171 8 Element reference 173 bar1 ................. 176 beam1, beam1t .............. 177 celas ................. 179 dktp ................. 180 flui4,flui6,flui8 .............. 182 fsc .................. 183 hexa8, hexa20, penta6, penta15, tetra4, tetra10 ..... 185 hexa8b, hexa20b, hexa27b, penta6b, penta15b, tetra4b, tetra10b 190 integrules ................ 194 mass1,mass2 ............... 202 quad4, quadb, mitc4 ............. 203 q4p, q5p, q8p, t3p, t6p ............ 205 4 q4pb, q8pb, t3pb, t6pb ............ 210 q9a ................. 211 rigid ................. 212 tria3, tria6 ............... 214 9 Function reference 215 ans2sdt ................ 222 basis ................. 223 commode ................ 226 comstr ................. 228 db, phaseb ............... 230 fe2ss ................. 231 fecom ................. 234 femesh, feutil ............... 248 feplot ................. 265 fesuper ................ 270 fe c ................. 273 fe case ................. 275 fe ceig ................. 282 fe coor ................. 284 fe curve ................ 285 fe cyclic ................ 291 fe eig ................. 293 fe exp ................. 296 fe load ................. 299 fe mat ................. 303 fe mk, fe mknl .............. 306 fe norm ................ 312 fe reduc ................ 313 fe sens ................. 316 fe simul ................ 320 fe stres ................ 322 fe super ................ 324 fe time,of time .............. 328 fe var ................. 333 idcom ................. 336 idopt ................. 341 id dspi ................. 344 id nor ................. 345 id poly ................ 348 5 CONTENTS id rc, id rcopt ............... 349 id rm ................. 353 iicom ................. 356 iimouse ................ 362 iiplot ................. 366 ii cost ................. 370 ii mac ................. 371 ii mmif ................ 382 ii plp ................. 385 ii poest ................ 386 ii pof ................. 388 m elastic ................ 390 m piezo ................ 392 nasread ................ 393 naswrite ................ 398 nor2res, nor2ss, nor2xf ............ 403 ofact ................. 409 p beam ................ 412 p shell ................. 414 p solid ................. 418 p spring ................ 421 perm2sdt ................ 422 psi2nor ................ 424 qbode ................. 426 res2nor ................ 428 res2ss, ss2res ............... 429 res2tf, res2xf ............... 431 rms ................. 432 setlines ................ 433 sdplot ................. 434 sdtdef ................. 436 sdth ................. 438 sp util ................. 439 stack get,stack set,stack rm ........... 441 ufread ................. 442 ufwrite ................ 449 upcom ................. 451 up.