Applications of ATILA FEM Software to Smart Materials: Case Studies in Designing Devices (Woodhead Publishing Series in Electronic and Optical Materials)

The Finite Element Method (FEM) is a modeling technique that allows entire designs to be constructed, refined and optimized before the product is manufactured. ATILA FEM software provides modeling and analysis for piezoelectric, magnetostrictor and shape memory material based applications, such as transducers, ultrasonic motors, sensors, MEMS and sonar devices. These acoustic and strain sensing devices are used in marine engineering, structural health monitoring, non destructive testing, environmental monitoring and medical applications. The book uses detailed case studies to show how to use the software to design and model these products. Y......Page 0 Woodhead Publishing Series in Electronic and Optical Materials 12......Page 12 1......Page 14 conductance for columns 3......Page 16 problem equations definition, 4-7......Page 17 variational principle, 7......Page 20 transient analysis, 16......Page 29 ATILA simulation comparison, 23......Page 36 new version capacity, 25-44......Page 39 Wilson method, 26......Page 40 contour fill of far-field, Plate IV contour fill of strain, Plate III pre-processor GiD, 27-31......Page 41 icon-elastic shell, 32......Page 46 cylinder model characteristics, 44......Page 58 nonlinearity, 45-56......Page 60 temperature rise for various soft PZT multilayer actuators, 57......Page 72 mesoscopic model, 60......Page 75 curves obtained from the mesoscopic approach, 63......Page 78 64......Page 79 finite element analysis of orthogonally stiffened cylindrical shells with ATILA, 69-92......Page 82 stiffness constant shell, 70-2......Page 83 repeating section of a ring of a cylindrical shell, 73......Page 86 boundary conditions for symmetry and anti-symmetry, 74-8......Page 87 frequency, 92......Page 105 utilisation in ATILA, 94-134......Page 107 stress tensor, 95......Page 108 piezoelectric polarisation Cartesian coordinates, 97-106......Page 110 cylindrical coordinates, 106-21......Page 119 cylindrical polarisation, 115-21......Page 128 original polarisation, 122-33......Page 135 statistical analysis, 133......Page 146 potential profile, 134......Page 147 time domain analysis of piezoelectric device with ATILA, 136-54......Page 150 acoustic signal propagation and reflection, 140-4......Page 154 future trends, 153-4......Page 167 excitation condition optimisation with user defined waveform modifications, 154......Page 168 designing with ATILA, 155-78......Page 169 finite element method (FEM) procedure, 156-7......Page 170 tiny ultrasonic linear motor, 157-66......Page 171 ultrasonic motors (USM) butterfly-shaped ultrasonic linear motor, 166-74......Page 180 7.5 Conclusions 175......Page 189 7.6 References 176......Page 190 overview, 177-8......Page 193 general formulation, 178-83......Page 194 transmitting voltage response (TVR), 183......Page 199 displacement field of the elementary cell, 185......Page 201 frequency variations of the transmitting voltage response (TVR), 188......Page 204 phononic crystal (PC) ATILA, 190-201......Page 206 different periodic lattices, 191......Page 207 modulus of the displacement field for the waveguide mode, Plate X plate of thickness h, 194......Page 210 negative refraction applications, 197-201......Page 213 gradient index phononic crystal, 201......Page 217 sonar piezoelectric single crystal behaviour study using ATILA, 203-28......Page 220 state of the art single crystal technology, 204-8......Page 221 single crystal material behaviour modelling, 209......Page 226 VDB8b, 210......Page 227 comparison of the admittance VDB8b, 217......Page 234 real part of the electrical displacement, 225......Page 243 contour fill of the Z displacement at the resonance frequency, Plate XI imaginary part of the admittance, 228......Page 246 thermal analysis piezoelectric and magnetostrictive materials using ATILA, 230-79......Page 248 heat generation in piezoelectric materials, 231-2......Page 249 piezoelectric materials implementation, 232-45......Page 250 strains and stresses in piezoelectric materials caused by thermal effect, 245-9......Page 263 stress analysis, 249......Page 267 model experimental validation, 253-65......Page 271 heat generation in magnetostrictive materials, 266-72......Page 284 3D inducer element, 272......Page 290 dissipated power for each material, 279......Page 297 11.10 References 280......Page 298 damping modelling with ATILA, 281-304......Page 301 resistor, 282-3......Page 302 equivalent circuit of piezoelectric device, 287......Page 307 dielectric coefficient and electrical network, 289......Page 309 304......Page 324 temperature and stress effect, 305-72......Page 325 material properties, 306-7......Page 326 non-linear analysis, 310-11......Page 330 piezoelectric constant g33, 312......Page 332 analytical solution, 330-3......Page 350 337......Page 357 analytical solution, 342-6......Page 362 temperature iterative computation of the sphere in air, 354......Page 374 temperature iterative computation of the sphere in water, 370......Page 390 circumferential stress along the thickness at start and final step of process, 372......Page 392 Index 374......Page 395 periodic boundary condition, 182......Page 198 Langevin transducer sending and receiving acoustic signals, 142......Page 156 ringing and damping, 144-8......Page 158 transient simulation parameters used for the Langevin transducer, 143......Page 157 modelled device, 137-40......Page 151 Langevin transducer, 138......Page 152 frequency variations, 184......Page 200 large aluminium plate, 298-304......Page 318 central transducer, 301......Page 321 modal analysis of quarter of plate, 302......Page 322 normalised displacement (RC damping at 69.1 Hz), 303......Page 323 320......Page 340 modal analysis results between analytical vs numerical solutions, 334......Page 354 344......Page 364 resonance frequency, 51......Page 66 assembly, 14-15......Page 27 static analysis, 15......Page 28 variational form, 12-14......Page 25 four-node quadrilateral element, 10......Page 23 shape function, 8......Page 21 quality factors derived by simulation and analytical calculation, 56......Page 71 55......Page 70 6......Page 19 contour fill of z-displacement, 31......Page 45 ‘A’ node displacements of the ring, 118......Page 131 strained structure, 125......Page 138 illustration, 120......Page 133 fifth resonant frequency of the stiffened target at 121 Hz......Page 134 123......Page 136 ring description, 127......Page 140 piezoelectric ring geometry, 108......Page 121 fifth resonant frequency of the stiffened target at 113 Hz......Page 126 ring deformation, 114......Page 127 radial electric field, 110......Page 123 poled Z-axis, 109......Page 122 ring potential profile, 112......Page 125 illustration, 111......Page 124 piezoelectric disk piezoelectric disk under external impulse shock pressure, 139......Page 153 aluminium tube boundary, 75......Page 88 local coordinate system boundary condition, 77-8......Page 90 circular cylindrical shell, 78-85......Page 91 model test of stiffened shell, 81......Page 94 frequencies (Hz) for a ring-stiffened shell, 82......Page 95 elastic band structures calculated with the ATILA code, 195......Page 211 band structure along the GX direction calculated with a supercell, 196......Page 212 configuration and operating principle, 167......Page 181 illustration, 174......Page 188 butterfly-shaped ultrasonic linear motor, 168-74......Page 182 sixth resonant frequency of the stiffened target at 173 Hz......Page 187 mesh generation, 172......Page 186 electrical potential condition, 171......Page 185 tube boundary condition faces, 76......Page 89 material condition of tiny motor, 170......Page 184 transverse vibration mode 66 kHz,......Page 81 damping of cantilever beam, 292-5......Page 312 deflection of the end of the beam for L damping vs frequency, 296......Page 316 experimental analysis of damping of cantilever beam, 295-8......Page 315 description, 297......Page 317 Young modulus, 294......Page 314 axial displacement with RC damping vs frequency, 293......Page 313 end of beam deflection - R damping, 299......Page 319 numerical results of damping of different circuits, 300......Page 320 finite element inductor, 284......Page 304 cube, 99-106......Page 112 mesh of the cube, 100......Page 113 poled X-axis, 101......Page 114 resistor and inductor in parallel, 285-6......Page 305 resistor, inductor and capacitor in parallel, 286-7......Page 306 inductor, 283-4......Page 303 SAS mode comparison, 79......Page 92 84......Page 97 85......Page 98 nodal patterns, 83......Page 96 358......Page 378 circumferential stress, 357-8......Page 377 piezoelectric transducer, 242-45......Page 260 illustration, 116......Page 129 first and third vibration modes, 21......Page 34 structured mesh for water, 22......Page 35 convert to ATI function for generation ATILA code file, 146......Page 160 operation optimisation with customised waveform, 148-53......Page 162 parameters for the piezoelectric disk simulation, 145......Page 159 project.ati file modification to provide pulse time length, 147......Page 161 transient displacement response of the piezoelectric disk, 149......Page 163 temperature dependence, 307-9......Page 327 real part of the longitudinal stress, 324......Page 344 shell geometry, 346......Page 366 one dimensional heat transfer, 326-8......Page 346 conductance for column 5......Page 18 elastic rigidity constant, 309......Page 329 vibration velocity jump and hysteresis during rising and falling frequency, 47......Page 62 stiffened shell of elastic target, 86-92......Page 99 piezoelectric voltage constant coefficient, 316......Page 336 345......Page 365 potential profile in the cube, Plate V parallel to Y-axis, 102-4......Page 115 illustration, 103......Page 116 potential profile in the cube, Plate VI parallel to Z-axis, 104......Page 117 illustration, 105......Page 118 cylindrical coordinates, 107......Page 120 electrical displacement, 317......Page 337 58......Page 73 equifrequency contour (EFC), 199......Page 215 sphere element, 343......Page 363 thermal stress, 246-7......Page 264 axis definition for a poled Z-axis, 98......Page 111 axial stress of the cylinder vs time, 254......Page 272 259......Page 277 approximate analytical vs axisymmetrical FE model for uncoated PZT-8, 257......Page 275 coated cylinder in water in-water cylinder 2 with epoxy......Page 15 coated cylinder, 256-8......Page 274 bare cylinder in air, 258-62......Page 276 uncoated cylinder, 255-6......Page 273 with thermocouple wire, 261......Page 279 piezoelectric ceramic cylinder dimensions and measured small signal properties, 260......Page 278 coated cylinder in air, 262-5......Page 280 thermocouple, 263......Page 281 in-air convection film coefficients for different ceramic cylinders, 264......Page 282 coating, 265......Page 283 stiffened shell, 72-3......Page 85 205......Page 222 transducer material condition, 161......Page 175 fluid pressure, 356-7......Page 376 Gibbs energy curves for various electric field E levels, 61......Page 76 Boltzmann probability, 62......Page 77 247......Page 265 mesh of the bar, 321......Page 341 heat transfer coefficient as a function of applied electric field, 59......Page 74 thermal analysis implementation, 267-8......Page 285 stresses definition in shell coordinates, 71......Page 84 relationship of polarisation vs electric field, 46......Page 61 loss anisotropy, 48-55......Page 63 lead zirconate titanate (PZT), 53-5......Page 68 piezoelectric loss, 54......Page 69 resonance and anti-resonance frequencies of the bar, 322......Page 342 real part of the longitudinal strain, 323......Page 343 steady problem, 325-6......Page 345 losses determination, 315-20......Page 335 tube, 80......Page 93 quality factors derivations, 49-53......Page 64 resonance and antiresonance, 50......Page 65 result, 275......Page 293 steady temperature profile, 276......Page 294 materials definition, 277......Page 295 steady temperature profile, 278......Page 296 material looses, 269-70......Page 287 model description, 274-5......Page 292 variational formulation, 273-4......Page 291 temperature and stress effects on material behaviour, 369-70......Page 389 single crystal properties between start vs final computational steps, 371......Page 391 piezoelectric transformer, 19-21......Page 32 disk shape piezoelectric transformer with crescent curved electrodes, 20......Page 33 resonant frequencies of the stiffened target, 87......Page 100 frequency, 90......Page 103 frequency, 91......Page 104 frequency, 89......Page 102 frequency, 88......Page 101 physical properties of the motor’s elements, 163......Page 177 phononic crystal, 198......Page 214 pressure field for PC-made flat lens, 200......Page 216 flow chart, 314......Page 334 stress iterative computation at the resonance frequency, 336......Page 356 temperature and stress effects on the shell, 352-3......Page 372 temperature effect on the bar non-linear material behaviour, 328-30......Page 348 mesh of the piezoelectric cylinder, 250......Page 268 temperature profile through the cylinder, 252......Page 270 modulus of the shell radial displacement along the thickness, 349......Page 369 1D shell thermal model, 351......Page 371 real part of the shell pressure in fluid vs frequency, 365......Page 385 shell transmitting voltage response (TVR), 367......Page 387 ring behaviour, 128......Page 141 rested and deformed ring, 130......Page 143 numerical results, 129-30......Page 142 ring strained structure, 131......Page 144 project.ati modification, 151......Page 165 project.exc with user defined wave form information, 152......Page 166 transient parameters for the bimorph actuator, 150......Page 164 windmill ultrasonic motor illustration and a metal ring/finger coupled vibration mode, 18......Page 31 p-shaped linear motor dimensions, 17......Page 30 eight-node quadrilateral element, 11......Page 24 description of one unit cell of the doubly periodic structure, 192......Page 208 Alberich anechoic coating, 179......Page 195 description of a doubly periodic structure, 180......Page 196 displacement field real and imaginary parts, 187......Page 203 frequency variations of the free field voltage sensitivity (FFVS), 186......Page 202 piezoelectric cylinder, 234-42......Page 252 axial displacement with no damping vs frequency, 291......Page 311 parallel electric field, 235......Page 253 1D thermal modelling, 239......Page 257 real part of the displacement, 238......Page 256 steady temperature profile, 241......Page 259 thermal harmonic analysis piezoelectric cylinder, 40-2......Page 54 illustration, 41......Page 55 piezoelectric cylinder, 42-4......Page 56 real time from a transient analysis for the cylinder., 43......Page 57 quartz oscillator, 206-7......Page 223 piezoelectric relations, 96-7......Page 109 233......Page 251 VDB8e, 213-15......Page 230 212......Page 229 VDB9e, 215......Page 232 comparison of the admittance VDB8b, 218......Page 235 model geometry, 222......Page 240 224......Page 242 imaginary part of the pressure, 226......Page 244 real part of the impedance, 227......Page 245 real part of the axial displacement, 223......Page 241 comparison of the impedance VDB8b, 219......Page 237 mock-up transducer tested in water, 211......Page 228 new item-eigenvalue shift, 33......Page 47 real time from a modal analysis for the structure, 36......Page 50 fluid, 37-40......Page 51 structure model characteristics, 35......Page 49 modal resonance, 34......Page 48 244......Page 262 element analysis, Plate XII, Plate XIII, Plate XIV tonpilz transducer, 243......Page 261 transducer model characteristics, 38......Page 52 real time from a harmonic analysis for the transducer, 39......Page 53 transducer configuration, 158......Page 172 polarisation three resonant modes, 208......Page 225 ATILA code architecture, 28......Page 42 condition icon-initial surface or displacement, 29......Page 43 material icon, 30......Page 44 illustration, 207......Page 224 124......Page 137 strained structure with Eq electric field, 126......Page 139 1D thermal modelling, 327......Page 347 temperature iterative computation of the bar, 329......Page 349 13......Page 26 generalised n-node linear element, 9......Page 22 piezoelectric constant g33, 313......Page 333 elastic compliance constant, 311......Page 331 piezoelectric constant d33, 308......Page 328 axial stress of the driver at the resonance frequency, 340......Page 360 single crystal properties between start vs final computational steps, 339......Page 359 modal analysis results between analytical vs numerical solution, 338......Page 358 temperature in the driver, 341......Page 361 fluid shell mesh in fluid, 359......Page 379 real part of the far field pressure in fluid vs frequency, 366......Page 386 real part of the shell circumferential deformation in fluid vs frequency, 362......Page 382 real part of the shell circumferential stress in fluid vs frequency, 364......Page 384 real part of the shell radial deformation in fluid vs frequency, 361......Page 381 real part of the shell radial displacement in fluid vs frequency, 360......Page 380 real part of the shell radial stress in fluid vs frequency, 363......Page 383 shell mesh, 347......Page 367 modulus of the shell circumferential stress along the thickness, 350......Page 370 modulus of the shell radial displacement vs frequency, 348......Page 368 shell temperature along the thickness, 353......Page 373 single crystal properties between start vs final computational steps, 355......Page 375 mesh, 333......Page 353 axial stress of the driver at the resonance frequency, 335......Page 355 free bodies diagram, 332......Page 352 model, 331......Page 351 electroded surfaces, 132......Page 145 ring potential profile, 119......Page 132 section, 270......Page 288 2D inducer element, 271......Page 289 transient potential boundary and transient parameters, 141......Page 155 elongation and contraction, 159......Page 173 sawtooth electrical potential, 160......Page 174 fabrication, 165-6......Page 179 material condition, 162......Page 176 admittance, 216......Page 233 comparison of the admittance VDB8b, 214......Page 231 ATILA Finite Element Method (FEM) software facilitates the modelling and analysis of applications using piezoelectric, magnetostrictor and shape memory materials. It allows entire designs to be constructed, refined and optimized before production begins. Through a range of instructive case studies, Applications of ATILA FEM software to smart materials provides an indispensable guide to the use of this software in the design of effective products.

Part one provides an introduction to ATILA FEM software, beginning with an overview of the software code. New capabilities and loss integration are discussed, before part two goes on to present case studies of finite element modelling using ATILA. The use of ATILA in finite element analysis, piezoelectric polarization, time domain analysis of piezoelectric devices and the design of ultrasonic motors is considered, before piezo-composite and photonic crystal applications are reviewed. The behaviour of piezoelectric single crystals for sonar and thermal analysis in piezoelectric and magnetostrictive materials is also discussed, before a final reflection on the use of ATILA in modelling the damping of piezoelectric structures and the behaviour of single crystal devices.

With its distinguished editors and international team of expert contributors, Applications of ATILA FEM software to smart materials is a key reference work for all those involved in the research, design, development and application of smart materials, including electrical and mechanical engineers, academics and scientists working in piezoelectrics, magenetostrictors and shape memory materials.

• Provides an indispensable guide to the use of ATILA FEM software in the design of effective products
• Discusses new capabilities and loss integration of the software code, before presenting case studies of finite element modelling using ATILA
• Discusses the behaviour of piezoelectric single crystals for sonar and thermal analysis in piezoelectric and magnetostrictive materials, before a reflection on the use of ATILA in modelling the damping of piezoelectric structures

Part I provides an introduction to ATILA finite element method (FEM) software, beginning with an overview of the software code. New capabilities and loss integration are discussed, before Part II goes on to present case studies of finite element modelling using ATILA. The use of ATILA in finite element analysis, piezoelectric polarization, time domain analysis of piezoelectric devices and the design of ultrasonic motors is considered, before piezo-composite and photonic crystal applications are reviewed. The behaviour of piezoelectric single crystals for sonar and thermal analysis in piezoelectric and magnetostrictive materials is also discussed, before a final reflection on the use of ATILA in modelling the damping of piezoelectric structures and the behaviour of single crystal devices With its distinguished editors and international team of expert contributors, Applications of ATILA FEM software, to smart materials will be a key reference work for all those involved in the research, design, development and application of smart materials, including electrical and mechanical engineers, academics and scientists working in piezoelectrics, magenetostrictors and shape memory materials. Book jacket