The Application Research of Inverse Finite Element Method for Frame Deformation Estimation

<table class="figure-group"><tr class="fig-image" id="a"><td><object data="https://static.hindawi.com/articles/ijae/volume-2017/1326309/figures/1326309.fig.004a.svgz" name="1326309.fig.004a" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(a) </b>Constant section strain</td></tr><tr class="fig-image" id="b"><td><object data="https://static.hindawi.com/articles/ijae/volume-2017/1326309/figures/1326309.fig.004b.svgz" name="1326309.fig.004b" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(b) </b>Linear section strain</td></tr><tr class="fig-image" id="c"><td><object data="https://static.hindawi.com/articles/ijae/volume-2017/1326309/figures/1326309.fig.004c.svgz" name="1326309.fig.004c" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(c) </b>Quadratic section strain</td></tr></table>

<div>Distribution and error of section strains in different orders. <svg height="10.1628pt" id="M109" style="vertical-align:-0.2064095pt" version="1.1" viewbox="-0.0498162 -9.95639 9.83625 10.1628" width="9.83625pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M391 364C391 409 353 448 295 448C249 448 198 426 152 393C65 331 23 225 23 139C23 14 96 -12 146 -12C198 -12 280 9 367 101L351 124C300 78 242 48 194 48C129 48 109 107 109 162V191C208 213 391 266 391 364ZM313 350C313 305 268 261 113 223C132 334 187 381 217 398C227 404 244 405 261 405C290 405 313 385 313 350Z" id="g113-102"></path></g><g transform="matrix(.0091,0,0,-0.0091,5.382,-5.741)"><path d="M396 374C396 399 365 451 262 451C173 451 84 405 84 327C84 295 107 257 157 243V241C91 226 24 184 24 119C24 41 92 -12 189 -12C272 -12 344 31 386 91L367 118C325 76 274 50 222 50C163 50 120 84 120 138C120 191 169 218 223 218C247 218 263 217 278 216L312 260L308 267H259C200 267 167 297 167 338S202 414 250 414C297 414 326 387 336 341C338 331 341 328 349 328C361 328 396 349 396 374Z" id="g50-247"></path></g></svg> is a section strain in <svg height="10.262pt" id="M110" style="vertical-align:-0.2325001pt" version="1.1" viewbox="-0.0498162 -10.0295 10.5383 10.262" width="10.5383pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M400 123C365 93 327 80 288 80C216 80 157 134 153 241C251 245 374 254 392 257C414 260 420 273 421 293C421 375 351 454 258 454H257C203 454 148 427 104 383C62 341 30 278 30 202C30 87 103 -12 237 -12C279 -12 357 8 417 99L400 123ZM237 414C276 414 299 362 298 311C298 294 292 291 277 291C236 290 199 289 157 288C164 367 198 414 237 414Z" id="g13-99"></path></g><g transform="matrix(.0091,0,0,-0.0091,5.681,-5.741)"><path d="M442 379C442 416 395 457 292 457C188 457 83 414 83 326C83 279 107 252 170 241V239C80 219 22 182 22 112C22 40 88 -12 200 -12C307 -12 386 39 436 101L412 135C364 93 311 70 258 70C214 70 176 100 176 142C176 185 212 214 273 214C295 214 317 213 333 212L370 270L367 279C345 276 322 275 304 275C253 275 216 301 216 338C216 374 241 412 289 412C331 412 352 375 364 345C370 331 374 327 380 327C404 327 442 355 442 379Z" id="g14-247"></path></g></svg> computed from surface strain measurements by (<a href="https://static.hindawi.com/articles/ijae/volume-2017/1326309/figures/#EEq6">8</a>). <svg height="6.1673pt" id="M111" style="vertical-align:-0.2063904pt" version="1.1" viewbox="-0.0498162 -5.96091 5.50181 6.1673" width="5.50181pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M391 364C391 409 353 448 295 448C249 448 198 426 152 393C65 331 23 225 23 139C23 14 96 -12 146 -12C198 -12 280 9 367 101L351 124C300 78 242 48 194 48C129 48 109 107 109 162V191C208 213 391 266 391 364ZM313 350C313 305 268 261 113 223C132 334 187 381 217 398C227 404 244 405 261 405C290 405 313 385 313 350Z" id="g113-102"></path></g></svg> is a section strain in <svg height="11.5564pt" id="M112" style="vertical-align:-2.26807pt" version="1.1" viewbox="-0.0498162 -9.28833 22.0737 11.5564" width="22.0737pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M400 123C365 93 327 80 288 80C216 80 157 134 153 241C251 245 374 254 392 257C414 260 420 273 421 293C421 375 351 454 258 454H257C203 454 148 427 104 383C62 341 30 278 30 202C30 87 103 -12 237 -12C279 -12 357 8 417 99L400 123ZM237 414C276 414 299 362 298 311C298 294 292 291 277 291C236 290 199 289 157 288C164 367 198 414 237 414Z" id="g13-99"></path></g><g transform="matrix(.013,0,0,-0.013,5.681,0)"><path d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z" id="g113-41"></path></g><g transform="matrix(.013,0,0,-0.013,10.179,0)"><path d="M542 56L520 58C483 62 478 72 478 124V449C455 445 422 441 387 438C351 435 316 432 287 431V402L318 395C345 389 350 383 350 336V93C328 71 306 65 279 65C245 65 211 88 211 153V298C211 356 211 407 214 449C187 445 151 441 118 438C84 435 53 432 28 431V402L51 395C77 388 83 383 83 337V130C83 42 131 -12 214 -12C245 -12 272 -1 300 18C322 31 333 41 350 55V-5L359 -12C389 -5 420 2 452 8C485 15 513 20 542 24V56Z" id="g13-115"></path></g><g transform="matrix(.013,0,0,-0.013,17.394,0)"><path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z" id="g113-42"></path></g></svg> deduced by (<a href="https://static.hindawi.com/articles/ijae/volume-2017/1326309/figures/#EEq2">3</a>).</div>

International Journal of Aerospace Engineering

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Figure 4

Figure 4: The Application Research of Inverse Finite Element Method for Frame Deformation Estimation 