An ES-MITC3 Finite Element Method Based on Higher-Order Shear Deformation Theory for Static and Free Vibration Analyses of FG Porous Plates Reinforced by GPLs

<table class="table-group" id="tab9"><tr><td><table class="table"><tr><td class="thead-hr" colspan="7"><hr/></td></tr><tr class="thead"><td class="align_left">Method</td><td class="align_center"><span style="width: 27.9831ptpx;"><svg height="11.9453pt" id="M193" style="vertical-align:-3.309401pt" version="1.1" viewbox="-0.0498162 -8.6359 27.9831 11.9453" width="27.9831pt" 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="M671 0V28C608 36 593 47 562 130C495 309 432 486 368 665L336 656C270 481 202 311 134 139C98 47 84 39 20 28V0H241V28C167 38 156 47 178 115C217 236 276 383 327 530H329C375 398 437 223 484 92C499 47 489 37 424 28V0H671Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,10.803,3.132)"><path d="M692 302H438V274C537 267 543 260 543 188V103C543 61 531 48 511 37C489 26 458 20 424 20C231 20 146 188 146 333C146 517 258 630 411 630C507 630 582 597 606 474L634 480C627 546 622 601 619 636C586 643 510 665 426 665C230 665 44 552 44 321C44 122 191 -15 411 -15C491 -15 573 7 635 21C629 49 628 81 628 116V202C628 261 632 266 692 274V302Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,17.31,3.132)"><path d="M46 650V622C120 617 128 613 128 525V125C128 42 120 34 40 28V0H311V28C221 34 212 39 212 124V281L286 262C297 261 316 261 331 263C429 275 526 338 526 468C526 533 501 579 462 609C422 638 364 650 293 650H46ZM212 559C212 588 215 600 223 606C230 613 251 618 279 618C361 618 430 572 430 464C430 337 350 302 285 302C252 302 225 309 212 314V559Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,22.387,3.132)"><path d="M495 163C480 117 462 85 444 65C421 39 387 34 332 34C290 34 256 36 236 47C218 57 213 77 213 131V526C213 612 222 616 301 622V650H40V622C122 616 128 611 128 526V126C128 41 120 34 36 28V0H489C498 31 519 126 525 157L495 163Z"></path></g></svg></span></td><td class="align_center">Aluminium</td><td class="align_center">Magnesium</td><td class="align_center">Copper</td><td class="align_center">Nickel</td><td class="align_center">Titanium</td></tr><tr><td class="thead-hr" colspan="7"><hr/></td></tr><tr><td class="align_left" colspan="7"><span style="width: 16.1365ptpx;"><svg height="9.49473pt" id="M194" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -9.28833 16.1365 9.49473" width="16.1365pt" 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="M494 514C482 587 419 712 303 712C238 712 174 667 174 603C174 561 205 514 249 449C219 438 187 422 162 407C93 366 23 283 23 177C23 69 87 -12 190 -12C244 -12 288 5 328 33C406 87 444 170 444 249C444 329 404 391 331 475C265 550 222 605 222 627C222 647 238 657 267 657C355 657 421 585 484 499L494 514ZM359 234C359 143 319 30 219 30C172 30 114 75 114 178C114 275 163 343 195 378C212 397 241 415 269 425C305 382 359 313 359 234Z"></path></g><g transform="matrix(.013,0,0,-0.013,6.722,0)"><path d="M689 332C689 394 670 448 646 448C620 448 597 421 597 396C597 386 600 381 608 372C619 359 620 334 620 315C620 150 538 45 454 45C414 45 386 67 386 122C386 138 388 158 394 180L457 426L452 432L377 416L315 156C302 100 259 45 216 45C176 45 148 67 148 122C148 133 152 158 156 180C162 212 173 259 194 332C201 357 206 384 206 405C206 430 198 448 174 448C125 448 66 406 23 342L43 319C84 368 110 383 121 383C126 383 128 382 128 377C128 370 127 359 122 343C99 268 84 204 77 156C74 137 70 111 70 104C70 25 125 -12 180 -12C228 -12 276 12 319 50C338 8 378 -12 418 -12C549 -12 689 166 689 332Z"></path></g></svg></span></td></tr><tr><td class="align_left">ES-MITC3</td><td class="align_center" rowspan="2"><span style="width: 43.535ptpx;"><svg height="8.99234pt" id="M195" style="vertical-align:-0.4673605pt" version="1.1" viewbox="-0.0498162 -8.52498 43.535 8.99234" width="43.535pt" 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="M384 0V27C293 34 287 42 287 114V635C232 613 172 594 109 583V559L157 557C201 555 205 550 205 499V114C205 42 199 34 109 27V0H384Z"></path></g><g transform="matrix(.013,0,0,-0.013,6.24,0)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z"></path></g><g transform="matrix(.013,0,0,-0.013,9.204,0)"><path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z"></path></g><g transform="matrix(.013,0,0,-0.013,17.619,0)"><path d="M696 437H516V411C580 402 587 397 574 345C555 271 527 183 505 114H503C461 222 420 328 383 432H357C315 316 278 214 241 118H239C214 195 189 274 165 350C151 396 156 402 216 411V437H9V411C57 405 65 398 83 346C125 226 162 108 199 -11H227C267 100 308 199 346 300C387 195 428 97 468 -11H497C542 124 587 257 617 337C637 392 646 404 696 411V437Z"></path></g><g transform="matrix(.013,0,0,-0.013,26.524,0)"><path d="M298 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class="align_center">19.354</td><td class="align_center">20.137</td></tr><tr><td class="align_left">IGA</td><td class="align_center">35.891</td><td class="align_center">22.277</td><td class="align_center">31.188</td><td class="align_center">19.802</td><td class="align_center">20.544</td></tr><tr><td class="align_left">ES-MITC3</td><td class="align_center" rowspan="2"><span style="width: 43.535ptpx;"><svg height="8.99234pt" id="M196" style="vertical-align:-0.4673605pt" version="1.1" viewbox="-0.0498162 -8.52498 43.535 8.99234" width="43.535pt" 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="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z"></path></g><g transform="matrix(.013,0,0,-0.013,6.24,0)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 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408L21 397H90V107C90 28 125 -12 188 -12C198 -12 213 -8 230 1L298 36Z"></path></g><g transform="matrix(.013,0,0,-0.013,30.538,0)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z"></path></g><g transform="matrix(.013,0,0,-0.013,33.502,0)"><path d="M594 629L561 652L159 -9L190 -32L594 629ZM194 635C92 635 49 534 49 453C49 374 92 272 193 272C295 272 338 374 338 454S295 635 194 635ZM193 605C257 605 265 504 265 453C265 405 257 302 194 302C133 302 122 403 122 454S133 605 193 605ZM567 351C465 351 421 250 421 169C421 90 465 -12 566 -12S710 90 710 170S667 351 567 351ZM566 322C628 322 637 221 637 169C637 121 628 18 567 18S494 119 494 170C494 223 506 322 566 322Z"></path></g></svg></span></td><td class="align_center">21.402</td><td class="align_center">35.155</td><td class="align_center">44.931</td><td class="align_center">31.429</td><td class="align_center">32.934</td></tr><tr><td class="align_left">IGA</td><td class="align_center">22.139</td><td class="align_center">36.386</td><td class="align_center">46.287</td><td class="align_center">32.425</td><td class="align_center">33.910</td></tr><tr class="table-tr"><td colspan="7"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>Percentage of central deflection of the FG porous plate with various metal matrices.</div>

Mathematical Problems in Engineering

tab9

Table 9

Table 9: An ES-MITC3 Finite Element Method Based on Higher-Order Shear Deformation Theory for Static and Free Vibration Analyses of FG Porous Plates Reinforced by GPLs 

Table 9 | An ES-MITC3 Finite Element Method Based on Higher-Order Shear Deformation Theory for Static and Free Vibration Analyses of FG Porous Plates Reinforced by GPLs 