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="tab10"><tr><td><table class="table"><tr><td class="thead-hr" colspan="7"><hr/></td></tr><tr class="thead"><td class="align_left" rowspan="2">GPL pattern</td><td class="align_center" colspan="6"><span style="width: 10.383ptpx;"><svg height="9.25202pt" id="M208" style="vertical-align:-3.29111pt" version="1.1" viewbox="-0.0498162 -5.96091 10.383 9.25202" width="10.383pt" 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"></path></g><g transform="matrix(.0091,0,0,-0.0091,5.317,3.132)"><path d="M245 635C92 635 37 457 37 312C37 149 91 -12 244 -12C395 -12 449 166 449 312C449 469 395 635 245 635ZM243 598C332 598 358 454 358 312C358 173 334 26 245 26C158 26 128 174 128 313S152 598 243 598Z"></path></g></svg></span></td></tr><tr class="thead"><td class="align_center">0.1</td><td class="align_center">0.2</td><td class="align_center">0.3</td><td class="align_center">0.4</td><td class="align_center">0.5</td><td class="align_center">0.6</td></tr><tr><td class="thead-hr" colspan="7"><hr/></td></tr><tr><td class="align_left" colspan="7">S-P</td></tr><tr><td class="align_left">GPL-S</td><td class="align_center">1.8911</td><td class="align_center">1.9760</td><td class="align_center">2.0695</td><td class="align_center">2.1737</td><td class="align_center">2.2909</td><td class="align_center">2.4250</td></tr><tr><td class="align_left">GPL-A</td><td class="align_center">2.4183</td><td class="align_center">2.5266</td><td class="align_center">2.6450</td><td class="align_center">2.7753</td><td class="align_center">2.9197</td><td class="align_center">3.0815</td></tr><tr><td class="align_left">GPL-U</td><td class="align_center">2.3398</td><td class="align_center">2.4401</td><td class="align_center">2.5489</td><td class="align_center">2.6673</td><td class="align_center">2.7971</td><td class="align_center">2.9403</td></tr><tr><td class="align_left" colspan="7">A-P</td></tr><tr><td class="align_left">GPL-S</td><td class="align_center">1.9349</td><td class="align_center">2.0784</td><td class="align_center">2.2522</td><td class="align_center">2.4689</td><td class="align_center">2.7495</td><td class="align_center">3.1326</td></tr><tr><td class="align_left">GPL-A</td><td class="align_center">2.4900</td><td class="align_center">2.6931</td><td class="align_center">2.9391</td><td class="align_center">3.2451</td><td class="align_center">3.6391</td><td class="align_center">4.1705</td></tr><tr><td class="align_left">GPL-U</td><td class="align_center">2.3972</td><td class="align_center">2.5735</td><td class="align_center">2.7850</td><td class="align_center">3.0456</td><td class="align_center">3.3785</td><td class="align_center">3.8247</td></tr><tr><td class="align_left" colspan="7">U-P</td></tr><tr><td class="align_left">GPL-S</td><td class="align_center">1.9439</td><td class="align_center">2.0944</td><td class="align_center">2.2703</td><td class="align_center">2.4790</td><td class="align_center">2.7317</td><td class="align_center">3.0457</td></tr><tr><td class="align_left">GPL-A</td><td class="align_center">2.4865</td><td class="align_center">2.6803</td><td class="align_center">2.9072</td><td class="align_center">3.1767</td><td class="align_center">3.5038</td><td class="align_center">3.9112</td></tr><tr><td class="align_left">GPL-U</td><td class="align_center">2.4096</td><td class="align_center">2.5975</td><td class="align_center">2.8172</td><td class="align_center">3.0782</td><td class="align_center">3.3945</td><td class="align_center">3.7882</td></tr><tr class="table-tr"><td colspan="7"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>Nondimensional central deflection <svg height="13.8595pt" id="M204" style="vertical-align:-2.2681pt" version="1.1" viewbox="-0.0498162 -11.5914 38.0685 13.8595" width="38.0685pt" 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="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z"></path></g><g transform="matrix(.013,0,0,-0.013,4.498,0)"><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,-0.013,10.738,0)"><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(.0091,0,0,-0.0091,17.025,-5.741)"><path d="M290 377C321 398 342 415 358 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Mathematical Problems in Engineering

tab10

Table 10

Table 10: 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 10 | 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 