A New and Efficient Boundary Element-Free Method for 2-D Crack Problems

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vert-adv-y="412"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,27.731,0)"><path d="M548 455L523 469C505 448 490 439 461 439C416 439 374 447 316 447C144 447 23 310 23 161C23 47 89 -12 179 -12C312 -12 429 106 429 244C429 303 419 344 368 386L371 388C404 383 440 378 474 378C507 378 530 411 548 455ZM350 274C350 191 308 25 198 25C144 25 108 75 108 157C108 264 170 395 276 395C296 395 320 384 333 360C347 334 350 316 350 274Z" id="g113-240"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="565" vert-adv-y="565"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,35.078,-.271)"><path d="M782 731H740L476 -79H474L280 352L133 274L151 239L242 286L473 -219L782 731Z" id="g119-37"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="764" vert-adv-y="764"></glyph.data></g><rect height="0.65243" width="13.0096" x="45.0472" y="-9.80939"></rect><g transform="matrix(.013,0,0,-0.013,45.047,0)"><path d="M574 449L545 460C526 432 516 430 487 430C404 430 311 435 226 435C104 435 56 379 25 341L43 318C81 354 121 372 181 372C161 246 87 53 23 3L30 -12C48 -12 88 -4 113 11C157 75 207 248 232 371L386 367L326 109C321 86 318 66 318 50C318 4 339 -12 366 -12C410 -12 461 21 505 69L492 96C467 79 434 60 418 60C406 60 400 78 411 147C422 217 439 300 457 366C487 366 524 367 536 370C547 385 558 408 574 449Z" id="g113-238"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="591" vert-adv-y="591"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,52.732,0)"><path d="M383 397C383 424 344 448 299 448C244 448 172 409 132 375C66 319 23 227 23 146C23 42 74 -12 146 -12C208 -12 298 30 359 103L343 124C315 95 248 48 192 48C145 48 111 85 111 163C111 228 129 294 151 330C171 363 201 401 241 401C275 401 302 384 325 356C332 347 339 344 348 348C373 360 383 381 383 397Z" id="g113-100"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="406" vert-adv-y="406"></glyph.data></g></svg></span></td></tr><tr class="thead"><td class="align_center">Present</td><td class="align_center">Ref [<a href="/journals/mpe/2017/1863714/#B8">8</a>]</td><td class="align_center">Present</td><td class="align_center">Ref [<a href="/journals/mpe/2017/1863714/#B8">8</a>]</td></tr><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr><td class="align_left">0.2</td><td class="align_center">0.5955</td><td class="align_center">0.604</td><td class="align_center">0.5613</td><td class="align_center">0.556</td></tr><tr><td class="align_left">0.4</td><td class="align_center">0.5683</td><td class="align_center">0.576</td><td class="align_center">0.6107</td><td class="align_center">0.603</td></tr><tr><td class="align_left">0.6</td><td class="align_center">0.5669</td><td class="align_center">0.570</td><td class="align_center">0.6296</td><td class="align_center">0.624</td></tr><tr class="table-tr"><td colspan="5"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

The normalized stress intensity factors for the crack tips <svg height="8.68572pt" id="M181" style="vertical-align:-0.0498209pt" version="1.1" viewbox="-0.0498162 -8.6359 7.94191 8.68572" width="7.94191pt" 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="M578 512C578 619 494 650 387 650H140L134 622C219 615 223 609 210 542L127 119C112 40 104 34 23 28L17 0H235C317 0 387 7 444 33C515 65 564 122 564 195C564 289 495 335 412 352V354C505 373 578 422 578 512ZM486 510C486 422 423 367 314 367H257L294 565C299 591 305 602 315 608C324 614 339 617 362 617C421 617 486 595 486 510ZM466 200C466 100 393 35 296 35C222 35 198 51 212 127L250 333H303C388 333 466 303 466 200Z" id="g113-67"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="601" vert-adv-y="601"></glyph.data></g></svg>.

Mathematical Problems in Engineering

tab3

Table 3

Table 3: A New and Efficient Boundary Element-Free Method for 2-D Crack Problems 