An Approach for Stability Analysis of Gas/Fluid-Filled Cylindrical Hole in Laminated Materials

<div>Schematic illustrates the hole coordinate system (HCS), in which the <i>z</i>-axis is along the hole axis direction and the <i>y</i>-axis is parallel to the material isotropic plane that is represented by the gray lines. <svg height="14.9452pt" id="M71" style="vertical-align:-0.04990005pt" version="1.1" viewbox="-0.0498162 -14.8953 13.3532 14.9452" width="13.3532pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.0091,0,0,-0.0091,.033,-8.971)"><path d="M588 236V289H72V236H588Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,4.221,-8.971)"><path d="M935 263C895 299 821 372 745 456L719 439L824 289H72V236H823L719 87L745 70C821 154 895 227 935 263Z"></path></g><g transform="matrix(.013,0,0,-0.013,3.352,-.45)"><path d="M495 86L479 114C446 82 419 66 409 66C401 66 401 72 406 97C420 166 436 231 453 297C489 435 454 448 428 448C406 448 384 439 354 422C305 394 222 327 161 247H159L183 345C200 415 194 448 173 448C143 448 82 410 23 351L38 325C64 349 95 371 105 371C111 371 116 365 109 336L25 -4L31 -12C50 -4 77 3 107 9C119 69 132 122 145 168C197 254 321 381 370 381C387 381 393 374 378 305L329 95C309 17 320 -12 345 -12C372 -12 430 19 495 86Z"></path></g></svg> is the normal to the material isotropic plane (i.e<i>.</i>, the material symmetry axis direction). <svg height="12.5794pt" id="M72" style="vertical-align:-3.29107pt" version="1.1" viewbox="-0.0498162 -9.28833 13.3646 12.5794" width="13.3646pt" 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="M475 507C475 612 440 712 326 712C139 712 23 420 23 215C23 96 58 -12 180 -12C369 -12 475 293 475 507ZM391 522C391 486 387 448 379 394H126C155 538 222 677 310 677C386 677 391 571 391 522ZM373 346C344 193 283 22 189 22C126 22 106 114 106 196C106 243 111 293 118 346H373Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,6.149,3.132)"><path d="M698 334C698 397 680 451 655 451C627 451 602 424 602 397C602 389 605 383 614 371C622 360 624 340 624 317C624 161 546 47 458 47C419 47 389 69 389 125C389 142 391 162 397 185L457 430L451 435L380 421L315 164C301 107 266 47 222 47C182 47 153 69 153 126C153 137 157 162 161 185C166 214 179 265 197 334C203 358 208 385 208 407C208 433 201 451 176 451C124 451 64 404 24 348L44 320C86 366 113 382 121 382C126 382 128 381 128 374C128 368 126 356 122 341C102 266 88 204 81 164C77 143 73 121 73 107C73 23 131 -12 187 -12C234 -12 281 10 322 45C343 5 383 -12 422 -12C559 -12 698 174 698 334Z"></path></g></svg> is the angle between <svg height="14.9452pt" id="M73" style="vertical-align:-0.04990005pt" version="1.1" viewbox="-0.0498162 -14.8953 13.3532 14.9452" width="13.3532pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.0091,0,0,-0.0091,.033,-8.971)"><path d="M588 236V289H72V236H588Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,4.221,-8.971)"><path d="M935 263C895 299 821 372 745 456L719 439L824 289H72V236H823L719 87L745 70C821 154 895 227 935 263Z"></path></g><g transform="matrix(.013,0,0,-0.013,3.352,-.45)"><path d="M495 86L479 114C446 82 419 66 409 66C401 66 401 72 406 97C420 166 436 231 453 297C489 435 454 448 428 448C406 448 384 439 354 422C305 394 222 327 161 247H159L183 345C200 415 194 448 173 448C143 448 82 410 23 351L38 325C64 349 95 371 105 371C111 371 116 365 109 336L25 -4L31 -12C50 -4 77 3 107 9C119 69 132 122 145 168C197 254 321 381 370 381C387 381 393 374 378 305L329 95C309 17 320 -12 345 -12C372 -12 430 19 495 86Z"></path></g></svg> and the <i>x</i>-axis.</div>

Mathematical Problems in Engineering

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Figure 3

Figure 3: An Approach for Stability Analysis of Gas/Fluid-Filled Cylindrical Hole in Laminated Materials 