An Analytical-Based Lightning-Induced Damage Model for an Aircraft Wing Exposed to Pressure Loading of Lightning

<table class="table-group" id="tab3"><tr><td><table class="table"><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr class="thead"><td class="align_left">Lightning current components</td><td class="align_center"><span style="width: 68.9575ptpx;"><svg height="12.5703pt" id="M24" style="vertical-align:-3.28197pt" version="1.1" viewbox="-0.0498162 -9.28833 68.9575 12.5703" width="68.9575pt" 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="M405 650H141L135 622C222 616 230 610 215 535L133 116C118 41 113 33 29 28L23 0H289L295 28C209 33 205 40 219 116L298 535C312 609 317 616 399 622L405 650Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,4.719,3.132)"><path d="M264 635C97 635 40 460 40 311C40 167 94 -12 262 -12C431 -12 484 166 484 312C484 457 431 635 264 635ZM261 595C330 595 347 450 347 314C347 174 330 28 263 28C195 28 177 174 177 315C177 450 194 595 261 595Z"></path></g><g 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390 653 345 653 274V107C653 36 642 32 583 26V0H797Z"></path></g><g transform="matrix(.013,0,0,-0.013,46.893,0)"><path d="M169 380V459C122 440 66 423 24 416V392C86 384 90 382 90 317V-135C90 -201 81 -207 17 -213V-240H253V-213C176 -207 169 -201 169 -125V6C182 -1 208 -11 238 -12C368 12 487 109 487 260C487 358 421 449 310 449C298 449 279 444 261 433L169 380ZM169 346C196 367 237 389 269 389C341 389 403 329 403 221C403 109 347 37 263 37C228 37 191 53 169 76V346Z"></path></g><g transform="matrix(.013,0,0,-0.013,53.823,0)"><path d="M380 106C343 72 306 56 265 56C195 56 116 112 115 248C235 252 361 262 377 265C396 269 400 277 400 297C400 374 333 449 250 449H249C198 449 144 421 103 376S37 269 37 201C37 88 109 -12 232 -12C263 -12 332 6 395 84L380 106ZM225 412C281 412 315 364 314 312C314 297 308 292 290 292C232 290 176 289 120 289C135 370 180 412 225 412Z"></path></g><g transform="matrix(.013,0,0,-0.013,59.348,0)"><path d="M181 342V451C133 431 89 419 40 411V388C98 381 102 377 102 311V104C102 38 95 32 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106ZM333 204C265 95 210 54 169 54C137 54 113 96 113 171C113 302 191 405 252 405C301 405 318 306 333 204Z"></path></g><g transform="matrix(.013,0,0,-0.013,20.434,0)"><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,-0.013,24.932,0)"><path d="M352 391C352 416 319 448 267 448C236 448 173 423 147 400C107 364 96 332 96 304C96 248 143 210 193 181C241 153 258 124 258 100C258 72 232 38 184 38C151 38 107 66 81 108C77 114 64 116 55 111C34 99 23 84 23 65C23 29 81 -12 134 -12C220 -12 325 61 325 141C325 184 297 215 234 256C194 282 161 309 161 346C161 380 188 401 217 401C255 401 279 380 301 353C308 344 313 341 325 347C341 355 352 371 352 391Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,29.807,-5.741)"><path d="M556 236V289H56V236H556Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,35.367,-5.741)"><path d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 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-16C308 -16 351 1 397 26C471 67 545 142 545 221C545 315 486 365 401 395C469 437 558 498 558 587Z"></path></g><g transform="matrix(.013,0,0,-0.013,20.603,0)"><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,-0.013,25.101,0)"><path d="M352 391C352 416 319 448 267 448C236 448 173 423 147 400C107 364 96 332 96 304C96 248 143 210 193 181C241 153 258 124 258 100C258 72 232 38 184 38C151 38 107 66 81 108C77 114 64 116 55 111C34 99 23 84 23 65C23 29 81 -12 134 -12C220 -12 325 61 325 141C325 184 297 215 234 256C194 282 161 309 161 346C161 380 188 401 217 401C255 401 279 380 301 353C308 344 313 341 325 347C341 355 352 371 352 391Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,29.976,-5.741)"><path d="M556 236V289H56V236H556Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,35.536,-5.741)"><path d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z"></path></g><g transform="matrix(.013,0,0,-0.013,40.504,0)"><path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z"></path></g></svg></span></td></tr><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr><td class="align_left">A</td><td class="align_center">218,810</td><td class="align_center">11,354</td><td class="align_center">647,265</td></tr><tr><td class="align_left">B</td><td class="align_center">11,300</td><td class="align_center">700</td><td class="align_center">2,000</td></tr><tr><td class="align_left">C</td><td class="align_center">400</td><td class="align_center">Not applicable</td><td class="align_center">Not applicable</td></tr><tr><td class="align_left">D</td><td class="align_center">109,405</td><td class="align_center">22,708</td><td class="align_center">1,294,530</td></tr><tr class="table-tr"><td colspan="4"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>Values of the lightning current parameters.</div>

Mathematical Problems in Engineering

tab3

Table 3

Table 3: An Analytical-Based Lightning-Induced Damage Model for an Aircraft Wing Exposed to Pressure Loading of Lightning 