Implementation of Structural Assemblies by Simultaneous Projection and Density-Based Topology Optimization

<div>Optimized topologies and compliance for various constraints values. (a) <i>f</i> = 178, <i>r</i><sub>min</sub> = 10, <i>r</i><sub>ɸ</sub> = 10, <i>r</i><sub>max</sub> = 10, <span class="nowrap"><svg height="11.7782pt" id="M208" style="vertical-align:-3.42938pt" version="1.1" viewbox="-0.0498162 -8.34882 40.7613 11.7782" width="40.7613pt" 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="M478 372C478 418 458 448 431 448C409 448 389 431 389 410C389 404 391 400 394 395C398 388 406 371 406 348C406 253 308 122 251 51H249C254 122 249 257 231 336C212 421 189 448 159 448C126 448 75 412 23 327L48 306C83 354 103 371 115 371C125 371 134 360 144 334C185 224 192 64 183 -19C146 -100 116 -202 110 -244L125 -261C154 -259 208 -234 222 -220C222 -194 225 -84 235 -23C247 -3 273 36 308 79C379 165 478 288 478 372Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,5.668,3.132)"><path d="M498 658H277V626C335 621 342 616 342 579C220 574 46 510 46 330C46 148 226 88 342 86C342 41 334 37 271 32V0H498V32C435 37 427 41 427 86C546 88 723 153 723 337C723 518 550 575 427 579C427 616 434 621 498 626V658ZM342 123C255 129 141 183 141 338C141 489 257 538 342 542V123ZM427 542C512 538 629 489 629 333C629 178 512 129 427 123V542Z"></path></g><g transform="matrix(.013,0,0,-0.013,16.822,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,28.085,0)"><path d="M285 378C315 398 338 416 353 432C373 451 384 474 384 503C384 579 325 635 236 635H235C182 635 136 610 108 579L65 516L85 496C110 533 150 575 205 575C258 575 300 543 300 481C300 407 232 369 141 339L147 310C163 315 188 321 211 321C268 321 338 284 338 192C338 94 288 40 217 40C160 40 119 68 93 91C85 98 77 97 69 91C60 84 47 71 46 58C44 46 48 35 62 22C75 10 116 -12 162 -12C234 -12 424 62 424 224C424 297 373 359 285 376V378Z"></path></g><g transform="matrix(.013,0,0,-0.013,34.325,0)"><path d="M412 140C382 77 369 73 315 73H129L270 222C362 320 402 379 402 466C402 571 322 635 234 635C177 635 130 609 99 576L42 495L64 475C90 514 133 568 201 568C274 568 318 519 318 435C318 349 255 267 193 193C144 135 87 78 32 23V0H405C417 45 427 89 440 131L412 140Z"></path></g></svg>,</span> and iterations = 50. (b) Shape of optimized projection area. (c) Graphical representation.</div>

Journal of Mathematics

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Figure 5

Figure 5: Implementation of Structural Assemblies by Simultaneous Projection and Density-Based Topology Optimization 