Corotational Finite Element Dynamic Analysis of Space Frames with Geometrically Nonlinear Behavior Based on Tait–Bryan Angles

<div>The <i>i</i><sup>th</sup> beam element displacement and internal force vector components with the attached corotational local frame in planes (<svg height="8.8553pt" id="M52" style="vertical-align:-0.04981995pt" version="1.1" viewbox="-0.0498162 -8.80548 6.28474 8.8553" width="6.28474pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><rect height="0.65243" width="6.1851" x="0" y="-8.10323"></rect><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M474 0V26C414 34 401 43 364 100L267 248C300 297 324 332 345 358C381 400 394 405 455 411V437H272V411C316 406 323 401 305 370C287 337 267 306 247 276L188 369C169 397 173 405 215 411V437H16V411C71 404 83 396 114 348L201 212C171 167 144 127 116 92C77 42 66 34 4 26V0H190V26C139 34 136 43 156 77C175 113 198 150 220 183L294 66C311 39 302 31 260 26V0H474Z"></path></g></svg><sub><i>i</i></sub> − <svg height="12.1892pt" id="M53" style="vertical-align:-3.38372pt" version="1.1" viewbox="-0.0498162 -8.80548 6.33692 12.1892" width="6.33692pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><rect height="0.65243" width="6.23729" x="0" y="-8.10323"></rect><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M478 437H297V411C355 404 361 392 349 355C329 292 285 174 257 106L167 356C153 394 158 404 205 411L204 437H2V411C57 404 66 391 88 336C117 265 162 144 202 30C208 13 209 0 204 -15C199 -28 191 -49 173 -84C149 -128 130 -153 98 -172C81 -184 73 -193 73 -209C73 -233 101 -257 129 -257C143 -257 156 -252 161 -232C175 -179 197 -122 264 38C333 203 364 286 390 339C417 395 425 403 478 411V437Z"></path></g></svg><sub><i>i</i></sub>) and (<svg height="8.8553pt" id="M54" style="vertical-align:-0.04981995pt" version="1.1" viewbox="-0.0498162 -8.80548 6.28474 8.8553" width="6.28474pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><rect height="0.65243" width="6.1851" x="0" y="-8.10323"></rect><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M474 0V26C414 34 401 43 364 100L267 248C300 297 324 332 345 358C381 400 394 405 455 411V437H272V411C316 406 323 401 305 370C287 337 267 306 247 276L188 369C169 397 173 405 215 411V437H16V411C71 404 83 396 114 348L201 212C171 167 144 127 116 92C77 42 66 34 4 26V0H190V26C139 34 136 43 156 77C175 113 198 150 220 183L294 66C311 39 302 31 260 26V0H474Z"></path></g></svg><sub><i>i</i></sub> − <svg height="9.28592pt" id="M55" style="vertical-align:-0.04981995pt" version="1.1" viewbox="-0.0498162 -9.2361 5.5801 9.28592" width="5.5801pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><rect height="0.65243" width="5.48047" x="0" y="-8.53385"></rect><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M387 138L374 114C336 54 316 33 240 33H141C223 167 303 295 385 423L379 437H149C112 437 100 443 94 458H73C65 415 50 352 39 314L64 305L78 332C106 388 119 403 191 403C214 403 246 403 280 403C198 270 117 142 31 15L38 0H367C382 40 399 86 413 125L387 138Z"></path></g></svg><sub><i>i</i></sub>).</div>

Shock and Vibration

fig3

Figure 3

Figure 3: Corotational Finite Element Dynamic Analysis of Space Frames with Geometrically Nonlinear Behavior Based on Tait–Bryan Angles 