Discontinuous Deformation Analysis Based on Wachspress Interpolation Function for Detailed Stress Distribution

<table class="figure-group"><tr class="fig-image" id="a"><td><object data="https://static-preview.hindawi.com/articles/mpe/volume-2018/4079035/figures/4079035.fig.0012a.svgz" name="4079035.fig.0012a" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(a) </b>Stress <svg height="9.32509pt" id="M246" style="vertical-align:-3.1815pt" version="1.1" viewbox="-0.0498162 -6.14359 11.8314 9.32509" width="11.8314pt" 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="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></g><g transform="matrix(.0091,0,0,-0.0091,6.76,3.132)"><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" id="g50-50"></path></g></svg> from the original DDA</td></tr><tr class="fig-image" id="b"><td><object data="https://static-preview.hindawi.com/articles/mpe/volume-2018/4079035/figures/4079035.fig.0012b.svgz" name="4079035.fig.0012b" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(b) </b>Stress <svg height="9.32509pt" id="M247" style="vertical-align:-3.1815pt" version="1.1" viewbox="-0.0498162 -6.14359 11.8314 9.32509" width="11.8314pt" 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="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></g><g transform="matrix(.0091,0,0,-0.0091,6.76,3.132)"><path d="M414 144C384 79 371 75 317 75H135L276 221C367 316 408 376 408 465C408 570 327 635 237 635C179 635 131 609 100 575L42 494L67 471C94 510 138 565 205 565C277 565 321 517 321 435C321 348 258 270 195 195C146 137 88 81 33 26V0H411C423 44 433 88 446 135L414 144Z" id="g50-51"></path></g></svg> from the original DDA</td></tr><tr class="fig-image" id="c"><td><object data="https://static-preview.hindawi.com/articles/mpe/volume-2018/4079035/figures/4079035.fig.0012c.svgz" name="4079035.fig.0012c" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(c) </b>Stress <svg height="9.32509pt" id="M248" style="vertical-align:-3.1815pt" version="1.1" viewbox="-0.0498162 -6.14359 11.8314 9.32509" width="11.8314pt" 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="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></g><g transform="matrix(.0091,0,0,-0.0091,6.76,3.132)"><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" id="g50-50"></path></g></svg> from the new formulation</td></tr><tr class="fig-image" id="d"><td><object data="https://static-preview.hindawi.com/articles/mpe/volume-2018/4079035/figures/4079035.fig.0012d.svgz" name="4079035.fig.0012d" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(d) </b>Stress <svg height="9.32509pt" id="M249" style="vertical-align:-3.1815pt" version="1.1" viewbox="-0.0498162 -6.14359 11.8314 9.32509" width="11.8314pt" 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="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></g><g transform="matrix(.0091,0,0,-0.0091,6.76,3.132)"><path d="M414 144C384 79 371 75 317 75H135L276 221C367 316 408 376 408 465C408 570 327 635 237 635C179 635 131 609 100 575L42 494L67 471C94 510 138 565 205 565C277 565 321 517 321 435C321 348 258 270 195 195C146 137 88 81 33 26V0H411C423 44 433 88 446 135L414 144Z" id="g50-51"></path></g></svg> from the new formulation</td></tr></table>

<div>Stress distribution after 30 time steps in the case of a 30° friction angle.</div>

Mathematical Problems in Engineering

fig12

Figure 12

Figure 12: Discontinuous Deformation Analysis Based on Wachspress Interpolation Function for Detailed Stress Distribution 