Efficient Finite Element Methodology Based on Cartesian Grids: Application to Structural Shape Optimization

<table class="table-group" width="800px"><tr class="fig-image" id="a"><td><img alt="953786.fig.001a" src="https://static.hindawi.com/articles/aaa/volume-2013/953786/figures/953786.fig.001a.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(a) </b>  Cartesian grid pile</td></tr></table></td></tr><tr class="fig-image" id="b"><td><img alt="953786.fig.001b" src="https://static.hindawi.com/articles/aaa/volume-2013/953786/figures/953786.fig.001b.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(b) </b>Analysis mesh. <svg height="6.7750001" id="M40" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 6.4250002 6.7750001" width="6.4250002" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,6.713)"><path d="M326 255q0 -56 -41 -96t-99 -40t-99 40t-41 96t41 96t99 40t99 -40t41 -96zM274 255q0 38 -25.5 65t-62.5 27t-62.5 -27t-25.5 -65t25.5 -65t62.5 -27t62.5 27t25.5 65z" id="x2218"></path></g>
</svg> nodes with multipoint constraints for <svg height="16.125" id="M41" style="vertical-align:-0.23206pt" version="1.1" viewbox="0 0 18.4375 16.125" width="18.4375" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,15.775)"><path d="M682 629q-1 -16 -1.5 -72t-2.5 -86l-31 -4q-5 92 -51 129t-139 37q-100 0 -177 -49t-116 -125t-39 -162q0 -122 66 -201t182 -79q83 0 137 42.5t112 128.5l26 -15q-12 -31 -42.5 -88t-45.5 -75q-139 -27 -199 -27q-148 0 -243 81.5t-95 226.5q0 173 129.5 274.5
t325.5 101.5q114 0 204 -38z" id="x1D436"></path></g>
<g transform="matrix(.012,-0,0,-.012,12.05,7.613)"><path d="M241 635q53 0 94 -28.5t63.5 -76t33.5 -102.5t11 -116q0 -58 -11 -112.5t-34 -103.5t-63.5 -78.5t-94.5 -29.5t-95 28t-64.5 75t-34.5 102.5t-11 118.5q0 58 11.5 112.5t34.5 103t64.5 78t95.5 29.5zM238 602q-32 0 -55.5 -25t-35.5 -68t-17.5 -91t-5.5 -105
q0 -76 10 -138.5t37 -107.5t69 -45q32 0 55.5 25t35.5 68.5t17.5 91.5t5.5 105t-5.5 105.5t-18 92t-36 68t-56.5 24.5z" id="x30"></path></g>
</svg> continuity</td></tr></table></td></tr></table>

<table>Difference between the <i>Cartesian grid pile</i> and the analysis mesh.</table>

Abstract and Applied Analysis

fig1

Figure 1

Figure 1: Efficient Finite Element Methodology Based on Cartesian Grids: Application to Structural Shape Optimization 