An 8-Node Shell Element for Nonlinear Analysis of Shells Using the Refined Combination of Membrane and Shear Interpolation Functions

<table class="table-group" id="tab16"><tr><td><table class="table"><tr><td class="thead-hr" colspan="6"><hr/></td></tr><tr class="thead"><td align="left" rowspan="2">Element size</td><td align="center" colspan="5">Normalized solutions</td></tr><tr class="thead"><td align="center"><span style="width: 27.299999px;"><svg height="16.6625" id="M273" style="vertical-align:-3.56265pt" version="1.1" viewbox="0 0 27.299999 16.6625" width="27.299999" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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<g transform="matrix(.012,-0,0,-.012,27.237,5.525)"><path d="M471 153q-22 -15 -61 -13q-25 31 -45.5 49.5t-56.5 41.5q4 -71 28 -134q-17 -33 -42 -46q-24 12 -42 46q24 63 28 134q-36 -23 -56.5 -41.5t-45.5 -49.5q-36 -2 -61 13q0 28 19 59q65 10 130 43q-65 33 -130 43q-19 31 -19 59q22 15 61 13q25 -31 45.5 -49.5t56.5 -41.5
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</svg></span></td><td align="center">XSHELL-8-ANS</td><td align="center">MITC8</td></tr><tr><td class="thead-hr" colspan="6"><hr/></td></tr><tr><td align="left"><span style="width: 33.974998px;"><svg height="10.8625" id="M276" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 33.974998 10.8625" width="33.974998" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,10.8)"><path d="M456 178h-96v-72q0 -51 12.5 -62.5t72.5 -16.5v-27h-256v27q65 5 78 17t13 62v72h-260v28q182 271 300 426h40v-407h96v-47zM280 225v295h-2q-107 -148 -196 -295h198z" id="x34"></path></g><g transform="matrix(.017,-0,0,-.017,11.996,10.8)"><path d="M528 54l-36 -38l-198 201l-198 -201l-36 38l197 200l-197 201l36 38l198 -202l198 202l36 -38l-197 -201z" id="xD7"></path></g><g transform="matrix(.017,-0,0,-.017,25.748,10.8)"><path d="M456 178h-96v-72q0 -51 12.5 -62.5t72.5 -16.5v-27h-256v27q65 5 78 17t13 62v72h-260v28q182 271 300 426h40v-407h96v-47zM280 225v295h-2q-107 -148 -196 -295h198z" id="x34"></path></g>
</svg></span></td><td align="center">0.687</td><td align="center">0.720</td><td align="center">0.781</td><td align="center">0.738</td><td align="center">0.833 (<svg height="11.125" id="M277" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 33.974998 11.125" width="33.974998" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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</svg>)</td></tr><tr><td align="left"><span style="width: 33.974998px;"><svg height="11.125" id="M278" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 33.974998 11.125" width="33.974998" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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</svg></span></td><td align="center">1.006</td><td align="center">1.024</td><td align="center">0.964</td><td align="center">0.945</td><td align="center">0.990</td></tr><tr class="table-tr"><td colspan="6"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

Results of pinched cylinder with end diaphragm (reference solution: <svg height="19.775" id="M272" style="vertical-align:-3.27605pt" version="1.1" viewbox="0 0 129.875 19.775" width="129.875" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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<g transform="matrix(.012,-0,0,-.012,9.213,19.713)"><path d="M716 28l-8 -28h-254l8 28q55 5 66 17.5t5 47.5l-30 145h-232l-74 -138q-21 -43 -11 -54.5t72 -17.5l-6 -28h-235l8 28q53 7 73.5 21t53.5 70l319 540l33 8q6 -43 33 -176l80 -381q10 -49 26.5 -63t72.5 -19zM495 281l-49 264h-2l-149 -264h200z" id="x1D434"></path></g>
<g transform="matrix(.017,-0,0,-.017,23.275,15.637)"><path d="M535 323h-483v50h483v-50zM535 138h-483v50h483v-50z" id="x3D"></path></g><g transform="matrix(.017,-0,0,-.017,37.962,15.637)"><path d="M384 0h-275v27q67 5 81.5 18.5t14.5 68.5v385q0 38 -7.5 47.5t-40.5 10.5l-48 2v24q85 15 178 52v-521q0 -55 14.5 -68.5t82.5 -18.5v-27z" id="x31"></path></g><g transform="matrix(.017,-0,0,-.017,46.121,15.637)"><path d="M113 -12q-24 0 -39.5 16t-15.5 42q0 24 16 40.5t40 16.5t40 -16.5t16 -40.5q0 -26 -16 -42t-41 -16z" id="x2E"></path></g><g transform="matrix(.017,-0,0,-.017,49.997,15.637)"><path d="M249 635q70 0 116 -43t46 -105q0 -46 -28 -80q-22 -25 -80 -64q62 -35 97 -75t35 -99q0 -81 -63 -131t-135 -50q-83 0 -137.5 45.5t-54.5 123.5q0 52 45 95q29 28 89 64q-109 62 -109 155q0 66 50.5 115t128.5 49zM238 603q-42 0 -67.5 -31t-25.5 -72q0 -50 32.5 -79.5
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<g transform="matrix(.012,-0,0,-.012,116.5,7.475)"><path d="M535 230h-483v50h483v-50z" id="x2212"></path></g><g transform="matrix(.012,-0,0,-.012,123.485,7.475)"><path d="M153 550l-26 -186q79 31 111 31q90 0 141.5 -51t51.5 -119q0 -93 -89 -166q-85 -69 -173 -71q-32 0 -61.5 11.5t-41.5 23.5q-18 17 -17 34q2 16 22 33q14 9 26 -1q61 -50 124 -50q60 0 93 43.5t33 104.5q0 69 -41.5 110t-121.5 41q-53 0 -102 -20l38 305h286l6 -8
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</svg>).

Mathematical Problems in Engineering

tab16

Table 16

Table 16: An 8-Node Shell Element for Nonlinear Analysis of Shells Using the Refined Combination of Membrane and Shear Interpolation Functions 