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="tab11"><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="M233" 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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</svg></span></td><td align="center"><span style="width: 34.912498px;"><svg height="18.1875" id="M234" style="vertical-align:-3.56265pt" version="1.1" viewbox="0 0 34.912498 18.1875" width="34.912498" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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q-4 71 -28 134q17 33 42 46q24 -12 42 -46q-24 -63 -28 -134q36 23 56.5 41.5t45.5 49.5q36 2 61 -13q0 -28 -19 -59q-65 -10 -130 -43q65 -33 130 -43q19 -31 19 -59z" id="x2217"></path></g>
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q-4 71 -28 134q17 33 42 46q24 -12 42 -46q-24 -63 -28 -134q36 23 56.5 41.5t45.5 49.5q36 2 61 -13q0 -28 -19 -59q-65 -10 -130 -43q65 -33 130 -43q19 -31 19 -59z" id="x2217"></path></g><g transform="matrix(.012,-0,0,-.012,27.237,18.712)"><path d="M137 343l67 33q37 17 63 17q79 0 129.5 -53t50.5 -131q0 -92 -58 -156.5t-147 -64.5t-147 68t-58 182q0 63 17 119t43 95.5t61.5 72t69 52t67.5 31.5q62 22 128 33l6 -32q-56 -11 -108 -35q-149 -71 -184 -231zM227 337q-47 0 -95 -27q-6 -23 -6 -70q0 -93 36 -155.5
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</svg></span></td><td align="center">QUAD8*</td><td align="center">QUAD8**</td></tr><tr><td class="thead-hr" colspan="6"><hr/></td></tr><tr><td align="left"><span style="width: 33.974998px;"><svg height="11.225" id="M236" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 33.974998 11.225" 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,.062,10.963)"><path d="M137 343l67 33q37 17 63 17q79 0 129.5 -53t50.5 -131q0 -92 -58 -156.5t-147 -64.5t-147 68t-58 182q0 63 17 119t43 95.5t61.5 72t69 52t67.5 31.5q62 22 128 33l6 -32q-56 -11 -108 -35q-149 -71 -184 -231zM227 337q-47 0 -95 -27q-6 -23 -6 -70q0 -93 36 -155.5
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</svg></span></td><td align="center">0.991</td><td align="center">0.991</td><td align="center">0.991</td><td align="center">0.869</td><td align="center">0.942</td></tr><tr class="table-tr"><td colspan="6"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

Results of curved beam (<svg height="12.4375" id="M231" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 48.512501 12.4375" width="48.512501" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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</svg>) under in-plane shear (reference solution: <svg height="15" id="M232" style="vertical-align:-3.27605pt" version="1.1" viewbox="0 0 87.862503 15" width="87.862503" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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</svg>).

Mathematical Problems in Engineering

tab11

Table 11

Table 11: An 8-Node Shell Element for Nonlinear Analysis of Shells Using the Refined Combination of Membrane and Shear Interpolation Functions 