The Incremental Hybrid Natural Element Method for Elastoplasticity Problems

<table>The radial displacement at <svg height="15.9" id="M134" style="vertical-align:-3.276pt" version="1.1" viewbox="0 0 55.212502 15.9" width="55.212502" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.762)"><path d="M536 404q0 -17 -13.5 -31.5t-26.5 -14.5q-8 0 -15 10q-11 14 -25 14q-22 0 -67 -50q-47 -52 -68 -82l37 -102q31 -88 55 -88t78 59l16 -23q-32 -48 -68.5 -78t-65.5 -30q-19 0 -37.5 20t-29.5 53l-41 116q-72 -106 -114.5 -147.5t-79.5 -41.5q-21 0 -34.5 14t-13.5 37
q0 16 13.5 31.5t28.5 15.5q12 0 17 -11q5 -10 25 -10q22 0 57.5 36t89.5 111l-40 108q-22 58 -36 58q-21 0 -67 -57l-19 20q81 107 125 107q17 0 30 -22t39 -88l22 -55q68 92 108.5 128.5t74.5 36.5q20 0 32.5 -14t12.5 -30z" id="x1D465"></path></g>
<g transform="matrix(.012,-0,0,-.012,9.563,15.838)"><path d="M412 140l28 -9q0 -2 -35 -131h-373v23q112 112 161 170q59 70 92 127t33 115q0 63 -31 98t-86 35q-75 0 -137 -93l-22 20l57 81q55 59 135 59q69 0 118.5 -46.5t49.5 -122.5q0 -62 -29.5 -114t-102.5 -130l-141 -149h186q42 0 58.5 10.5t38.5 56.5z" id="x32"></path></g>
<g transform="matrix(.017,-0,0,-.017,26.288,11.762)"><path d="M535 323h-483v50h483v-50zM535 138h-483v50h483v-50z" id="x3D"></path></g><g transform="matrix(.017,-0,0,-.017,46.652,11.762)"><path d="M476 337q0 -157 -63 -254q-63 -96 -162 -96t-163 96q-64 95 -64 251q0 51 7 99.5t24.5 95.5t43 81.5t65.5 56t89 21.5q75 0 127 -55q96 -97 96 -296zM318 224v225q0 111 -16 161t-53 50t-52 -48.5t-15 -162.5v-225q0 -112 16 -160.5t53 -48.5t52 47.5t15 161.5z" id="x1D7CE"></path></g>
</svg>.</table>

Mathematical Problems in Engineering

fig9

Figure 9

Figure 9: The Incremental Hybrid Natural Element Method for Elastoplasticity Problems 