Analysis of Functionally Graded Material Plates Using Triangular Elements with Cell-Based Smoothed Discrete Shear Gap Method

<table>A triangular element is divided into three subtriangles. <svg height="16.4625" id="M138" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 54.375 16.4625" width="54.375" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.625,11.762)"><path d="M799 12l-7 -12h-758l-7 12l381 643h10zM711 50l-298 503l-298 -503h596z" id="x25B3"></path></g>
<g transform="matrix(.012,-0,0,-.012,14.662,15.837)"><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,-.017,21,11.762)"><path d="M95 130q31 0 61 -30t30 -78q0 -53 -38 -87.5t-93 -51.5l-11 29q77 31 77 85q0 26 -17.5 43t-44.5 24q-4 0 -8.5 6.5t-4.5 17.5q0 18 15 30t34 12z" id="x2C"></path></g><g transform="matrix(.017,-0,0,-.017,33.358,11.762)"><path d="M799 12l-7 -12h-758l-7 12l381 643h10zM711 50l-298 503l-298 -503h596z" id="x25B3"></path></g>
<g transform="matrix(.012,-0,0,-.012,47.412,15.837)"><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>
</svg>, and <svg height="16.6" id="M139" style="vertical-align:-3.25793pt" version="1.1" viewbox="0 0 21.625 16.6" width="21.625" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.625,11.762)"><path d="M799 12l-7 -12h-758l-7 12l381 643h10zM711 50l-298 503l-298 -503h596z" id="x25B3"></path></g>
<g transform="matrix(.012,-0,0,-.012,14.662,15.838)"><path d="M285 378v-2q65 -13 102 -54.5t37 -97.5q0 -57 -30.5 -104.5t-74 -75t-85.5 -42t-72 -14.5q-31 0 -59.5 11t-40.5 23q-19 18 -16 36q1 16 23 33q13 10 24 0q58 -51 124 -51q55 0 88 40t33 112q0 64 -39 96.5t-88 32.5q-29 0 -64 -11l-6 29q77 25 118 57.5t41 84.5
q0 45 -26.5 69.5t-68.5 24.5q-67 0 -120 -79l-20 20l43 63q51 56 127 56h1q66 0 107 -37t41 -95q0 -42 -31 -71q-22 -23 -68 -54z" id="x33"></path></g>
</svg> are the subtriangles created by connecting the central point <svg height="12.875" id="M140" style="vertical-align:-0.13794pt" version="1.1" viewbox="0 0 14.3 12.875" width="14.3" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.625,11.963)"><path d="M745 361q0 -166 -116 -272t-291 -106q-136 0 -225.5 83t-89.5 218q0 161 115.5 272t288.5 111q137 0 227.5 -83t90.5 -223zM643 359q0 126 -56 199.5t-167 73.5q-130 0 -213.5 -104t-83.5 -246q0 -117 58 -190.5t165 -73.5q91 0 160.5 52t103 128.5t33.5 160.5z" id="x1D442"></path></g>
</svg> with three field nodes.</table>

Mathematical Problems in Engineering

fig2

Figure 2

Figure 2: Analysis of Functionally Graded Material Plates Using Triangular Elements with Cell-Based Smoothed Discrete Shear Gap Method 