Stability of the Shallow Axisymmetric Parabolic-Conic Bimetallic Shell by Nonlinear Theory

<table>The shell middle surface displacement <svg height="12.1375" id="M89" style="vertical-align:-0.11285pt" version="1.1" viewbox="0 0 7.5374999 12.1375" width="7.5374999" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,12.1375)">
<g transform="translate(72,-62.29)">
<text transform="matrix(1,0,0,-1,-65.2,62.45)">
<tspan style="font-size: 12.50px; " x="0" y="0">⃗</tspan>
<tspan style="font-size: 12.50px; " x="-6.7391171" y="0">𝑢</tspan>
</text>
</g>
</g>
</svg> and displacement <svg height="12.1375" id="M90" style="vertical-align:-0.11285pt" version="1.1" viewbox="0 0 13.6125 12.1375" width="13.6125" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,12.1375)">
<g transform="translate(72,-62.29)">
<text transform="matrix(1,0,0,-1,-65.7,62.45)">
<tspan style="font-size: 12.50px; " x="0" y="0">⃗</tspan>
<tspan style="font-size: 12.50px; " x="-6.238997" y="0">𝑢</tspan>
</text>
<text transform="matrix(1,0,0,-1,-66.02,67.45)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝑧</tspan>
</text>
</g>
</g>
</svg> depending on the local coordinate <svg height="7.375" id="M91" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 7.9250002 7.375" width="7.9250002" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,7.375)">
<g transform="translate(72,-66.1)">
<text transform="matrix(1,0,0,-1,-71.95,66.32)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑧</tspan>
</text>
</g>
</g>
</svg> as well as the rotation of the shell element <svg height="7.1875" id="M92" style="vertical-align:-0.13794pt" version="1.1" viewbox="0 0 10.7625 7.1875" width="10.7625" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,7.1875)">
<g transform="translate(72,-66.25)">
<text transform="matrix(1,0,0,-1,-71.95,66.44)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝜔</tspan>
</text>
</g>
</g>
</svg>.</table>

Mathematical Problems in Engineering

fig4

Figure 4

Figure 4: Stability of the Shallow Axisymmetric Parabolic-Conic Bimetallic Shell by Nonlinear Theory 