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

<table>The function <svg height="13.55" id="M281" style="vertical-align:-2.29482pt" version="1.1" viewbox="0 0 53.474998 13.55" width="53.474998" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.55)">
<g transform="translate(72,-61.16)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝜏</tspan>
<tspan style="font-size: 12.50px; " x="9.8648672" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="21.905256" y="0">𝜏</tspan>
<tspan style="font-size: 12.50px; " x="28.306791" y="0">(</tspan>
<tspan style="font-size: 12.50px; " x="32.470291" y="0">𝜉</tspan>
<tspan style="font-size: 12.50px; " x="38.509239" y="0">)</tspan>
</text>
</g>
</g>
</svg> as an example of parabolic axisymmetric shell expressing the phenomenon of a system snap-through between points <svg height="10.55" id="M282" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 22.8375 10.55" width="22.8375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.55)">
<g transform="translate(72,-63.56)">
<text transform="matrix(1,0,0,-1,-71.95,63.61)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝐴</tspan>
<tspan style="font-size: 12.50px; " x="8.9646511" y="0">𝐵</tspan>
</text>
</g>
</g>
</svg> in the process of heating up and the points <svg height="10.6125" id="M283" style="vertical-align:-0.15048pt" version="1.1" viewbox="0 0 23.1875 10.6125" width="23.1875" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.6125)">
<g transform="translate(72,-63.51)">
<text transform="matrix(1,0,0,-1,-71.95,63.71)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝐶</tspan>
<tspan style="font-size: 12.50px; " x="8.389513" y="0">𝐷</tspan>
</text>
</g>
</g>
</svg> in the process of cooling.</table>

Mathematical Problems in Engineering

fig12

Figure 12

Figure 12: Stability of the Shallow Axisymmetric Parabolic-Conic Bimetallic Shell by Nonlinear Theory 