Effect of Material Nonlinearity on Large Deflection of Variable-Arc-Length Beams Subjected to Uniform Self-Weight

<table>Variations of the dimensionless uniform self-weight <svg height="11.7625" id="M90" style="vertical-align:-1.32405pt" version="1.1" viewbox="0 0 12.225 11.7625" width="12.225" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,1.3,11.5)"><use xlink:href="#xF5C02"></use></g><g transform="matrix(.017,-0,0,-.017,.076,11.5)"><use xlink:href="#x1D464"></use></g>
</svg> with respect to the end rotation <svg height="16.3125" id="M91" style="vertical-align:-3.276pt" version="1.1" viewbox="0 0 17.9375 16.3125" width="17.9375" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,12.162)"><use xlink:href="#x1D703"></use></g>
<g transform="matrix(.012,-0,0,-.012,8.525,16.25)"><use xlink:href="#x1D434"></use></g>
</svg> for <svg height="7.9499998" id="M92" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 8.6625004 7.9499998" width="8.6625004" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,7.675)"><use xlink:href="#x1D45B"></use></g>
</svg> = 1, 1.5, 2, 3, and 4.</table>

Mathematical Problems in Engineering

fig3

Figure 3

Figure 3: Effect of Material Nonlinearity on Large Deflection of Variable-Arc-Length Beams Subjected to Uniform Self-Weight 