Chapter 16, Problem 15P

A finite-element model of a cantilever beam subject to loading and moments (Fig. P16.15) is given by optimizing

$f\left(x,y\right)=5x^2-5xy+2.5y^2-x-1.5y$

where $x=\text{end}$ displacement and $y=\text{end}$ moment. Find the values of x and y that minimize $f\left(x,y\right)$.

FIGURE P16.15

A cantilever beam.