Question: The following integral represents the strain energy in a bar of length L and cross-sectional area A: Where and E is the modulus of elasticity.
The following integral represents the strain energy in a bar of length L and cross-sectional area A:
-1.png){kind=small}
Where
![{d} = |u2 [B] = [D] = E](https://dsd5zvtm8ll6.cloudfront.net/si.question.images/image/images16/1414-P-T-H-T(1637)-2.png){kind=small}
and E is the modulus of elasticity.
Show that dU/d{d} yields [k]{d}, where [k] is the bar stiffness matrix given by
![{d}"[B]"[D][B]{d} dx U = A 2 2 Jo {d} = |u2 [B]](https://dsd5zvtm8ll6.cloudfront.net/si.question.images/image/images16/1414-P-T-H-T(1637)-3.png){kind=small}
{d}"[B]"[D][B]{d} dx U = A 2 2 Jo {d} = |u2 [B] = [D] = E
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