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.
Show that dU/d{d} yields [k]{d}, where [k] is the bar stiffness matrix given by

Transcribed Image Text:

{d}"[B]"[D][B]{d} dx U = A 2 2 Jo {d} = |u2 [B] = [D] = E