Using force equilibrium; i.e., internal force caused by stress is equal to external force.
Problem
A force F is applied at the tip of the uniform bar shown in the figure. The displacement of the bar is given as u(X) = λX where λ is the principal stretch. The initial length and the cross-sectional area of the bar are, respectively, A0 and L0.
The elastic modulus of the material is E. Calculate the tip displacement by solving for the principal stretch using the total Lagrangian formulation with the St. Venant-Kirchhoff material model.
Assume the following numerical values: E = 700 MPa, A0 = 1.0 X 10-4 m2, L0 = 1.0 m, and F = 10 kN. Compare the tip displacement with that of the linear elastic model when (a) E = 700 MPa and (b) E = 70 GPa.
