Calculate the tip displacement by solving the total

Question

Solve Problem 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 element shown in the figure. 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 the total Lagrangian variational equation with the St. Venant-Kirchhoff nonlinear elastic material model.

Assume the following numerical values: E = 700 MPa, A₀ = 1.0 X 10^-4 m², L₀ = 1.0 m, and R = 10kN.

Compare the tip displacement with that from the linear elastic model when (a) E = 700 MPa and (b) E = 70GPa.