5.1-1: Show that approximate result stated in EQ 5.1-10 is also produced by the ũ field of Eq. 5.1-8 and
the potential energy expression stated in Eq. 5.1-11.
5.3-1: The uniform elastic bar shown is loaded by axial force P at its left end. The bar is embedded in an
elastic medium that applies end load F and distributed axial load q, both of which are directly
proportional to axial displacement u of the bar. Use the Galerkin method to establish matrices of a oneelement FE formulation based on a linear axial displacement field.
5.5-1: Show that Eq. 5.5-7 can also be obtained from Eq. 5.5-3 and the stationary conditional of the
functional
5.6-1: Use the FE formulation of Eq. 5.6-8 to solve for nodal stresses and nodal displacements in the
uniform two-element bar shown. (Four unknowns remain after boundary conditions are imposed.)