We consider the problem of finding the equilibria of a planar electrically-charged elastic strut subject to endloading. Ideas from the calculus of variations are applied to identify the equilibria of the energy functional of the elastic strut. Namely, equilibria are found by solving the Euler-Lagrange system of integro-differential equations with boundary conditions at the endpoints. Parameter continuation techniques are used to solve this system for a family of solutions parameterized by λ. As λ varies, the electrostatic repulsion applied to the strut causes convergence issues in the continuation steps in the contact regions of the strut.

First a generalized, nonuniform discretization is developed for the Euler-Lagrange system of integro-differential equations, so that the system may be solved with a nonuniform mesh. Then two automated adaptivity schemes, a backward scheme and a central scheme, are developed and embedded into the computations of the problem with the intention of moving the mesh points into the contact region. Both the backward and central adaptivity schemes moved the mesh points into the contact regions.