Existence and continuous dependence of solutions for equilibrium configurations of cantilever beam

This article explores the equilibrium configurations of a cantilever beam described by the minimizer of a generalized total energy functional. We reformulate the problem as a boundary value problem using the Euler-Lagrange condition and investigate the existence and uniqueness of minimizers. Furthermore, we discuss the dependence of solutions on the parameters of the boundary value problems. In addition, the Adomian decomposition method is derived for approximating the solution in terms of series. Finally, numerical results for the equilibrium configurations of cantilever beams are presented to support our theoretical analysis.

Automated summary

This article investigates the equilibrium configurations of a cantilever beam, discussing the minimization of a generalized total energy functional and the solution to the boundary value problem. It also explores the dependence of solutions on the parameters of the problem and presents the Adomian decomposition method for approximating the solution. Numerical results are provided to support the theoretical analysis.