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Finite element solution, Ritz-Galerkin method, Nonlinear Euler-Bernoulli beam, Power-law, Work hardening material, Hollomon's equation, Convergence, Error estimate, Hermite elements
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Analytic And Finite Element Solutions Of The Power-Law Euler-Bernoulli Beams, Dongming Wei, Yu Liu
Analytic And Finite Element Solutions Of The Power-Law Euler-Bernoulli Beams, Dongming Wei, Yu Liu
Dongming Wei
In this paper, we use Hermite cubic finite elements to approximate the solutions of a nonlinear Euler-Bernoulli beam equation. The equation is derived from Hollomon’s generalized Hooke’s law for work hardening materials with the assumptions of the Euler-Bernoulli beam theory. The Ritz-Galerkin finite element procedure is used to form a finite dimensional nonlinear program problem, and a nonlinear conjugate gradient scheme is implemented to find the minimizer of the Lagrangian. Convergence of the finite element approximations is analyzed and some error estimates are presented. A Matlab finite element code is developed to provide numerical solutions to the beam equation. Some …