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FEM solution to the dynamic graphene Euler-Bernoulli beam equation in 1d

Author: Mansur Shakipov

The fully nonlinear variation of the dynamic Euler-Bernoulli beam equation corresponding to the graphene material is solved using Hermite cubic elements with a special nonlinear approximation. The time discretization scheme is taken from [1]. The Gauss-Legendre quadrature nodes and weights generator routine is taken from [2].

References:

  1. S. Larsson and V. Thomee, Partial Differential Equations with Numerical Methods, ser. Texts in Applied Mathematics. Springer Berlin Heidelberg, 2008, p. 204. [Online]. Available: https://books.google.com/books?id=vZGCaLoEqwgC

  2. Greg von Winckel (2022). Legendre-Gauss Quadrature Weights and Nodes (https://www.mathworks.com/matlabcentral/fileexchange/4540-legendre-gauss-quadrature-weights-and-nodes), MATLAB Central File Exchange. Retrieved January 3, 2022.