Journal of Theoretical
and Applied Mechanics
56, 3, pp. 741-749, Warsaw 2018
DOI: 10.15632/jtam-pl.56.3.741

Collocation method based on barycentric interpolation iteration for analysis of nonlinear microbeams

Meiling Zhuang, Changqing Miao, Zhaoqing Wang
A powerful computational methodology, named the barycentric Lagrange interpolation ite-
ration collocation method (BLIICM), for solving nonlinear bending problems of a doubly
clamped microbeam under electrostatic loads is presented. The nonlinear governing equation
of the microbeam is converted into a linear differential equation by assuming the initial
function. The barycentric Lagrange interpolation collocation method (BLICM) is used to
solve the linear differential equation. The direct linearization formulations and Newton li-
nearization calculation formulations for the nonlinear differential equation have been given.
The calculation method and formulation of the nonlinear integral term have been discussed
in details. By applying a barycentric Lagrange interpolation differential matrix, a matrix-
-vector calculation formula of BLIICM has been established. Numerical results of calculation
examples show that the advantages of the proposed methodology are efficient, simple and
of high precision.
Keywords: nonlinear microbeams, barycentric Lagrange interpolation, collocation method, linearization method, iteration method

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