ARTICLE
Collocation method based on barycentric interpolation iteration for analysis of nonlinear microbeams
 
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1
Key Laboratory of Concrete and Prestressed Concrete Structures of Ministry of Education, Southeast University, Nanjing, School of Civil Engineering, Southeast University, Nanjing
2
Key Laboratory of Concrete and Prestressed Concrete Structures of Ministry of Education, Southeast University, Nanjing, School of Civil Engineering, Southeast University, Nanjing
3
Institute of Mechanics, Shandong Jianzhu University, Jinan
Publication date: 2018-07-20
 
Journal of Theoretical and Applied Mechanics 2018;56(3):741–749
 
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ABSTRACT
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.
eISSN:2543-6309
ISSN:1429-2955