1. Augmented Lagrangian method for treating multi-freedom constraint in geometrically nonlinear buckling analysis of truss structures using FEM.
- Author
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Quyen, Vu Thi Bich, Tien, Dao Ngoc, Van, Tran Thi Thuy, and Dat, Pham Van
- Subjects
NONLINEAR analysis ,LAGRANGE multiplier ,NONLINEAR equations ,FINITE element method ,ARC length - Abstract
This paper introduces a way to analyze the geometrical nonlinear buckling problem of truss structures with dependent boundary constraints using the finite element method. For determining the nonlinear buckling behavior of the structural system with multi-freedom boundary constraints based on the finite element method it is necessary to implement the dependent boundary conditions to the nonlinear master stiffness equation for building a modified solving system. The author proposes using the augmented Lagrangian method, the connection between the penalty augmentation method and the Lagrange multiplier adjunction method, to implement linear multi-freedom constraints to the nonlinear master stiffness equation. The solving system of equation is constructed by minimization of augmented Lagrange multiplier function to convert a constrained problem into an unconstrained problem. The incremental-iterative algorithm is established based on the arc length method to solve the nonlinear system of equations. Based on the proposed incremental-iterative algorithm the calculation program is written for analyzing the buckling and post-buckling behavior of truss structures with multi-freedom constraints. The numerical test is presented using a written calculation program to investigate the buckling behavior, equilibrium path for plan truss with multi-freedom constraints. The results of the numerical test show the advantages of the proposed method in geometrical nonlinear analysis of truss structures having complicated equilibrium path. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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