Penalty function method for imposing nonlinear multi freedom and multi node constraints in finite element analysis of frame systems

Abstract

This paper focuses on the treatment of nonlinear multi-freedom and multi-point boundary condition in finite element analysis of frame systems. The treatment of boundary constraints is required to produce modified system of equations based on master stiffness equations considering nonlinear constraints. For imposing nonlinear multi freedom and multi point constraints, the Penalty Augmentation method and Lagrange Multiplier Adjunction method are better in many applications. In present paper, the Penalty Augmentation method is using for implementation of nonlinear boundary constraints. The nonlinear relationship considerably increases the difficulty in constructing and solving the modified system of equations. The Newton Raphson method, have been the most powerful and popular method for solution of nonlinear equations, is used for solving studied problem. Using the Newton Raphson technique, this paper develops the incremental-iterative algorithm to solve the nonlinear modified system of equations. Based on the presented algorithm, the paper proposed calculation procedure and established programs for determining internal forces and displacements of frames having nonlinear multi freedom and multi point constrains boundary. The numerical test results using the proposed method show the efficiency and reliability of proposed algorithm.