Abstract
This paper focuses on the treatment of nonlinear multi freedom constraints using an augmented Lagrangian method in finite element analysis of frames. The process of imposing boundary constraints is developed by changing the assembly stiffness equation to produce a modified system of equation considering nonlinear multi freedom constraints. For imposing the nonlinear constraints two better methods are the penalty augmentation method and Lagrange multiplier adjunction method. But there are not free of disadvantages. Using penalty method has a disadvantage in the choice appropriate weight values that balance solution accuracy with the violation of constraint conditions. Using the Lagrange multiplier adjunction method requires additional unknowns, and more complicated storage allocation procedures. This research proposes the connection between these methods using the augmented Lagrangian method for imposing the nonlinear multi freedom constraints in finite element analysis of frame. Based on the Newton Raphson method the incremental-iterative algorithm for solving the nonlinear balanced equations is established.
Highlights
The establishment of solving algorithm for finite element analysis of frames is highly dependent on the implementation of the boundary constraints
Implementing boundary constraints is developed by applying constraints and changing the unmodified master stiffness equation to produce a modified system of equations based on the master stiffness equation [1, 2]
The better techniques suited to the implementation of nonlinear constraints are the penalty augmentation method and Lagrange multiplier adjunction method, employed in the solution of equality constrained optimization problems [3]
Summary
The establishment of solving algorithm for finite element analysis of frames is highly dependent on the implementation of the boundary constraints. Lagrange multiplier adjunction has the advantage of being exact, providing the constraints forces, not requiring guesses as regards weights and it can be effectively employed for treating nonlinear constraints [6]. This method is not free of disadvantage. This research proposes using the augmented Lagrangian method [7,8], the useful connection between penalty function and Lagrange multiplier methods, for imposing the nonlinear multi freedom constraints in finite element analysis of frame. Based on the augmented Lagrangian method, the increment equation is constructed for finite element analysis of frame having nonlinear multi freedom constraints. Based on the proposed algorithm, the calculation program is written for numerical investigations
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