A modified penalty function method for treating multi freedom constraints in finite element analysis of frames

Abstract

In finite element analysis, treating boundary condition having multi freedom constraints is needed to produce modified system of equation based on master stiffness equation considering multi freedom constraint. Generally the operation of imposing multi freedom constraints can be developed using Master-Slave Elimination, Penalty Augmentation or Lagrange Multiplier Adjunction methods. The master-slave method is useful only for simple cases but exhibits serious shortcomings for treating arbitrary constraints. The Penalty Augmentation method and Lagrange Multiplier Adjunction are better in many applications. But there are not free of disadvantages. The penalty method has difficulty of choice of weight values that balance solution accuracy with the violation of constraint conditions. The multiplier method is sensitive to the degree of linear independence of the constraints, and the bordered stiffness is singular in the case of the dependent constrains. To reduce the disadvantages of these methods, this paper presents a new method for treating multi freedom constraint. Proposed method is similar to penalty function method and it is called “modified penalty function method”. The concept of the modified penalty function method is based on the constructing equivalent solver system of equations from traditional modified system using regulatory parameters. The basic of method for selecting the regulatory parameters is reducing the violation of modified system. For solving equivalent system the authors proposed an iterative algorithm for seeking the solution. The calculation programs are established based on proposed algorithm. The calculation results using the proposed method matched with the calculation results using other methods.