A matlab program for plastic analysis of 2-d frames

Abstract

This paper describes a program for plastic analysis of 2-d frames written in matlab programming language. The program is developed using the object oriented programming approach as an alternative to traditional procedural programming. A step by step incremental linear analysis is used for the solution. The two node frame element represents the finite element. The element stiffness matrix for frame element is constructed by super imposing both axial and bending stiffness. Hermite polynomials are used as interpolation functions for the solution of the finite element analysis. Element nodal forces and stiffness matrices are obtained using Gauss quadrature scheme as a numerical integration technique. This integration scheme for polynomial functions leads in a very accurate solution. Matlab library has served for the solution of systems of linear equations. The two most important classes in the program are the cstruct_lin_static_preprocess class which calculates all preprocess data and the cstruct_lin_plastic_postprocess class, which gets as input argument the object of preprocess class and calculates all postprocess data. A simple frame structure under lateral loads is presented as an example and solved by the program. The stress state represented by internal moment diagram, shear force diagram and axial force diagram is given for each step and the final step. The presentation of this data is in tabular form and graphical form. A plot of the deformed shape for every step is also provided by the program. The history of force-displacement and the plot of plastic hinges is displayed.