Development of Truss Linear Macro-Element

Abstract

Macro-elements are among the powerful means in reducing the number of equations to be solved in finite element analysis. In the proposed method, several finite truss elements will be transformed into a single element called the macro-element. This is done by equating the potential energy of the macro-element to the potential energy of the equivalent truss finite elements. If the order of the macro-element function corresponds to the order of the structural behavior that it models, an exact solution is achieved. In this paper, a truss linear macro-element is developed. The developed macro-element was tested and the results were compared with the results of conventional finite element solutions and with closed form solutions. Excellent results were achieved with substantial reduction in the number of equations.