Simplified analysis of structures using applied element method

Abstract

The Applied Element Method (AEM) is a numerical method of structural analysis. The degrees of freedom are located at the centroid of an element, which is rigid. In AEM, many pairs of springs are provided on the faces of the element. Although the AEM is very efficient, it is not popular due to the limited literature discussing stiffness matrix of AEM in detail. In this paper, the formulation of the stiffness matrix for two-dimensional and three-dimensional analysis by AEM is discussed. To improve the accuracy of AEM, a simplified stiffness matrix is developed when an infinite number of springs is considered. The strains, stresses, bending moment and shear forces are also derived. The efficiency of AEM is studied by solving a few conventional problems on beams. Comparison of AEM with FEM is also done. The AEM could predict displacements, strains, stresses, bending moment, shear force, natural frequency and mode shapes with reasonable accuracy.

Keywords

• applied element method
• stiffness matrix
• formulation
• natural frequency
• mode shape