On the Optimisation of fundamental frequency to determine the Optimal Design of Bracing System for A Three Storey One Bay Two Dimensional Planar Structure

Abstract

Bracing systems are useful to improve the resistance of multi-storey buildings subjected to wind forces acting in lateral direction on the structure.  The main focus of this paper is to find the optimal design of the bracing for a three storey one bay two dimensional planar structure.  The eigen frequency of the structure is maximized to determine the relative density using a stress based criteria of each element for every iteration.  The finite element mesh consists of first order four node quadrilateral elements in plane stress condition.  Solid Isotropic Material with penalization is adopted to penalize the Young’s modulus of elasticity.  The fundamental frequency of the distribution of material is calculated for every iteration.  The finite element analysis is performed and the elemental stress is calculated at the centroid of each element and the nodal displacements are calculated at each node.  The structure is found to be safe in stress and displacement.  A standard example from the literature is analysed and the results are compared.  The results show that the optimal bracing system arrived on optimization satisfies the basic principles of structural mechanics.  The coding to perform this study is done in MATLAB®.