This paper presents the mathematical model to solve the topological optimization problem. Effect of higher order element on the optimum topology of the isotropic structure has been studied by using 8-node elements which help in decreasing the numerical instability due to checkerboarding problem in the final topologies obtained. The algorithms are investigated on a number of two-dimensional benchmark problems. MATLAB code has been developed for different numerical two dimensional linear isotropic structure and SIMP approach is applied. Models are discretized using linear quadratic 4-node and 8-node elements and optimal criteria method is used in the numerical scheme. Checkerboarding instability in the final topology is greatly reduces when incorporated 8-node element instead of 4-node element which can be confirmed through comparing the final topologies of the structure.
 Dáz, A. R., O. Sigmund. Checkerboard Patterns in Layout Optimization. Struct. Optim., 10 (1995), 40-45.
 Sigmund, O., J. Petersson. Numerical Instabilities in Topology Optimization: A Survey on Procedures Dealing with Checkerboards, Mesh-Dependencies and Local Minima. Struct. Optim., 16 (1998), 68-75.
 Bruggi, M. On the Solution of the Checkerboard Problem in Mixed-FEM Topology Optimization. Comput. Struct., 86 (2008), 1819-1829.