Topology Optimization of Structures Using Higher Order Finite Elements in Analysis.

Mukherjee, Sougata Lu, Dongcheng Dutta, Subhrajit Raghavan, Balaji Breitkopf, Piotr Xiao, ManyuTopology optimization in general progresses with numerical instability i.e. checkerboard patterns if no filtering radius is used i.e. imposement of minimum length scale. Many studies are done in past decades to get rid of numerical instability or checkerboard pattern while optimizing the topology of mechanical structures. The proposed solution in this paper the structure is meshing structure twice (dual mesh) where first mesh defines the material distribution, and another mesh is utilized for computing the stress and displacement on an element which lets us to a stress-based refinement of mesh without modification of optimum design variables. Optimality criteria method is used for optimizing the design variable i.e. relative density over the domain. Another significance of this approach is that imposition minimum radius not needed to optimize design variables over the structural domain, instead the length scale is determined by the design mesh. A comparison is done between the topology obtained, compliance value and time taken after discretizing the structure with 4 noded element, 8 noded element and 9 noded quadrilateral element and a graph is also plotted to show the compliance value.