Structure Isogeometric Topology Optimization Using Density Distribution Function

Topology optimization is considered to take place during the creative designing process.It may accurately establish the volume,interconnection,and presence of holes in the structural designing domain and develop design features to enhance the relevant functionality.In general,topology optimization helps determine the best material allocation.It has already been recognized among the most encouraging sub-fields of structural optimization because of its outstanding characteristics,which occur during the design development stage and require no previous knowledge of the design domain.Topology optimized models have various kinds of challenges during manufacturing.It’s because of insufficient smoothness,discontinuous boundaries and corners,and checkerboard problems.An extensive literature review of topology optimization found that many pieces of research have been conducted to improve smoothness but found that it isn’t sufficiently smooth and continuous.First,in this Project,Isogeometric analysis,B-spline,and NURBS basis functions have been briefly explained with several numerical examples validated with Finite element analysis and Analytical solutions.Additionally,Topology Optimization has been extensively covered with its types(SIMP,LSM,and BESO)provided numerical examples and some significant case studies in it.The primary goal of this study is to develop an Isogeometric analysis modeling technique for topology optimization that is more productive,smooth,and useful for models and systems using the density distribution function(DDF)method.Second,isogeometric topology optimization(ITO),is a more efficient and costeffective topology optimization approach based on isogeometric analysis for continuous structures with an increased DDF.There are two phases to constructing the DDF.(1)Smoothness: The Shepard function is initially used to increase the nodal densities’ overall smoothness.Each nodal density is associated with a geometry control point.(2)Continuity:the DDF for the design domain is constructed by linearly combining the high-order NURBS basis functions with the smoothed nodal densities.The actual significance of element densities in the model is guaranteed by the non-negativity,partition of unity,and constrained limits [0,1] of both the Shepard function and NURBS basis functions.Third,the response of the structural topology optimization approach centered on the DDF and isogeometric analysis is devised to minimize structural mean compliance is addressed.A combination of geometry parameterization with numerical methods provided unique optimization advantages.For the construction of continuum structures,the much more efficient and appropriate ITO approach with an upgraded DDF that has the requisite smoothness and continuity is provided.Finally,the DDF with the appropriate smoothness and continuity has a significant impact on the optimization of 2D structures,such as the rectangular design domain,curved shapes,and complicated geometry demonstrated.Which showed,that smooth borders and identifiable interfaces between solids and voids characterized the final topologies throughout all numerical cases.