Tolerance range section of topologically optimized structure using combined array design of experiments approach

Abstract

Topology optimization is a popular method to optimize the material for structural components. For minimum compliance problem, the effectiveness of the obtained topology is characterized by its compliance value. Here, compliance value depends on many factors. Due to uncertainties in these factors, desired compliance value is difficult to achieve. The sensitivities of these factors have already been investigated by researchers. Present work focuses on the selection and the significance of tolerance of these factors. The tolerance of input factors like applied force, volume fraction, aspect ratio of material domain and modulus of elasticity are selected to investigate the effect on compliance. To select tolerance range, the concept of inner and outer orthogonal arrays proposed by Taguchi is employed along with solid isotropic microstructure with penalization method of topology optimization. Different tolerance ranges are selected for each factor and tolerance combinations are generated using inner array. Thereafter outer array is used to create replications of a particular combination. For each replicate, compliance value is simulated using solid isotropic microstructure with penalization method. Based on statistical analysis of obtained values, significant factors are identified and optimal tolerance ranges are selected. In similar way, maximum deflection values are also simulated for analysis. Proposed methodology is applied on four different benchmark problems. The presented approach provides the effect of each possible set of tolerance on performance functions, which are compliance and deflection values. This work will be helpful to designers to select optimum tolerance of factors to achieve desired compliance value and performance for a topologically optimized structure prior to manufacturing in the realistic environment.