Structural Optimization Using the Grouping Method and the 1/3rd Rule Based on Specific Strain Energy

Abstract

Abstract-Structural optimization approaches may be categorized into three major types. One type of approach is topological optimization, which involves many sensitivity analysis variables. This type of approach sometimes results in odd shapes, such as checkerboard patterns. The other types are shape optimization and parametric optimization, which involve certain difficulties in dealing with the selection of proper parameters and require repeated meshing for the purpose of finite element analysis. We propose an efficient method for grouping finite elements to reduce the number of degrees of freedom of the system considerably and to perform the optimization of several groups of elements. If we reject elements using a cutoff criterion based on the specific strain energy for several steps, we may obtain a topologically optimized result for the discrete configuration, without any irregularity. This optimization may have a higher-speed process based on the grouping method. The grouping method divides the elements into three groups on the basis of strain energy-a high-energy group, a low-energy group, and a mid-energy group. By moving the high-energy group to a high-priority group and eliminating the lowenergy group, a 1/3rd rule can be used to obtain an optimized design. The 1/3rd rule is fast and effective and provides a way to obtain a realistic result. Several examples were considered to test the optimization efficacy of the grouping technique.Keyword-Grouping Method, 1/3rd rule, Strain Energy, Structural Optimization I. INTRODUCTIONThe importance of optimization [1], which can be used to remove unnecessary parts and improve the effectiveness of a design, has grown gradually in engineering design. Structural optimization approaches may be categorized into three major types. One type of approach is topological optimization, which considers many variables in a sensitivity analysis [2]-[4]. This type of approach sometimes results in odd shapes, such as checkerboard patterns. The other two major types of approaches are shape optimization and parametric optimization. These types of approaches have certain difficulties in dealing with the selection of proper parameters and require repeated meshing for finite element analysis. This is a complex and time-consuming execution method, and a single execution involves considerable effort and cost. Therefore, producing objects using this approach involves considerable costs and time expenditures, which decreases its economic efficiency.Therefore, it is necessary to develop a new and more realistic optimization method. In this paper, we propose an efficient method for grouping finite elements to reduce the number of degrees of freedom of the system and performing optimization for several groups of elements. If we reject elements using a cutoff criterion based on the specific strain energy [5]-[9] for several steps, we can obtain a topologically optimized result with a discrete configuration and without any irregularity. This method exhibits fast calculation times and yields real...