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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...

Structural elements like bars, trusses, beams, frames, plates, and shells have long been used in structures and machines because of their large stiffness-to-weight ratios. The Euler–Bernoulli theory for beam elements is currently used in a wide range of engineering fields. Frames may essentially be considered to be a type of general beam with axial loads. In the analysis of a right-angle frame, the stiffness of a corner has been assumed to be infinite, which is allowable only when the frame is sufficiently slender. However, a comparison of the results of a finite element analysis showed that the assumption of rigid corner stiffness is unacceptable for most cases because of the considerable errors that result. To resolve this problem, we assumed that the stiffness of a corner in a right-angle frame was finite, which is mostly the case, and solved the problem of a right-angle frame with round corners under internal pressure. Using the derived formula based on the assumption of finite corner stiffness and the formula for the round corner stiffness, we analyzed the entire right-angle frame structure and compared the results to finite element analysis results. As a final attempt, the quasi-optimal dimension of the corner was found to exhibit the lowest von Mises equivalent stress. This proposed approach could be applied to many problems involving frames with various boundary conditions to improve the accuracy.