Papers by Keyword: Design Variable

Abstract: This paper reveals the popular error and problem in optimization design of helical springs. Most of the engineers and researchers regard wire diameter d, mean coil diameter D and number of active coils n as design variables in the mathematical model of optimization design for helical springs. In fact, only two variables are independent variables in the three design variables. The dependent variable in the optimization design model influences the behavior of the systems to be optimized, which is also possible to calculate wrong results. This paper analyses relationship of wire diameter d, mean coil diameter D and number of active coils n. To take number of active coils n as the dependent variable is reasonable. It can lead to wrong results to take n as the independent variable. The right independent variables in optimization design of helical spring are wire diameter d and mean coil diameter D.

Abstract: In order to reduce the elastic recovery of a sheet material and eliminate a great number of solid dies used in the forming process of various shapes, a flexible stretch forming process (FSFP) is considered in this study. Especially, the relationship among design variables, such as the punch size, objective radius of curvature, and elastic pad thickness is quantitatively evaluated to find out their respective influences on the shape errors of a formed sheet plate using the statistical method based on the FE simulation result planned by the three-way factorial design. The shape errors are divided into two types based on the material behavior according to the widthwise- and tensile- directions. The correlations of the shape errors and the design variables are estimated through the Pearson correlation analyses. The punch size has a strong positive linear correlation with the widthwise- and tensile- shape errors, and the correlation between the objective curvature radius and tensile-direction shape error is weak and negative. Although the effect of the elastic pad thickness is less than those of the other variables, it prevents effectively surface defects. Subsequently, the mathematical model is assumed to clarify their relationship. Two regression equations are estimated in terms of the design variables regarding the widthwise- and tensile- shape errors. The shape errors could be inferred by the assumed model in the particular combination of the design variables; then, the acceptable punch size and elastic pad thickness can be determined according to the objective curvature radius.

Abstract: The Hybrid Cellular Automata (HCA) algorithm has been used by several researchers to optimise structures during the last decade. Close observation of their work shows that the proposed optimisation algorithms are sensitive to the controller (local rule), the design variable and the field variable used. The aim of this work is to identify and understand the important parameters when using the HCA algorithm to optimise structures. For static loading, it is shown that the most important parameters are the design variable, the constraints on the design variable, the local rule, and the mesh density of the structure. The choice of the design variable affects the selection of the target value and the homogeneity of the resulting optimum structure. With constraints on the design variable, it is shown that the algorithm cannot always drive the structure to an optimum solution, as stresses in the resulting structure can be significantly higher than expected. Besides, the choice of the local rule and the mesh density of the structure can affect the convergence rate and may cause the algorithm to arrive at a local optimum rather than the global optimum solution.