Accurately controlling the nodal lines of vibrating structures with topology optimization is a highly challenging task.The major difficulties in this type of problem include a large number of design variables,the high...Accurately controlling the nodal lines of vibrating structures with topology optimization is a highly challenging task.The major difficulties in this type of problem include a large number of design variables,the highly nonlinear and multi-peak characteristics of iteration,and the changeable orders of eigenmodes.In this study,an effective material-field series-expansion(MFSE)-based topology optimization design strategy for precisely controlling nodal lines is proposed.Here,two typical optimization targets are established:(1)minimizing the difference between structural nodal lines and their desired positions,and(2)keeping the position of nodal lines within the specified range while optimizing certain dynamic performance.To solve this complex optimization problem,the structural topology of structures is first represented by a few design variables on the basis of the MFSE model.Then,the problems are effectively solved using a sequence Kriging-based optimization algorithm without requiring design sensitivity analysis.The proposed design strategy inherently circumvents various numerical difficulties and can effectively obtain the desired vibration modes and nodal lines.Numerical examples are provided to validate the proposed topology optimization models and the corresponding solution strategy.展开更多
基金supported financially by the Guangdong Basic and Applied Basic Research Foundation,China(Grant No.2022A1515240059)the National Natural Science Foundation of China(Grant No.52275237)the Shenzhen Stability Support Key Program in Colleges and Universities of China(Grant No.GXWD20220817133329001).
文摘Accurately controlling the nodal lines of vibrating structures with topology optimization is a highly challenging task.The major difficulties in this type of problem include a large number of design variables,the highly nonlinear and multi-peak characteristics of iteration,and the changeable orders of eigenmodes.In this study,an effective material-field series-expansion(MFSE)-based topology optimization design strategy for precisely controlling nodal lines is proposed.Here,two typical optimization targets are established:(1)minimizing the difference between structural nodal lines and their desired positions,and(2)keeping the position of nodal lines within the specified range while optimizing certain dynamic performance.To solve this complex optimization problem,the structural topology of structures is first represented by a few design variables on the basis of the MFSE model.Then,the problems are effectively solved using a sequence Kriging-based optimization algorithm without requiring design sensitivity analysis.The proposed design strategy inherently circumvents various numerical difficulties and can effectively obtain the desired vibration modes and nodal lines.Numerical examples are provided to validate the proposed topology optimization models and the corresponding solution strategy.
