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该文研究了结构阻尼频率的拓扑优化过程和进化结构优化中棋盘格式的抑制方法。首先利用正交化原理推导了进化拓扑优化中用于阻尼频率优化的灵敏度数,接着推导了进化拓扑优化的最优化条件,在此基础上通过引入周长灵敏度数和联合灵敏度数对传统周长约束的实施方法进行了改进,为了处理频率优化中目标函数的不连续性,引入了连续性的目标函数并对其灵敏度数进行了推导。最后的数值算例表明,该文提出的方法不仅可以改善结构的频率特性,而且能对进化结构优化中的棋盘格式现象进行抑制。
In this paper, the topological optimization of structural damping frequencies and the suppression of checkerboard format in evolutionary structure optimization are studied. First of all, using the principle of orthogonalization, the sensitivity numbers for damping frequency optimization in evolutionary topology optimization are deduced. Then the optimal conditions of evolutionary topology optimization are deduced. Based on this, by introducing perimeter sensitivity number and joint sensitivity number, In order to deal with the discontinuity of the objective function in the frequency optimization, the objective function of continuity is introduced and its sensitivity is deduced. The numerical examples show that the proposed method can not only improve the frequency characteristics of the structure, but also restrain the checkerboard format in the optimization of evolutionary structure.