| 不同离散网格下的拓扑优化结果相似，且体现了网格无关性。
算例2结构尺寸同算例1，右端面中心处无集中质量点，右下角点受垂直向下载荷作用，载荷幅值为10kN，激振频率10Hz，比例阻尼系数 ， 。拓扑优化模型以载荷作用点垂直方向振幅平方最小化为目标。当采用48×30个均匀和随机两种尺寸场时，分别优化迭代69步和77步收敛，两种不同尺寸场分布下的最优拓扑结果如图9所示。
(a)均匀分布
(b)随机分布
图9不同尺寸场分布下的拓扑优化结果
Fig.9comparisonofoptimumtopologywithdifferentsizefield
6结论
提出了基于空间连续尺寸场的连续体结构动态拓扑优化方法。方法基于均匀化理论，采用蜂窝状微孔结构作为材料描述方式的基础，其近似各向同性简化了微孔结构方位角的确定问题。同时，合理的刚度描述避免了动态拓扑优化中局部模态现象。采用物质点对应的微孔尺寸为设计变量，构造了具有空间连续性的尺寸场，在拓扑数学描述中克服了棋盘格等数值不稳定性问题。基于复合函数链式求导法则，推导了总刚度阵、总质量阵等敏度表达式。以动态结构响应量最小或最大化为目标，体积比为约束，建立了动态结构拓扑优化模型。通过二维结构数值算例验证了方法的可行性和有效性。
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参考文献
4 敏度表达式(18),(19)和(21)修改为对r 求导;
5 上述所有修改均采用蓝色标识;
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