This paper presents a Material Mask Overlay topology optimization approach with the improved material assignment at the element level for achieving the desired discreteness of the optimized designs for pressure-loaded problems. Hexagonal elements are employed to parametrize the design domain. Such elements provide nonsingular local connectivity; thus, checkerboard patterns and point connections inherently get subdued. Elliptical negative masks are used to find the optimized material layout. Each mask is represented via seven parameters that describe the location, shape, orientation, material dilation, and erosion variables of the mask. The latter two variables are systematically varied in conjunction with a grayscale measure constraint to achieve the solutions' sought 0-1 nature. Darcy's law with a drainage term is used to model the pressure load. The obtained pressure field is converted into the consistent nodal forces using Wachspress shape functions. Sensitivities of the objective and pressure load are evaluated using the adjoint-variable method. The efficacy and robustness of the approach are demonstrated by solving various pressure-loaded structures and pressure-driven compliant mechanisms. Compliance is minimized for loadbearing structures, whereas a multicriteria objective is minimized for mechanism designs. The boundary smoothing scheme is implemented within each optimization iteration to subdue the designs' undulated boundaries.
翻译:本文展示了一种材料面罩重叠表层优化法, 使物质分布在元素一级得到改进, 以实现最佳压力加载问题优化设计所需的离散性。 使用六边形元素来对设计域进行对称。 这些元素可以提供非单向本地连接; 因此, 检查板模式和点连接自然会减弱。 使用 Elliptical 负面罩来寻找优化的材料布局。 每个面罩都通过七个参数来表示, 这些参数描述面罩的位置、 形状、 方向、 材料变异和侵蚀变量。 后两个变量与灰度测量限制一起系统地变化, 以实现所寻求的解决方案的 0-1 性质。 使用达西法律的排水术语来模拟压力负载。 获得的压力字段被转换为使用Wachspress 形状功能的一致的节点力量。 目标和压力负荷的敏感度是通过联合可变方法进行评估的。 通过解决各种压力加载结构和压力驱动的合规机制来显示这一方法的功效和坚固性。 在负载结构中, 尽可能降低合规性, 而每个最优的边界设计为最优度为最优度。