An improved Material Mask Overlay Strategy for the desired discreteness of pressure-loaded optimized topologies

Abstract

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.