Design of Functionally Graded Lattice Structures using B-splines for Additive Manufacturing

Abstract

Abstract Additive manufacturing methods have recently been used to make light-weight parts using lattice structures for various applications. Functionally graded lattice structures (FGLs) are structures that are designed using lattices with a varying distribution of porosity by virtue of varying the volume fractions of each unit cell in the 3D design domain. This graded design helps to achieve advanced properties related to structural strength, allow functionalities such as bone ingrowth and optimum heat transfer etc. Compliance minimization is one such classic problem where topology optimization techniques are used to determine the optimum distribution of material in the design domain while obtaining the desired reduction in weight. This material distribution is typically populated with lattices of variable volume fraction unit cells to generate FGLs. Truss type unit cells such as BCC are commonly used to develop FGLs. To develop such structures with truss type unit cells there is a need for a methodology that can maintain smooth connectivity among unit cells of varying densities. This paper discusses a new method to achieve smoothly connected FGLs, based on a BCC unit cell geometry, using a B-spline surface-based unit cell design methodology. The lead author’s previous work in [1] on generating bifurcating geometries using B-spline surfaces is extended to lattices as a case of multi-furcation geometries. First, a control polyhedron net is developed on the basis of desired unit cell geometry which is then further processed to construct water-tight boundary representation of the unit cell using a 3 rd order B-spline surface. This design methodology is used in conjunction with an algorithm to populate the density distribution from SIMP based topology optimization using unit cells with different volume fractions. The resulting lattice structure is compared with a uniform density lattice structure of similar light-weighting. It is shown that the methodology discussed in this paper could be successfully used to construct FGLs with high stiffness.