Beam-Based Lattice Topology Transition With Function Representation

Abstract

A lattice structure is a porous periodic structure with unit cells organized according to a pattern. Lattice structures are lightweight parts that are commonly produced by additive manufacturing techniques. Lattice structures require their topology defined which effectively defines the connectivity of their unit cell. Many of these topologies are beam-based, i.e. their unit cell is represented by a network of nodes connected with beams. Such lattice structures require a geometric modeling tool capable of generating their solid model. This paper presents a method to support the topology transition for beam-based lattice structures by controlling the geometric parameters of topologies. This control is made possible with the function representation of the geometry. The work also analyzes how suitable different beam-based lattice topologies are to support the transition. A few case studies are carried out to demonstrate the feasibility of the proposed method.

Geometric Modelling of Heterogeneous Lattice Structures Through Function Representation With Latticequery

“…For example, Figure 1b shows a lattice structure with a truncated cube topology. The truncation can be a variable parameter 𝜏 that allows a gradual transition from the simple cubic topology to the cuboctahedron topology (Letov and Zhao, 2023). Figure 1c shows a lattice structure with the thickness varying in the 𝑦-direction and the beam's cross-section gradually changing from circle to square along the 𝑧-axis.…”

Geometric modeling of advanced cellular structures with skeletal graphs

“…where P (X) defines geometric parameters distribution, and T (X) defines the cellular structure topology using skeletal graphs. The function T (X), in particular, is enhanced to include adaptive topology control, allowing for the optimization of structural performance under varying load conditions [44].…”

“…Multi-topology surface-based cellular structures embody a unique blend of challenges and opportunities in the realm of geometric modeling [43]. With cubic unit cells, beam-based cellular structures facilitate relatively straightforward topology transitions [44]. However, ensuring defect-free structures in surface-based cellular structures demands smooth topology transitions, a requirement often overlooked in current homogenized models, potentially impacting their mechanical properties [45].…”

“…Rhinoceros 3D [60], with its powerful parametric design capabilities and Grasshopper [61] plugin, is a versatile CAD software that enables efficient generation and exploration of conformal cellular structures [62]. However, these software solutions still fall short in providing an interface for modify-ing cellular structure parameters other than thickness, limiting design freedom [63,44].…”

Design for Additive Manufacturing: Recent Innovations and Future Directions

“…Voronoi models are suitable for applications that need mechanical efficiency and have geometry-dependent needs, such as tissue growth based on a scaffold's shape [65]. Further strategies for configuring AM structures include functional gradients that gradually change parametric values spatially through a lattice [66], altering topologies of unit cells for transitioning properties throughout a lattice [67], or using multiple materials placed within a lattice to generate anisotropic properties [68]. Due to the diversity of strategies and decisions at local and global levels during design generation, optimization is often necessary to maximize the potential of configuration strategies.…”