Lattice Structure Optimization

A novel solution to create blended Solid and Lattice structures from concept to detailed final design.

This technology is developed in particular to assist design innovation for additive layer manufacturing (3D printing). The solution is achieved through two optimization phases. Phase I carries out classic Topology Optimization, albeit reduced penalty options are provided to allow more porous material with intermediate density to exist. Phase 2 transforms porous zones from Phase 1 into explicit lattice structure. Then lattice member dimensions are optimized in the second phase, typically with detailed constraints on stress, displacements, etc. The final result is a structure blended with solid parts and lattice zones of varying material volume. For this release two types of lattice cell layout are offered: tetrahedron and pyramid/diamond cells derived from tetrahedral and hexahedral meshes, respectively. For this release the lattice cell size is directly related to the mesh size in the model.

Motivation

Lattice Structure Optimization is initially similar to topology optimization; however, design domains can now include elements with intermediate densities. Theoretically, from a physical point of view, such structures can be more efficient compared to those in which design elements are penalized to densities of 0 or 1.


Figure 1. Difference between Lattice Optimization (Phase 1) and Topology Optimization

A possible major application of Lattice Structure Optimization is Additive Layer Manufacturing which can take advantage of the intricate lattice representation of the intermediate densities. This can lead to more efficient structures as compared to blocky structures, which require more material to sustain similar loading.

It should be noted that typically porous material represented by periodic lattice structures exhibits lower stiffness per volume unit compared to fully dense material. For tetrahedron and diamond lattice cells, the homogenized Young's modulus to density relationship is approximately given as E = ρ 1.8 E 0 , where E 0 specifies Young's modulus of the dense material. Varying levels of lattice/porous domains in topology results are controlled by the parameter POROSITY. With POROSITY defined as LOW, the natural penalty of 1.8 is applied, which would typically lead to a final design with mostly fully dense materials distribution (or voids) if a simple 'stiffest structure' formulation (compliance minimization for a given target volume) is applied. However, you may favor higher proportion of lattice zones in the design for considerations other than stiffness. These can include considerations for buckling behavior, thermal performance, dynamic characteristics, and so on. Also, for applications such as biomedical implants porosity of the component can be an important functional requirement. For such requirements, there are two different options for POROSITY. At HIGH, no penalty is applied to Young's modulus to density relationship, typically resulting in a high portion of lattice zones in the final results of Phase I. At MED, a reduced penalty of 1.25 is applied for a medium level of preference for lattice presence.

Design constraints can be defined in both Phase 1 and 2 of the Lattice Optimization process. Some specific constraints, like stresses (via LATSTR) are not applied to the first phase, but passed to the second phase. Although some design constraints are applied during Phase 1, it is important to consider every required design constraint during Phase 2 of the optimization process. The design constraints defined in Phase 2 should be sufficiently exhaustive to sustain the use case if the final design is expected to be '3D printed' directly. For traditional structures, users usually go through a second stage where the topology concept is interpreted and then fine-tuned by size optimization with all design constraints included. The second phase of the lattice optimization process should be viewed as the fine-tuning stage for the design since further manual manipulation of a lattice structure with hundreds of thousands cell members is close to impossible.
Note: During Phase 2, Euler Buckling constraints are automatically applied to the Lattice Structure model. In theory, the column effective length factor in the Euler buckling calculation for the lattice beams, varies depending on the boundary conditions affecting a particular beam. The main boundary condition influencing the column effective length factor is the way the beam is attached at its ends. Typically, the factor varies from ideally hinged (1.0) to rigidly fixed (0.5). In OptiStruct, the column effective length factor is internally set equal to a value between the two. This value is set equal to the same value for all beams. Therefore, this implies that the resulting structure will be less conservative as compared to an ideally hinged model. If buckling performance is critical to the model, then you need to make sure the performance of the final structure is as expected. Additionally, the Buckling Safety Factor (LATPRM, BUCKSF) can be used to adjust the safety factor of the buckling load calculation. If you reset the internally created parameter LATPRM, LATTICE, YES is reset to NO, the Euler Buckling constraints are deactivated (not recommended).
Restriction:
  1. Global-Local Analysis and Multi-Model Optimization are currently not supported in Lattice Optimization.
  2. Shape, Free-size, Equivalent Static Load (ESL), Topography, and Level-set Topology optimizations are not supported in conjunction with Lattice Optimization.
  3. Heat-Transfer Analysis and Fluid-Structure Interaction are not supported.