Structural Analysis of Voxel-Based Lattices Using 1D Approach

Abstract

Lightweight bioinspired structures are extremely interesting in industrial applications for their known advantages, especially when Additive Manufacturing technologies are used. Lattices are composed of axial elements called ligaments: several unit cells are repeated in three directions to form bodies. However, their inherent structure complexity leads to several problems when lattices need to be designed or numerically simulated. The computational power needed to capture the overall component is extremely high. For this reason, some alternative methodologies called homogenization methods were developed in the literature. However, following these approaches, the designers do not have a local visual overview of the lattice behavior, especially at the ligament level. For this reason, an alternative mono-dimensional (1D) modeling approach, called lattice-to-1D is proposed in this work. This method approximates the ligament element with its beam axis, uses the real material characteristics, and gives the cross-sectional information directly to the solver. Several linear elastic simulations, involving both stretching and bending dominated unit cells, are performed to compare this approach with other alternatives in the literature. The results show a comparable agreement of the 1D simulations compared with homogenization methods for real tridimensional (3D) objects, with a dramatic decrease of computational power needed for a 3D analysis of the whole body.

Keywords: homogenization; lattice structure; periodic structure; structural analysis; voxel.

FIG. 1.

3D cantilevered beam filled with a uniform lattice; a tensile load is applied on the free end. Two different unit cells are examined in this work: simple cube unit cell which is bending dominated; FCC unit cell which is stretching dominated. FCC, face-centered cubic.

FIG. 2.

Ray intersection method for object's voxelization: in this picture, only the rays in the X-direction are shown; the algorithm passes sorted rays along the X-axis incrementing Y- and Z-coordinates and finds their intersections with the facets. Adapted from the study of Patil and Ravi.

FIG. 3.

Flowchart describing the algorithm to get the 1D model in Patran from a 3D object in .STL file format. The L1D methodology is applied to an aircraft engine bracket: from the .STL mesh of the dense part, the algorithm obtains a voxelized model of the object; finally, the 1D lattice structure in Patran is depicted. L1D, lattice-to-1D.

FIG. 4.

Same 1D lattice with two different displaying options in Patran.

FIG. 5.

Methodology layout used to compare and estimate in terms of accuracy the performances of the alternative 1D modeling for uniform periodic structures along with a detailed view of meshing elements of 3D full model, 1D model and 3D homogenized model.

FIG. 6.

Schematic view of loads and constraints applied on the aircraft engine bracket.

FIG. 7.

View of strain field of 3D period structure with simple cube unit cells: (a) zoom view for the circular cross section; (b) detailed view for the square cross section.

FIG. 8.

Mesh size convergence study on a simplified version of the full 3D lattice model of the cantilever beam with simple cube and square cross-sectional geometry.

FIG. 9.

View of strain field of period structure with simple cube unit cells: (a) detailed view for circular cross section for the 1D lattice model; (b) zoom view for the 3D equivalent fully dense material using the AH method from the study of Vigliotti and Pasini. AH, asymptotic homogenization.

FIG. 10.

View of strain field of engine bracket filled with period structure with simple cube unit cells: (a) view for the 3D equivalent fully dense material using the AH method from the study of Vigliotti and Pasini; (b) view for circular cross section for the 1D lattice model.