Abstract: Methods, systems, and apparatus, including medium-encoded computer program products, for designing three dimensional lattice structures include, in one aspect, a method including: obtaining a mechanical problem definition including a 3D model of an object; generating a numerical simulation model for the 3D model of the object using one or more loading cases and one or more isotropic solid materials identified as a baseline material model for a design space; predicting performance of different lattice settings in different orientations in the design space using a lattice structural behavior model in place of the baseline material model in the numerical simulation model; and presenting a set of lattice proposals for the design space based on the predicted performance of the different lattice settings in the different orientations; wherein the lattice structural behavior model has been precomputed for the different lattice settings, which are generable by the 3D modeling program.

Abstract: Methods, systems, and apparatus, including medium-encoded computer program products, for designing three dimensional lattice structures include, in one aspect, a method including: creating nodes in a plane normal to an axis in accordance with a spiral, wherein proper subsets of the nodes occur at successive radii positions away from the axis in the plane normal to the axis; repositioning every other one of the proper subsets, from at least a portion of the nodes, in a direction in 3D space along the axis; creating a three dimensional (3D) structure in the 3D space, the 3D structure comprising beams placed between the repositioned and non-repositioned proper subsets; duplicating the 3D structure one or more times to form a lattice in the 3D space; and selecting at least a portion of the lattice for inclusion in a 3D model.

Abstract: Methods, systems, and apparatus, including medium-encoded computer program products, for designing three dimensional lattice structures include, in one aspect, a method including: calculating a radius of incidence for respective pairings of beams of different sizes that converge at a junction in a lattice; determining a maximized radius of incidence for each of the beams based on the radii of incidence for the pairings with that beam; comparing the maximized radii of incidence to find a global radius for the junction; calculating local intersection points and global intersection points, respectively, for each of the beams with a local sphere defined by the maximized radius of incidence for that beam and with a global sphere defined by the global radius for the junction; and generating meshing with sockets for the beams at the junction using the local intersection points and the global intersection points.

Abstract: Methods, systems, and apparatus, including medium-encoded computer program products, for designing three dimensional lattice structures include, in one aspect, a method including: obtaining a lattice within a 3D lattice design space for a 3D model being created with a 3D modeling program; identifying junctions in the lattice that are potential sources of particle traps at an interface between the 3D lattice design space and a surface present in the 3D model; and removing the potential sources of particle traps by modifying cell space defined between the identified junctions and the surface. In addition, the surface can be a surface of a solid region defined in the 3D model, and the method can include: identifying beams in the lattice having junctions lying on the surface; and extending each of the identified beams by a length amount to cause overlap between the identified beams and the solid region.

Abstract: A method of authenticating the printing of a three-dimensional (3D) article at a 3D printer according to a 3D print file describing a three-dimensional design is described.