Junction Meshing for Lattice Structures Using Radius of Incidence
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Solution Overview
Problem
Current methods for generating meshes at the junctions of lattice structures in 3D modeling for additive manufacturing are computationally intensive and often produce degenerate junctions with voids and brittle sharp angles, reducing mechanical strength and requiring excessive processing time, especially when dealing with non-uniform lattices of hundreds of thousands of beams.
Innovation Solution
A method that calculates the radius of incidence for beams at junctions, determines a maximized radius, and generates meshing with sockets using stereographic projection and Constrained Delaunay Triangulation to connect beams, forming a mechanically robust structure with near-optimal material usage and controlled polygon numbers, capable of handling varying beam sizes and shapes at arbitrary angles.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If current meshing methods are used at junctions of lattice structures, then the process can be completed, but the computational time is excessive and the junctions produced are degenerate with voids and brittle sharp angles
Solution Approach 1:
The meshing process is segmented into distinct phases: calculating radius of incidence for beam pairings, determining maximized radius for each beam, finding global radius for the junction, calculating local and global intersection points, and generating meshing with sockets. This segmentation allows each phase to be optimized independently, reducing overall computational time while improving junction quality by ensuring proper socket formation and beam connectivity.
Solution Approach 2:
The method performs preliminary calculations of radius of incidence and maximized radius values before generating the actual mesh. By pre-determining these critical geometric parameters and intersection points, the subsequent meshing operation can proceed efficiently without iterative adjustments, eliminating degenerate junctions and voids while reducing computational time.
2Strength
If traditional meshing methods are used, then processing can be completed, but the junctions have voids and brittle sharp angles reducing mechanical strength
Solution Approach 1:
The method introduces sockets as intermediary elements at junctions where beams converge. These sockets act as mediators that properly connect beams of different sizes and orientations, eliminating voids and brittle sharp angles. The socket geometry is precisely controlled through the radius of incidence calculations and intersection point determinations, ensuring smooth transitions and robust mechanical connections.
Solution Approach 2:
The method dynamically adjusts geometric parameters including radius of incidence, maximized radius, and intersection points based on the specific configuration of beams at each junction. By changing these parameters locally at each junction rather than using fixed meshing rules, the method achieves high manufacturing precision and eliminates geometric defects while maintaining mechanical strength.
3Reliability
If complex meshing algorithms are used to improve junction quality, then better structural integrity is achieved, but computational complexity increases excessively
Solution Approach 1:
The method replaces complex iterative meshing algorithms with a direct geometric construction approach based on radius of incidence calculations and sphere intersections. Instead of using complex mechanical-style iterative optimization, the solution uses analytical geometry to directly determine intersection points and socket geometries, reducing computational complexity while maintaining structural integrity.
Solution Approach 2:
The method uses the thickest beam at the junction as a reference or master beam, and copies its orientation and geometric properties to define the local coordinate system and projection plane. This copying approach simplifies the meshing process by establishing a consistent reference frame, reducing algorithmic complexity while ensuring proper structural integrity through consistent geometric relationships.
Data Source
AI summary
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.