A General Meta-graph Strategy for Shape Evolution under Mechanical Stress

Abstract

The challenges that a shape or design stands are central in its evolution. In the particular domain of stress/strain challenges, existing approaches eliminate under-demanded neighborhoods from the shape, thus producing the evolution. This strategy alone incorrectly (a) conserves disconnected parts of the shape and (b) eliminates neighborhoods which are essential to maintain the boundary conditions (supports, loads). The existing analyses preventing (a) and (b) are conducted in an ad-hoc manner, by using graph connectivity. This manuscript presents the implementation of a meta-graph methodology, which systematically lumps together finite element subsets of the current shape. By considering this meta-graph connectivity, the method impedes situations (a) and (b), while maintaining the pruning of under-demanded neighborhoods. Research opportunities are open in the application of this methodology with other types of demand on the shape (e.g., friction, temperature, drag, and abrasion).

Topology Optimization for Design of a 3D-Printed Constant-Force Compliant Finger

“…The MMA method [31] is used to update the design variables. In addition, the meta-graph strategy presented by Montoya-Zapata et al [32] is used to ensure a better connectivity for the material layout after optimization.…”

“…The method of moving asymptotes (MMA) [31] is applied to update the design variables. In addition, a meta-graph strategy [32] is used to ensure a better connectivity for the optimized material layout. The proposed method is used to design a constant-force compliant finger which can provide a nearly constant gripping force at the fingertip over a range of the input displacements.…”

Density-Sensitive Implicit Functions Using Sub-Voxel Sampling in Additive Manufacturing

“…The second strategy acts by removing and adding material in different locations of the domain. It is called bi-directional evolutionary structural optimization [10,11]. Finally, the third approach only modifies the boundary of the domain, which is represented by level set functions [12].…”

“…Topology optimization in additive manufacturing seeks to (1) design lightweight and functional pieces [8,10], (2) suppress or minimize the amount of support structures needed during the manufacturing stage [13,14], and (3) define optimal infill strategies for existing designs [15,16].…”

“…The reader may notice that the functions t N and t are equal for 0.5 ≤ ρ ≤ 1 (Equations 7and (11)). Moreover, the left piece of t N for 0 ≤ ρ < 0.5 was obtained using Equations (10) and (11), by replacing ρ → 1 − ρ and then multiplying by −1. Iso-value (t) Figure 6.…”