Exploring feasible design spaces for heterogeneous constraints

Abstract

We demonstrate an approach of exploring design spaces to simultaneously satisfy kinematics-and physics-based requirements. We present a classification of constraints and solvers to enable postponing optimization as far down the design workflow as possible. The solvers are organized into two broad classes of design space 'pruning' and 'exploration' by considering the types of constraints they can satisfy. We show that pointwise constraints define feasible design subspaces that can be represented and computed as first-class entities by their maximal feasible elements. The design space is pruned upfront by intersecting maximal elements, without premature optimization. To solve for other constraints, we apply topology optimization (TO), starting from the pruned feasible space. The optimization is steered by a topological sensitivity field (TSF) that measures the global changes in violation of constraints with respect to local topological punctures. The TSF for global objective functions is augmented with TSF for global constraints, and penalized/filtered to incorporate local constraints, including set constraints converted to differentiable (in)equality constraints. We demonstrate application of the proposed workflow to nontrivial examples in design and manufacturing. Among other examples, we show how to explore pruned design spaces via TO to simultaneously satisfy physics-based constraints (e.g., minimize compliance and mass) as well as kinematics-based constraints (e.g., maximize accessibility for machining).

Topology optimization with accessibility constraint for multi-axis machining

“…If we use the same resolution to resolve the cutter as the grid size for convolution, then n K n G since the cutter is typically much smaller in size than the design domain. Even if we downsample the sharp points to one or a few representative points on the boundary (i.e., n K = O(1)) the approximate IMF captures most of the qualitative features of the exact IMF, as we showed for simple 2D examples in [45].…”

“…Accessibility constraint becomes pointwise only when the motion is independent of the global shape, e.g., if the collisions can only occur between the tool and fixtures, regardless of the workpiece's evolving shape. See [45] (Section 4.4) for an example with 2.5D wire-/laser-cutting of a sheet material. Pointwise constraints directly lead to the definition of a point membership classification (PMC) for a maximal pointset that represents the entire feasible design subspace of the constraint, hence is used to 'prune' the design space prior to optimization.…”

“…Global constraints are widely used in TO and are typically expressed as a differentiable functional, for which a continuous sensitivity field can be computed at every point in the 3D design domain. We showed in [45] that local constraints can be directly incorporated into the sensitivity field as a penalty. However, if the penalty function is not continuous, the resulting discontinuities in the "augmented" sensitivity field can adversely affect the convergence of TO to useful designs.…”

“…Every point in the design domain is assigned the value of convolution corresponding to the collision measure for the translation that takes the representative point to the query point. In [45], we demonstrated that the resulting field makes for an effective penalty for filtering the sensitivity field for producing manufacturable designs in simple 2D examples with small 2D tools at a few orientations. In this paper, we present a generic definition of IMF that is usable for arbitrary shapes in 2D and 3D and motions including rotations.…”

Optimizing Build Orientation for Support Removal using Multi-Axis Machining

“…Our method primarily relies on accessibility analysis used in spatial planning. In particular, we extend the inaccessibility measure field (IMF) introduced in [1,2] to hybrid AM-then-SM processes. Previous work on topology optimization for multi-axis machining [2] demonstrated the effectiveness of IMF as a continuous field in the Euclidean space that quantifies the collisions occurring between the part, fixture, and tool geometries to provide a penalty function to enforce accessibility by collision avoidance.…”