Amir M. Mirzendehdel

Aaditya Chandrasekhar, Amir Mirzendehdel, Morad Behandish et al.

In this paper, we present a topology optimization (TO) framework to simultaneously optimize the matrix topology and fiber distribution of functionally graded continuous fiber-reinforced composites (FRC). Current approaches in density-based TO for FRC use the underlying finite element mesh both for analysis and design representation. This poses several limitations while enforcing sub-element fiber spacing and generating high-resolution continuous fibers. In contrast, we propose a mesh-independent representation based on a neural network (NN) both to capture the matrix topology and fiber distribution. The implicit NN-based representation enables geometric and material queries at a higher resolution than a mesh discretization. This leads to the accurate extraction of functionally-graded continuous fibers. Further, by integrating the finite element simulations into the NN computational framework, we can leverage automatic differentiation for end-to-end automated sensitivity analysis, i.e., we no longer need to manually derive cumbersome sensitivity expressions. We demonstrate the effectiveness and computational efficiency of the proposed method through several numerical examples involving various objective functions. We also show that the optimized continuous fiber reinforced composites can be directly fabricated at high resolution using additive manufacturing.

George P. Harabin, Amir Mirzendehdel, Morad Behandish

One of the main concerns in design and process planning for multi-axis additive and subtractive manufacturing is collision avoidance between moving objects (e.g., tool assemblies) and stationary objects (e.g., a part unified with fixtures). The collision measure for various pairs of relative rigid translations and rotations between the two pointsets can be conceptualized by a compactly supported scalar field over the 6D non-Euclidean configuration space. Explicit representation and computation of this field is costly in both time and space. If we fix $O(m)$ sparsely sampled rotations (e.g., tool orientations), computation of the collision measure field as a convolution of indicator functions of the 3D pointsets over a uniform grid (i.e., voxelized geometry) of resolution $O(n^3)$ via fast Fourier transforms (FFTs) scales as in $O(mn^3 \log n)$ in time and $O(mn^3)$ in space. In this paper, we develop an implicit representation of the collision measure field via deep neural networks (DNNs). We show that our approach is able to accurately interpolate the collision measure from a sparse sampling of rotations, and can represent the collision measure field with a small memory footprint. Moreover, we show that this representation can be efficiently updated through fine-tuning to more efficiently train the network on multi-resolution data, as well as accommodate incremental changes to the geometry (such as might occur in iterative processes such as topology optimization of the part subject to CNC tool accessibility constraints).

Amir M. Mirzendehdel, Krishnan Suresh

This paper presents STORX: Shape and Topology Optimization for Research and Experimentation, an open-source MATLAB-based educational framework for learning and teaching computational design optimization. STORX provides a platform for parametric and level-set shape optimization, as well as topology optimization methods including density, level-set, and topological sensitivity approaches such as evolutionary and Pareto-tracing methods. All modules follow a consistent object-oriented structure and integrate visualization, sensitivity analysis, and finite element routines, enabling users to explore the continuum between shape and topology optimization in a transparent and reproducible manner. The code is designed to complement graduate-level coursework and independent research by emphasizing modularity and extensibility through a clear separation of intent. Core software interfaces are defined via abstract base classes, enabling new objective functionals and design/manufacturing constraints to be implemented by adding derived classes without modifying the core code. The paper also describes the software architecture and demonstrates how the framework maps mathematical formulations directly to executable code through a series of illustrative problems.

Rahul Kumar Padhy, Aaditya Chandrasekhar, Amir M. Mirzendehdel

Polypills are single oral dosage forms that combine multiple active pharmaceutical ingredients and excipients, enabling fixed-dose combination therapies, coordinated multi-phase release, and precise customization of patient-specific treatment protocols. Recent advances in additive manufacturing facilitate the physical realization of multi-material excipients, offering superior customization of target release profiles. However, polypill formulations remain tuned by ad hoc parameter sweeps. The current design workflows are ill-suited for the systematic exploration of the high-dimensional space of shapes, compositions, and release behaviors. We present PILL-CoDe, a polypill co-design framework that simultaneously optimizes tablet geometry and excipient distribution to match prescribed drug-release kinetics. The framework couples a supershape parametrization of the pill geometry with a coordinate-based neural network representation of the excipient distribution, and governs dissolution through a coupled system of modified Allen-Cahn and Fickian diffusion equations. Implemented in JAX, the entire pipeline is end-to-end differentiable, with automatic differentiation providing exact sensitivities for gradient-based co-optimization of shape and composition under manufacturability constraints. We demonstrate the method through single-phase and multi-excipient case studies, showing accurate matching of both monotonic and non-monotonic target release profiles.

Naresh S. Iyer, Amir M. Mirzendehdel, Sathyanarayanan Raghavan et al.

In this paper, we propose PATO-a producibility-aware topology optimization (TO) framework to help efficiently explore the design space of components fabricated using metal additive manufacturing (AM), while ensuring manufacturability with respect to cracking. Specifically, parts fabricated through Laser Powder Bed Fusion are prone to defects such as warpage or cracking due to high residual stress values generated from the steep thermal gradients produced during the build process. Maturing the design for such parts and planning their fabrication can span months to years, often involving multiple handoffs between design and manufacturing engineers. PATO is based on the a priori discovery of crack-free designs, so that the optimized part can be built defect-free at the outset. To ensure that the design is crack free during optimization, producibility is explicitly encoded within the standard formulation of TO, using a crack index. Multiple crack indices are explored and using experimental validation, maximum shear strain index (MSSI) is shown to be an accurate crack index. Simulating the build process is a coupled, multi-physics computation and incorporating it in the TO loop can be computationally prohibitive. We leverage the current advances in deep convolutional neural networks and present a high-fidelity surrogate model based on an Attention-based U-Net architecture to predict the MSSI values as a spatially varying field over the part's domain. Further, we employ automatic differentiation to directly compute the gradient of maximum MSSI with respect to the input design variables and augment it with the performance-based sensitivity field to optimize the design while considering the trade-off between weight, manufacturability, and functionality. We demonstrate the effectiveness of the proposed method through benchmark studies in 3D as well as experimental validation.

Amir M. Mirzendehdel, Morad Behandish, Saigopal Nelaturi

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).

Saigopal Nelaturi, Morad Behandish, Amir M. Mirzendehdel et al.

An additive manufacturing (AM) process often produces a {\it near-net} shape that closely conforms to the intended design to be manufactured. It sometimes contains additional support structure (also called scaffolding), which has to be removed in post-processing. We describe an approach to automatically generate process plans for support removal using a multi-axis machining instrument. The goal is to fracture the contact regions between each support component and the part, and to do it in the most cost-effective order while avoiding collisions with evolving near-net shape, including the remaining support components. A recursive algorithm identifies a maximal collection of support components whose connection regions to the part are accessible as well as the orientations at which they can be removed at a given round. For every such region, the accessible orientations appear as a 'fiber' in the collision-free space of the evolving near-net shape and the tool assembly. To order the removal of accessible supports, the algorithm constructs a search graph whose edges are weighted by the Riemannian distance between the fibers. The least expensive process plan is obtained by solving a traveling salesman problem (TSP) over the search graph. The sequence of configurations obtained by solving TSP is used as the input to a motion planner that finds collision free paths to visit all accessible features. The resulting part without the support structure can then be finished using traditional machining to produce the intended design. The effectiveness of the method is demonstrated through benchmark examples in 3D.