Publications

2026

1. arXiv

   

   STORX: An Open-Source Object-Oriented Framework for Shape and Topology Optimization in MATLAB

   Amir M. Mirzendehdel, and Krishnan Suresh

   arXiv preprint arXiv:2606.17291, 2026

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   STORX is an open-source MATLAB framework that unifies parametric and level-set shape optimization with multiple topology optimization formulations in a consistent object-oriented architecture.

2. Journal (CAD)

   

   PILLCoDe: Multi-Material Topology Optimization of Polypills for Prescribed Drug-Release Kinetics

   Rahul Kumar Padhy, Aaditya Chandrasekhar, and Amir M. Mirzendehdel

   Computer-Aided Design, 2026

   Special Issue on AI + Design

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   A differentiable design framework co-optimizes polypill shape and multi-material excipient distributions to match prescribed drug-release kinetics.

2025

1. In preparation

   

   Material Integrated Design Optimization

   Amir M. Mirzendehdel, Adrian Lew, and Morad Behandish

   In preparation, 2025

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   We present a computational framework for simultaneous component design and material discovery, in which the selection of material properties and their spatial distribution within the part volume are co-optimized. Current practice in materials engineering is oblivious to part design, which, in turn, is limited to a palette of predetermined material options that are suboptimal for that specific part. Our approach bridges this divide by enabling the design engineers to explore a broad design space of graded material properties that are deemed "feasible" with adjustable risk thresholds, providing target properties for material engineers to tailor for high-end applications.

2. Patent

   

   Automated design generation for additive manufacturing with an accessible support volume

   Amirmassoud Mirzendehdel, Morad Behandish, and Saigopal Nelaturi

   Mar 2025

   US Patent 12,240,182

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   A method includes receiving a representation of an initial design domain. The method also includes iteratively generating intermediate part designs by redistributing material within the initial design domain. The intermediate part designs each include a 3D part and a support volume. The method also includes calculating a measure of inaccessibility of the support volume of each intermediate part design by at least one subtractive tool assembly. At least one of the intermediate part designs is generated based at least partially upon the measure of inaccessibility of a previous one of the intermediate part designs.

2024

1. Journal (IJIDeM)

   

   PATO: producibility-aware topology optimization using deep learning for metal additive manufacturing

   Naresh Iyer, Amir M. Mirzendehdel, Sathya Raghavan, Yang Jiao, Erva Ulu, and 3 more authors

   International Journal on Interactive Design and Manufacturing (IJIDeM), Mar 2024

   Special Issue on Recent Advances in Materials, Manufacturing and Machine Learning

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   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 (LPBF) 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, in order to estimate MSSI, is a coupled, multi-physics, time-complex computation and incorporating it in the TO loop can be computationally prohibitive. We leverage the current advances in deep convolutional neural networks (DCNN) 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.

2. Patent

   

   Modifying shape based on level set representation to reduce support in additive manufacturing

   Qian Ye, Matt Patterson, Amirmassoud Mirzendehdel, and Morad Behandish

   Oct 2024

   US Patent 12,125,161

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   The present disclosure provides techniques for automatically modifying shape features related to overhangs such that support structures can be reduced or avoided. In an example, a shape modification processing device may obtain an initial shape and relevant production information (eg, overhang angle threshold). The shape modification processing device may modify the shape to improve various aspects of production, including reduction or removal of the need for support materials or structures during additive manufacturing, with considerations that allow the modified portion (eg, added features) be accessible for removal by subtractive manufacturing. For example, the shape modification processing device may modify a model to reduce or remove support structures needed during production. The added features may later be removed by subtractive manufacturing to restore any functional or desired shape.

3. Patent

   

   Avoiding trapping unused additive manufacturing materials during production

   Amirmassoud Mirzendehdel, Morad Behandish, and Saigopal Nelaturi

   Feb 2024

   US Patent App. 17/816,483

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   The present disclosure provides techniques for analyzing trapped unused materials during AM. For example, given a geometry or shape to be manufactured using one or more AM materials, a tool path for solidifying the one or more AM materials is generated to turn the geometry into a physical object based on one or more manufacturing parameters related to AM resolutions. A processing device may compute a simulated manufactured geometry (e.g., a realistic representation of the actual shape of the corresponding physical object to be produced) based on the tool path and the one or more manufacturing parameters. The processing device analyzes the simulated manufactured geometry for a portion of removable AM materials trapped inside the simulated manufactured geometry. The processing device then generates a report regarding the portion of the removable AM materials trapped inside the simulated manufactured geometry.

4. Patent

   

   Topology optimization with locally differentiable complement space connectivity

   Clinton Morris, Amirmassoud Mirzendehdel, and Morad Behandish

   Feb 2024

   US Patent App. 18/086,048

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   One or more physical constraints are selected from a plurality of physical constraints for a part. The physical constraints are for use by a physics solver and define a physical performance of the part. One or more connectivity constraints are defined for use by the physics solver. The connectivity constraints enforce connectivity to or from at least one region over a complement space of the part. The connectivity constraints include locally differentiable violation measures that are modeled after at least one of the physical constraints. A topology of the part is optimized in the physics solver by enforcing the physical constraints and the connectivity constraints while satisfying a primary objective function that optimizes the physical performance of the part. A computer-aided design of the part is produced based on the optimized topology.

2023

1. Journal (CAD)

   

   FRC-TOuNN: Topology optimization of continuous fiber reinforced composites using neural network

   Aaditya Chandrasekhar, Amir M. Mirzendehdel, Morad Behandish, and Krishnan Suresh

   Computer-Aided Design, Feb 2023

   Special Issue on Solid and Physical Modeling 2022

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   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.

2. CAD

   

   Co-design Optimization of Moving Parts for Compliance and Collision Avoidance

   Amir M. Mirzendehdel, and Morad Behandish

   Computer-Aided Design, Feb 2023

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   Design requirements for moving parts in mechanical assemblies are typically specified in terms of interactions with other parts. Some are purely kinematic (e.g., pairwise collision avoidance) while others depend on physics and material properties (e.g., deformation under loads). Kinematic design methods and physics-based shape/topology optimization (SO/TO) deal separately with these requirements. They rarely talk to each other as the former uses set algebra and group theory while the latter requires discretizing and solving differential equations. Hence, optimizing a moving part based on physics typically relies on either neglecting or pruning kinematic constraints in advance, e.g., by restricting the design domain to a collision-free space using an unsweep operation. In this paper, we show that TO can be used to co-design two or more parts in relative motion to simultaneously satisfy physics-based criteria and collision avoidance. We restrict our attention to maximizing linear-elastic stiffness while penalizing collision measures aggregated in time. We couple the TO loops for two parts in relative motion so that the evolution of each part’s shape is accounted for when penalizing collision for the other part. The collision measures are computed by a correlation functional that can be discretized by left- and right-multiplying the shape design variables by a pre-computed matrix that depends solely on the motion. This decoupling is key to making the computations scalable for TO iterations. We demonstrate the effectiveness of the approach with 2D and 3D examples.

3. CAD

   

   Deep Neural Implicit Representation of Accessibility for Multi-Axis Manufacturing

   George Harabin, Amir M. Mirzendehdel, and Morad Behandish

   Computer-Aided Design, Feb 2023

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   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(n3) via fast Fourier transforms (FFTs) scales as in O(mn3logn) in time and O(mn3) 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).

4. Conference (AIAA)

   

   Topology Optimization for Design of Resilient Structures using Smart Materials

   Anurag Bhattacharyya, and Amir M. Mirzendehdel

   In AIAA AVIATION 2023 Forum, Feb 2023

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   Design for the next generation of resilient and multifunctional structures requires the integration of sensors and stimuli-sensitive actuators to enable reconfiguration of the structures from a perturbed damaged state to their native healthy state. However, the design of such structures often requires finding the trade-off between performance, resilience, and cost. In this paper, we propose a computational framework for designing resilient truss systems by simultaneously optimizing the shape as well as the placement of sensors and actuators. We provide the adjoint formulation for automated sensor placement and introduce the notion of Sensor Sensitivity Matrix to maximize damage detection using only a limited number of sensors. Further, we employ the finite difference method to compute the sensitivity values for actuator placement. Our truss optimization scheme is based on a novel bi-level and multi-material Solid Isotropic Material with Penalization (SIMP) formulation. We demonstrate the effectiveness of the proposed approach through several case studies of designing resilient structures with various damage levels across domains of various shapes and functional requirements.

5. Patent

   

   Method and system for part design using heterogeneous constraints

   Amirmassoud Mirzendehdel, Morad Behandish, and Saigopal Nelaturi

   Oct 2023

   US Patent 11,775,703

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   A method of classifying design criteria includes receiving design criteria for a product part. The criteria comprise one or both of performance and manufacturing criteria. The design criteria are sorted into different classes of one or both of one or more objective functions and one or more constraints based on when they can be satisfied or optimized. Constraint violations are determined. A design workflow is produced to generate one or more designs of a part to comply with one or more of satisfying constraints and optimizing objective functions.

6. Patent

   

   Hybrid manufacturing system and method that reduces inaccessible support structures

   Amirmassoud Mirzendehdel, Morad Behandish, and Saigopal Nelaturi

   Feb 2023

   US Patent 11,577,321

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   A geometry model is defined of a part targeted for a manufacturing operation that includes an additive process followed by a subtractive process. Potential build orientations of the geometry model used in the additive processes are defined, as are one or more removal tools of the subtractive process. For each of the potential build orientations, supports that are used by the additive process at the orientation are determined. One of the build orientations is selected that minimizes portions of one of the supports that are inaccessible via at least one of the removal tools.

7. Patent

   

   Automated design and optimization for accessibility in subtractive manufacturing

   Amirmassoud Mirzendehdel, Morad Behandish, and Saigopal Nelaturi

   Jun 2023

   US Patent 11,669,661

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   A representation of an initial design domain, at least one subtractive tool assembly, machine degrees of freedom, and a termination criterion are used to iteratively generate intermediate part designs by redistributing the material within the design domain. A measure of inaccessibility of exteriors of the intermediate part designs by the at least one subtractive manufacturing tool assembly are generated. The measure of inaccessibility is used to inform generation of an intermediate part design at a next iteration. The iterative algorithm is terminated when the termination criterion is satisfied, the result of the iterative algorithm being a part design accessible for subtractive manufacturing.

8. Patent

   

   Physics-aware automatic spatial planning for subtractive and hybrid manufacturing

   Amirmassoud Mirzendehdel, Morad Behandish, and Saigopal Nelaturi

   May 2023

   US Patent 11,656,602

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   A method includes receiving a representation of a near-net shape including a 3D part and a support volume. The method also includes calculating a measure of inaccessibility of the support volume by at least one subtractive tool assembly. The method also includes calculating a measure of change in a physical quantity of interest with respect to a change in the near-net shape. The method also includes constructing a physics-aware inaccessibility measure based at least partially upon the measure of inaccessibility, the measure of change, or both. The method also includes creating a plan to remove at least a portion of the support volume using the at least one subtractive tool assembly based at least partially upon the physics-aware inaccessibility measure.

9. Patent

   

   Generating consolidated designs of a production model to replace multiple parts of an assembly

   Amirmassoud Mirzendehdel, and Morad Behandish

   Aug 2023

   US Patent App. 18/172,138

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   Techniques, devices, and systems for automatically generating consolidated designs of a production model to replace multiple parts of an assembly are disclosed herein. For example, a set of digital models may be originally designed to be separately manufactured and assembled post production. The present disclosure analyzes the set of digital models and computes candidates of consolidated designs that consolidates a subset number of the digital models into a single part to be manufactured. The computation may be based on certain complexity level (eg, based on manufacturing capability and/or user preference/input). The consolidated designs simplify the manufacturing process by reducing individual parts to be manufactured and the subsequent assembly, as well as improving reliability, improving automation, and reducing manufacturing costs.

10. Patent

    

    Method and system for automated design generation for additive manufacturing utilizing machine learning based surrogate model for cracking

    Amirmassoud Mirzendehdel, Morad Behandish, and Saigopal Nelaturi

    Sep 2023

    US Patent App. 17/706,068

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    This disclosure teaches techniques, devices, and systems for automatically generating design parameters of a structural model (or any component that is defined by one or more parameters) to be produced by additive manufacturing, using machine-learning models to avoid production failures. In aspects, a topology optimization framework (eg, with optimization iterations, or loops) is used to efficiently explore the expanded design space of additive manufacturing components is disclosed.

11. Patent

    

    Optimization of a design using a physics solver integrated with a neural network

    Aaditya Chandrasekhar, Amirmassoud Mirzendehdel, and Morad Behandish

    Oct 2023

    US Patent App. 17/714,849

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    A computer-implemented physics solver operates within a neural network framework. A neural network accepts a coordinate for each location within a design domain and outputs a local composition for each location. A model of the design domain is formed in a physics solver. The model includes discrete elements that encompass the design domain. A solution of the model provides a value of a design objective. For a plurality of iterations, the following is performed: the neural network determines current local compositions for the locations in the design domain corresponding to the discrete elements; the current local compositions are input into the discrete elements of the physics solver to obtain a current value of the design objective; and the current value of the design objective is used to find a loss gradient of a loss function. The loss gradient is used to update the neural network during the iterations.

12. Patent

    

    Co-generation of collision-free shapes in arbitrary relative motion

    Clinton Morris, Amirmassoud Mirzendehdel, and Morad Behandish

    Dec 2023

    US Patent App. 17/831,790

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    The present disclosure provides techniques for automatically generating shapes (e.g., geometric representations) of two or more interacting objects based on arbitrary motions specified for the two or more interacting objects. In an example system. the system receives specifications of motions or movements of two or more objects and the associated design spaces and generates collision-free shapes for the two or more objects while the two or more objects undergo the specified motions. As such, the system solves for unknown or undefined shapes based on desired motion profiles. For example, given respective movement or motion characterizations of two or more objects, such as at least one of a function translation or a function rotation over time in at least one of the three axes in a Euclidean space, topology optimizations may be performed to generate the respective shapes or geometric representations of the two or more objects.

13. Patent

    

    Methods and systems of geometric representation generation based on a system-level model

    Randi Wang, Anurag Bhattacharyya, Qian Ye, Clinton Morris, Amirmassoud Mirzendehdel, and 1 more author

    Dec 2023

    US Patent App. 17/831,125

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    This disclosure provides techniques for automatically generating a geometric representation based on a system-level model (e.g., a lumped parameter model, or LPM). The geometric representation may include a three-dimensional (3D) or cross-sectional shape, resulting from topology optimization within a design space automatically generated without human intervention. An example method may include identifying one or more constraints for each of two or more components of an LPM. One or more conditions are generated for the LPM. The one or more conditions are mapped to the one or more constraints. A processing device may generate a design space for a geometric representation to perform functions represented by the LPM. The geometric representation is subject to the generated one or more conditions. The processing device may then perform topology optimization of the geometric representation in the design space to generate an optimized geometry (e.g., a converged and/or final output).

2022

1. CAD

   

   Topology optimization for manufacturing with accessible support structures

   Amir M. Mirzendehdel, Morad Behandish, and Saigopal Nelaturi

   Computer-Aided Design, Dec 2022

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   Metal additive manufacturing (AM) processes often fabricate a near-net shape that includes the as-designed part as well as the sacrificial support structures that need to be machined away by subtractive manufacturing (SM), for instance multi-axis machining. Thus, although AM is capable of generating highly complex parts, the limitations of SM due to possible collision between the milling tool and the workpiece can render an optimized part non-manufacturable. We present a systematic approach to topology optimization (TO) of parts for AM followed by SM to ensure removability of support structures, while optimizing the part’s performance. A central idea is to express the producibility of the part from the near-net shape in terms of accessibility of every support structure point using a given set of cutting tool assemblies and fixturing orientations. Our approach does not impose any artificial constraints on geometric complexity of the part, support structures, machining tools, and fixturing devices. We extend the notion of inaccessibility measure field (IMF) to support structures to identify the inaccessible points and capture their contributions to non-manufacturability by a continuous spatial field. IMF is then augmented to the sensitivity field to guide the TO towards a manufacturable design. The approach enables efficient and effective design space exploration by finding nontrivial complex designs whose near-net shape can be 3D printed and post-processed for support removal by machining with a custom set of tools and fixtures. We demonstrate the efficacy of our approach on nontrivial examples in 2D and 3D.

2. ASME IDETC

   

   Automatic shape modification for self-supporting structures in additive manufacturing

   Jiangce Chen, Matt Patterson, Amir M. Mirzendehdel, and Morad Behandish

   In International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Dec 2022

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   Additive manufacturing (AM) is a class of advanced manufacturing technologies that facilitates fabrication of geometrically complex, high-performance functional parts. AM processes often produce a “near-net” shape comprising the intended design and sacrificial support structures to be removed in postprocessing. The amount of extra material in the near-net shape directly increases fabrication cost and clean-up time. This paper presents a shape modification method for AM parts to minimize the need for sacrificial material in the near-net shape. Given an existing triangulated boundary representation of the part, we formulate the problem as a generic shape optimization that minimizes the changes made to the original geometry by locally modifying vertex coordinates while both maintaining the manifold nature of the representation and satisfying the overhang angle constraints, when possible. Specifically, we augment a pseudo-energy regularization term to our primary objective function for self-supporting to ensure that the optimized shape is valid and suitable for AM. We propose two mesh regularization methods, using virtual springs and sphere packing, and provide differentiable expressions of the objective function and constraints to enable efficient gradient-based optimization. We show that the sphere packing is more robust and retains the quality of the mesh during optimization. Finally, we demonstrate the effectiveness and efficiency of our method in modifying realistic models in 3D.

3. Patent

   

   Method and system for hierarchical multi-scale part design with the aid of a digital computer

   Morad Behandish, Amir M. Mirzendehdel, and Saigopal Nelaturi

   Nov 2022

   US Patent 11,507,054

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   The present disclosure is directed to a method and system for hierarchical multi-scale design with the aid of a digital computer. A hierarchical representation of a shape and material distribution is constructed which satisfies a top level constraint at a top-level of representation. Properties for families of designs at each of the lower levels of representation that satisfy additional constraints link each of the lower levels of representation to at least a next higher level of the representation.

2021

1. CG

   

   Optimizing build orientation for support removal using multi-axis machining

   Amir M. Mirzendehdel, Morad Behandish, and Saigopal Nelaturi

   Computers & Graphics, Nov 2021

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   Parts fabricated by additive manufacturing (AM) are often fabricated first as a near-net shape, a combination of intended nominal geometry and sacrificial support structures, which need to be removed in a subsequent post-processing stage using subtractive manufacturing (SM). In this paper, we present a framework for optimizing the build orientation with respect to removability of support structures. In particular, given a general multi-axis machining setup and sampled build orientations, we define a Pareto-optimality criterion based on the total support volume and the “secluded” support volume defined as the support volume that is not accessible by a given set of machining tools. Since total support volume mainly depends on the build orientation and the secluded volume is dictated by the machining setup, in many cases the two objectives are competing and their trade-off needs to be taken into account. The accessibility analysis relies on the inaccessibility measure field (IMF), which is a continuous field in the Euclidean space that quantifies the inaccessibility of each point given a collection of tools and fixturing devices. The value of IMF at each point indicates the minimum possible volumetric collision between objects in relative motion including the part, fixtures, and the tools, over all possible tool orientations and sharp points on the tool. We also propose an automated support removal planning algorithm based on IMF, where a sequence of actions are provided in terms of the fixturing devices, cutting tools, and tool orientation at each step. In our approach, each step is chosen based on the maximal removable volume to iteratively remove accessible supports. The effectiveness of the proposed approach is demonstrated through benchmark examples in 2D and realistic examples in 3D.

2. Conference (ASME IDETC)

   

   Topology optimization with locally evaluable complement space connectivity

   Clinton B Morris, Amir M. Mirzendehdel, and Morad Behandish

   In International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Nov 2021

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   Enforcing connectivity of parts or their complement space during automated design is essential for various manufacturing and functional considerations such as removing powder, wiring internal components, and flowing internal coolant. The global nature of connectivity makes it difficult to incorporate into generative design methods that rely on local decision making, e.g., topology optimization (TO) algorithms whose update rules depend on the sensitivity of objective functions or constraints to locally change the design. Connectivity is commonly corrected for in a post-processing step, which may result in suboptimal designs. We propose a recasting of the connectivity constraint as a locally differentiable violation measure, defined as a “virtual” compliance, modeled after physical (e.g., thermal or structural) compliance. Such measures can be used within TO alongside other objective functions and constraints, using a weighted penalty scheme to navigate tradeoffs. By carefully specifying the boundary conditions of the virtual compliance problem, the designer can enforce connectivity between arbitrary regions of the part’s complement space while satisfying a primary objective function in the TO loop. We demonstrate the effectiveness of our approach using both 2D and 3D examples, show its flexibility to consider multiple virtual domains, and confirm the benefits of considering connectivity in the design loop rather than enforcing it through post-processing.

3. Book Chapter

   

   Efficient Multi-Material Topology Optimization

   Amir M. Mirzendehdel, and Krishnan Suresh

   Nov 2021

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   This chapter focuses on generating optimized topologies using multiple materials. The interest in multi-material topology optimization (MMTO) stems from the well-recognized synergy between topology optimization (TO) and additive manufacturing (AM), where organic structures created through TO can be directly fabricated by a variety of AM processes. Given the rapidly increasing capabilities of AM, there is an opportunity to improve the performance of consumer products, biomedical, and aerospace components, through simultaneous optimization of topology and distribution of multiple materials.

2020

1. Journal (CAD)

   

   Topology optimization with accessibility constraint for multi-axis machining

   Amir M. Mirzendehdel, Morad Behandish, and Saigopal Nelaturi

   Computer-Aided Design, Nov 2020

   Special Issue on Process Planning for Additive/Hybrid Manufacturing

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   In this paper, we present a topology optimization (TO) framework to enable automated design of mechanical components while ensuring the result can be manufactured using multi-axis machining. Although TO improves the part’s performance, the as-designed model is often geometrically too complex to be machined and the as-manufactured model can significantly vary due to machining constraints that are not accounted for during TO. In other words, many of the optimized design features cannot be accessed by a machine tool without colliding with the part (or fixtures). The subsequent post-processing to make the part machinable with the given setup requires trial-and-error without guarantees on preserving the optimized performance. Our proposed approach is based on the well-established accessibility analysis formulation using convolutions in configuration space that is extensively used in spatial planning and robotics. We define an inaccessibility measure field (IMF) over the design domain to identify non-manufacturable features and quantify their contribution to non-manufacturability. The IMF is used to penalize the sensitivity field of performance objectives and constraints to prevent formation of inaccessible regions. Unlike existing discrete formulations, our IMF provides a continuous spatial field that is desirable for TO convergence. Our approach applies to arbitrary geometric complexity of the part, tools, and fixtures, and is highly parallelizable on multi-core architecture. We demonstrate the effectiveness of our framework on benchmark and realistic examples in 2D and 3D. We also show that it is possible to directly construct manufacturing plans for the optimized designs based on the accessibility information.

2. Patent

   

   Support structure constrained topology optimization for additive manufacturing

   Krishnan Suresh, and Amirmassoud Mirzendehdel

   Apr 2020

   US Patent 10,613,496

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   Systems and methods for generating designs of objects for additive manufacturing (AM) include a topological optimization framework that facilitates optimized computer generated designs requiring significantly reduced support structures. Towards this end, the concept of ‘support structure topological sensitivity’ is introduced. This is combined with performance sensitivity to result in a TO framework that maximizes performance, subject to support structure constraints. The robustness and efficiency of the proposed method is demonstrated through numerical experiments, and validated through fused deposition modeling, a popular AM process.

2019

1. Journal (CAD)

   

   Automatic support removal for additive manufacturing post processing

   Saigopal Nelaturi, Morad Behandish, Amir M. Mirzendehdel, and Johan Kleer

   Computer-Aided Design, Apr 2019

   Special Issue on Solid and Physical Modeling 2019

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   An additive manufacturing (AM) process often produces a 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.

2. Journal (CAD)

   

   A classification of topological discrepancies in additive manufacturing

   Morad Behandish, Amir M. Mirzendehdel, and Saigopal Nelaturi

   Computer-Aided Design, Apr 2019

   Special Issue on Solid and Physical Modeling 2019

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   Additive manufacturing (AM) enables enormous freedom for design of complex structures. However, the process-dependent limitations that result in discrepancies between as-designed and as-manufactured shapes are not fully understood. The tradeoffs between infinitely many different ways to approximate a design by a manufacturable replica are even harder to characterize. To support design for AM (DfAM), one has to quantify local discrepancies introduced by AM processes, identify the detrimental deviations (if any) to the original design intent, and prescribe modifications to the design and/or process parameters to countervail their effects. Our focus in this work will be on topological analysis. There is ample evidence in many applications that preserving local topology (e.g., connectivity of beams in a lattice) is important even when slight geometric deviations can be tolerated. We first present a generic method to characterize local topological discrepancies due to material under- and over-deposition in AM, and show how it captures various types of defects in the as-manufactured structures. We use this information to systematically modify the as-manufactured outcomes within the limitations of available 3D printer resolution(s), which often comes at the expense of introducing more geometric deviations (e.g., thickening a beam to avoid disconnection). We validate the effectiveness of the method on 3D examples with nontrivial topologies such as lattice structures and foams.

3. Journal (CAD)

   

   Exploring feasible design spaces for heterogeneous constraints

   Amir M. Mirzendehdel, Morad Behandish, and Saigopal Nelaturi

   Computer-Aided Design, Apr 2019

   Special Issue on Advances in Generative Design

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   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).

2018

1. Journal (CAD)

   

   Strength-based topology optimization for anisotropic parts

   Amir M. Mirzendehdel, Behzad Rankouhi, and Krishnan Suresh

   Additive Manufacturing, Apr 2018

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   Additive manufacturing (AM) is emerging as a promising technology to fabricate cost-effective, customized functional parts. Designing such functional, i.e., load bearing, parts can be challenging and time consuming where the goal is to balance performance and material usage. Topology optimization (TO) is a powerful design method which can complement AM by automating the design process. However, for TO to be a useful methodology, the underlying mathematical model must be carefully constructed. Specifically, it is well established that parts fabricated through some AM technologies, such as fused deposition modeling (FDM), exhibit behavioral anisotropicity. This induced anisotropy can have a negative impact on functionality of the part, and must be considered. To the best of our knowledge, a robust TO method to handle anisotropy has not been proposed. In the present work, a strength-based topology optimization method for structures with anisotropic materials is presented. More specifically, we propose a new topological sensitivity formulation based on strength ratio of non-homogeneous failure criteria, such as Tsai-Wu. Implementation details are discussed throughout the paper, and the effectiveness of the proposed method is demonstrated through numerical and experimental tests.

2017

1. PhD Thesis

   

   Towards Integrating Topology Optimization and Additive Manufacturing

   Amir M. Mirzendehdel

   The University of Wisconsin-Madison, Apr 2017

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2. Tutorial

   

   A Hands-On Introduction to Topology Optimization

   Amir M. Mirzendehdel, and K Suresh

   Apr 2017

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2016

1. Journal (CAD)

   

   Support structure constrained topology optimization for additive manufacturing

   Amir M. Mirzendehdel, and Krishnan Suresh

   Computer-Aided Design, Apr 2016

   Special Issue on Solid and Physical Modeling 2017

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   Additive manufacturing (AM) enables the fabrication of complex geometries that are not possible with traditional manufacturing methods. However, the design of parts for AM is often constrained by the need for support structures to prevent overhangs from collapsing during fabrication. In this paper, we present a topology optimization framework that incorporates support structure constraints to generate designs that are manufacturable using AM. The proposed method uses a density-based approach to optimize the material distribution in the design domain while ensuring that the resulting part can be fabricated without requiring excessive support structures. We demonstrate the effectiveness of our approach on several benchmark problems and show that it can produce designs with significantly reduced support requirements compared to traditional methods.

2015

1. Journal (JMD)

   

   A Pareto-optimal approach to multimaterial topology optimization

   Amir M. Mirzendehdel, and Krishnan Suresh

   Journal of Mechanical Design, Apr 2015

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   As additive manufacturing (AM) expands into multimaterial, there is a demand for efficient multimaterial topology optimization (MMTO), where one must simultaneously optimize the topology and the distribution of various materials within the topology. The classic approach to multimaterial optimization is to minimize compliance or stress while imposing two sets of constraints: (1) a total volume constraint and (2) individual volume-fraction constraint on each of the material constituents. The latter can artificially restrict the design space. Instead, the total mass and compliance are treated as conflicting objectives, and the corresponding Pareto curve is traced; no additional constraint is imposed on the material composition. To trace the Pareto curve, first-order element sensitivity fields are computed, and a two-step algorithm is proposed. The effectiveness of the algorithm is demonstrated through illustrative examples in 3D.

2. JCND

   

   A deflated assembly free approach to large-scale implicit structural dynamics

   Amir M. Mirzendehdel, and Krishnan Suresh

   Journal of Computational and Nonlinear Dynamics, Apr 2015

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   The primary computational bottle-neck in implicit structural dynamics is the repeated inversion of the underlying stiffness matrix. In this paper, a fast inversion technique is proposed by merging four distinct but complementary concepts: (1) voxelization with adaptive local refinement, (2) assembly-free (a.k.a. matrix-free or element-by-element) finite element analysis (FEA), (3) assembly-free deflated conjugate gradient (AF-DCG), and (4) multicore parallelization. In particular, we apply these concepts to the well-known Newmark-beta method, and the resulting AF-DCG is well-suited for large-scale problems. It can be easily ported to many-core central processing unit (CPU) and multicore graphics-programmable unit (GPU) architectures, as demonstrated through numerical experiments.

3. Conference (ASME IDETC)

   

   Multi-Material topology optimization for additive manufacturing

   Amir M. Mirzendehdel, and Krishnan Suresh

   In International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Apr 2015

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   Additive manufacturing (AM) and topology optimization strongly complement each other in that the complex and optimal designs created through the latter can directly be fabricated through AM, leading to reduced design and fabrication time. As AM expands into multi-material fabrication, there is a natural need for efficient multi-material topology optimization methods, where one must simultaneously optimize the topology, and the distribution of various materials within the topology. In this paper we generalize the single-material Pareto tracing method of topology optimization to multiple materials, and discuss its implementation using assembly-free finite element analysis, and first-order element-sensitivity. The effectiveness of the algorithm is demonstrated through illustrative examples.

2014

1. Conference (ASME IDETC)

   

   A Fast Time-Stepping Strategy for the Newmark-Beta Method

   Amir M. Mirzendehdel, and Krishnan Suresh

   In International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Apr 2014

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   In this paper, we develop a fast time-stepping strategy for the Newmark-beta method; the latter is used extensively in structural dynamics. In particular, we speed up the repeated inversion of the linear systems in the Newmark-beta method by implementing and merging four distinct but complementary concepts: (1) voxelization, (2) assembly-free finite element analysis, (3) deflated conjugate gradient, and (4) adaptive local refinement. The resulting assembly-free deflated conjugate gradient (AF-DCG) version of the Newmark-beta is well-suited for large-scale problems, and can be easily ported to multi-core architectures. Numerical experiments demonstrate the efficacy of the proposed method.

2. MSc Thesis

   

   Assembly-free Structural Dynamics on CPU and GPU

   Amir M. Mirzendehdel

   Apr 2014

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