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Tortorelli, Daniel A.

Publications and source records attributed to Tortorelli, Daniel A..

At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Level-set topology optimization with PDE generated conformal meshes

This paper presents a level-set topology optimization approach that uses conformal meshes for the analysis of the displacement field. The structure’s boundary is represented by the iso-contour of a level-set field discretized on a fixed background design mesh. The conformal mesh is updated for each design iteration via a PDE based mesh morphing process that identifies the set of facets in the background mesh that are homeomorphic to the boundary and relaxes the homeomorphic mesh to conform to the structure’s boundary and ensure high element quality. The conformal mesh allows for a more accurate computation of the response versus density and some level-set based methods which interpolate material properties using the volume fraction. Numerical examples illustrate the proposed approach by optimizing linear-elastic two- and three-dimensional structures, wherein insight into the performance of the mesh morphing process is provided. The examples also highlight the scalability of the approach.

42 ENGINEERING↗
DOE OSTI2023

Yet another parameter-free shape optimization method

The use of node coordinates as design variables in shape optimization offers a larger design space than computer-aided design (CAD)-based shape parameterizations. It also allows for the optimization of legacy designs, i.e., a finite element mesh from an existing design can be readily optimized to meet new performance requirements without involving a CAD model. However, it is well known that the node coordinate parameterization method is fraught with numerical difficulties, which makes it impractical to use. This has led to several of “parameter-free” shape optimization methods that seek the advantages and avoid the pitfalls of the naïve node coordinate parameterization method. These methods come in two main varieties: sensitivity filtering (or gradient smoothing) and consistent filtering. The latter is analogous to the density filter method used in topology optimization (TO). In this work, we use the PDE filter from TO and energy-based filters to implement consistent shape optimization filtering schemes easily and efficiently. Numerical experiments demonstrate that consistent methods are more robust than sensitivity filtering methods.

42 ENGINEERING↗
DOE OSTI2023

Design and additive manufacturing of optimized electrodes for energy storage applications

Supercapacitors exhibit fast charging/discharging ability and have attracted considerable attention within the automotive, aerospace, and telecommunication industries. Porous carbons, prized for their high electrical conductivity and high surface area, have been attractive candidates for supercapacitor electrodes. Moving to thick electrodes is one strategy to further increase energy density due to a higher volume fraction of active material. However, thick electrodes suffer from sluggish charged species transport, which is why thin electrodes are currently favored. In this work, we investigate the use of computational optimization and additive manufacturing to design and fabricate thick porous electrodes with improved performance. Electrode performance was maximized by designing their morphologies via topology optimization and printing by projection micro stereolithography (PμSL) using commercial resin (PR48). The PR48 resin was then pyrolyzed (PR48-P) to create the final conductive electrode. The optimized PR48-P electrodes exhibited 99% improvement in capacitance compared to control electrodes printed with cubic lattice morphologies. To further improve performance, we formulated a resin combining graphene oxide (GO) and trimethylolpropane triacrylate (TMPTA). Electrodes printed with 3 wt% GO in TMPTA exhibited improved capacitance retention after pyrolysis compared to the PR48-P electrodes. Finally, this work demonstrates the benefits of using topology optimization to design electrodes and material development to improve functional properties of 3D printable electrodes.

25 ENERGY STORAGE↗
DOE OSTI2022

Fracture-based shape optimization built upon the topological derivative

In Silva et al. (2011) and Alidoost et al. (2020), the authors developed an approximation of the energy release rate field associated with a small edge or surface crack at any boundary location and with any orientation using the topological derivative. The approximation is computationally attractive because it requires only a single analysis on the non-cracked domain in contrast with conventional boundary-element and finite-element-based methods, which require a separate and costlier analysis for each crack length-location-orientation combination. Here, a shape optimization scheme for fracture-resistant structures is developed using the energy release rate approximation. In the gradient-based optimization scheme, the domain and its boundary are defined implicitly using level-set functions. The level-set functions of arbitrary geometries are constructed using Boolean operations from the level-set functions of simple primitives. This geometrical representation has the dual advantage of (i) allowing shapes to intersect and/or separate during the optimization and (ii) simplifying the computation of the shape sensitivities.

42 ENGINEERING↗
DOE OSTI2022

Manufacturing and stiffness constraints for topology optimized periodic structures

Topology optimization (TO) is commonly applied to design the unit cells of periodic structures. For example, metamaterials, lattice structures, phononic crystals (PhC), and photonic crystals (PC) have all been previously designed via TO. Unfortunately, the optimal structures for certain design objectives, e.g., bandgaps, are often impossible to manufacture as they have disconnected regions or “islands” of solid material (ISM) that are not self-supporting. Additionally, designs with enclosed void space (EVS) are problematic for additive manufacturing (AM) since support material or pre-sintered powder cannot be removed after manufacturing. We present a series of constraints that may be incorporated into any TO framework to ensure structures are self-supporting without enclosed voids. Additionally, we employ homogenization-based constraints that allow the designer to tune the elastic stiffness and isotropy of the optimized design. The proposed constraints are evaluated on example microstructures and utilized in a simple optimization test problem to highlight their abilities and limitations so that guidelines for appropriate combinations of constraints may be proposed. Effective constraint combinations are demonstrated on the design of 3D photonic crystals for maximum bandgap subject to manufacturing and stiffness constraints.

42 ENGINEERING↗
DOE OSTI2021

Parallel projection—An improved return mapping algorithm for finite element modeling of shape memory alloys

Here, we present a novel finite element analysis of inelastic structures containing Shape Memory Alloys (SMAs). Phenomenological constitutive models for SMAs lead to material nonlinearities, that require substantial computational effort to resolve. Finite element analysis methods, which rely on Gauss quadrature integration schemes, must solve two sets of coupled differential equations: one at the global level and the other at the local, i.e. Gauss point level. In contrast to the conventional return mapping algorithm, which solves these two sets of coupled differential equations separately using a nested Newton procedure, we propose a scheme to solve the local and global differential equations simultaneously. In the process we also derive closed-form expressions used to update the internal/constitutive state variables, and unify the popular closest-point and cutting plane methods with our formulas. Numerical testing indicates that our method allows for larger thermomechanical loading steps and provides increased computational efficiency, over the standard return mapping algorithm.

42 ENGINEERING↗
DOE OSTI2021

Two Dimensional Topology Optimization of Heat Exchangers with the Density and Level-Set Methods

We design heat exchangers using two topology optimization approaches: the density, i.e. volume fraction and level set methods. Our goal is to maximize the heat exchange between two fluids in separate channels while constraining the pressure drop across each channel. The heat exchanger is modeled with a coupled thermal-flow formulation. The flow is governed by an isothermal and incompressible Stokes-Brinkman equation and the heat transfer is governed by a convection-diffusion equation with high Peclet number. We solve one set of Stokes-Brinkman equations per fluid. Each Brinkman term in the flow equation serves to model the other phase as a solid, thereby preventing mixing. We first represent the solid and fluid phases using a volume fraction variable and apply a SIMP-like penalization in the Brinkman term to drive the optimization to a discrete design. The cost and constraint function derivatives are automatically calculated with the library pyadjoint and the optimization is performed by the Method of Moving Asymptotes. In a second optimization formulation, we use the level set approach to define the interface that separates the two fluids. Pyadjoint calculates the shape derivatives of the cost and constraint functions and the Hamilton-Jacobi advects the interface, allowing for topological changes. We present results in two dimensions and discuss the advantages and disadvantages of each approach.

42 ENGINEERING↗
DOE OSTI2021

Computational design of microarchitected porous electrodes for redox flow batteries

Porous electrodes are used as the core reactive component across electrochemical technologies. In flowing systems, controlling the fluid distribution, species transport, and reactive environment is critical to attaining high performance. However, conventional electrode materials like felts and papers provide few opportunities for precise engineering of the electrode and its microstructure. To address these limitations, architected electrodes composed of unit cells with spatially varying geometry determined via computational optimization are proposed. Resolved simulation is employed to develop a homogenized description of the constituent unit cells. These effective properties serve as inputs to a continuum model for the electrode when used in the negative half-cell of a vanadium redox flow battery. Porosity distributions minimizing power loss are then determined via computational design optimization to generate architected porosity electrodes. The architected electrodes are compared to bulk, uniform porosity electrodes and found to lead to increased power efficiency across operating flow rates and currents. The design methodology is further used to generate a scaled-up electrode with comparable power efficiency to the bench-scale systems. Finally, the variable porosity architecture and computational design methodology presented here thus offers a novel pathway for automatically generating spatially engineered electrode structures with improved power performance.

25 ENERGY STORAGE↗
DOE OSTI2021

Structural stability and artificial buckling modes in topology optimization

Abstract This paper demonstrates how a strain energy transition approach can be used to remove artificial buckling modes that often occur in stability constrained topology optimization problems. To simulate the structural response, a nonlinear large deformation hyperelastic simulation is performed, wherein the fundamental load path is traversed using Newton’s method and the critical buckling load levels are estimated by an eigenvalue analysis. The goal of the optimization is to minimize displacement, subject to constraints on the lowest critical buckling loads and maximum volume. The topology optimization problem is regularized via the Helmholtz PDE-filter and the method of moving asymptotes is used to update the design. The stability and sensitivity analyses are outlined in detail. The effectiveness of the energy transition scheme is demonstrated in numerical examples.

Dalklint, Anna (ORCID:0000000346195205)↗
DOE OSTI2021

Topology optimization of 3D photonic crystals with complete bandgaps

The design of photonic crystals with complete bandgaps has recently received considerable research focus for numerous reasons. This work leverages well-known nonlinear programming techniques to alleviate the non-smoothness caused by degenerate eigenvalues such that topology optimization problems can be solved with the open-source IPOPT software. A fully-vectorial plane wave expansion technique is used with an iterative eigensolver to efficiently predict dispersion properties of candidate structures. Nonlinear programming is employed to solve the inverse problem of designing three-dimensional periodic structures that exhibit complete two-dimensional (2D) and three-dimensional (3D) photonic bandgaps. Mesh refinement is performed to alleviate the large computational burden of designing and analyzing photonic crystals, and a periodic density filter is implemented to impose a minimum feature size for manufacturability considerations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Plastic work constrained elastoplastic topology optimization

An elastoplastic topology optimization framework for limiting plastic work generation while maximizing stiffness is presented. The kinematics and constitutive model are based on finite strain linear isotropic hardening plasticity, and the balance laws are solved using a total Lagrangian finite element formulation. Aggregation of the specific plastic work combined with an adaptive normalization scheme efficiently constrains the maximum specific plastic work. The optimization problem is regularized using an augmented partial differential equation filter, and is solved by the method of moving asymptotes where path-dependent sensitivities are derived using the adjoint method. The numerical examples show a clear dependence on the optimized maximum stiffness structures for different levels of constrained specific plastic work. It is also shown that due to the history dependency of the plasticity, the load path significantly influences the structural performance and optimized topology.

42 ENGINEERING↗
DOE OSTI2021

Multiscale design of nonlinear materials using a Eulerian shape optimization scheme

Motivated by recent advances in manufacturing, the design of materials is the focal point of interest in the material research community. One of the critical challenges in this field is finding optimal material microstructure for a desired macroscopic response. This work presents a computational method for the mesoscale-level design of particulate composites for an optimal macroscale-level response. The method relies on a custom shape optimization scheme to find the extrema of a nonlinear cost function subject to a set of constraints. Three key “modules” constitute the method: multiscale modeling, sensitivity analysis, and optimization. Multiscale modeling relies on a classical homogenization method and a nonlinear NURBS-based generalized finite element scheme to efficiently and accurately compute the structural response of particulate composites using a nonconformal discretization. A three-parameter isotropic damage law is used to model microstructure-level failure. An analytical sensitivity method is developed to compute the derivatives of the cost/constraint functions with respect to the design variables that control the microstructure's geometry. The derivation uncovers subtle but essential new terms contributing to the sensitivity of finite element shape functions and their spatial derivatives. Several structural problems are solved to demonstrate the applicability, performance, and accuracy of the method for the design of particulate composites with a desired macroscopic nonlinear stress-strain response.

42 ENGINEERING↗
DOE OSTI2021

Optimal toolpath design of additive manufactured composite cylindrical structures

Structural design optimization for additive manufacturing is primarily focused on planar layer-by-layer processes and design of composite cylindrical structures does not often accommodate manufacturing constraints. In this study, we propose to optimize the toolpath trajectory of additively manufactured composite cylinders comprised of multiple thin cylindrical annuli. Additionally, our printing process is based on direct ink writing in which short carbon fibers in a thermoset resin are extruded through a moving nozzle to build up a structure. Since the fibers are primarily aligned in the flow direction of the extrudate, the printing trajectory influences the material properties of the composite structure. To accommodate this, we define the toolpaths as contours of parameterized level-set functions. This parameterization allows us to optimize the material properties and impose manufacturing constraints such as no-overlap, no-sag, minimum radius of curvature, and continuity of the toolpaths. Several examples illustrate the optimization procedure.

42 ENGINEERING↗
DOE OSTI2020

Simultaneous material, shape and topology optimization

Using three design fields we develop an optimization environment that can simultaneously optimize material, shape and topology. We use the implicit representation of the boundaries with level-set functions that define the shape and topology. Differentiable R-functions allow us to combine these shapes and topology descriptions with Boolean operations. Additionally, we incorporate design dependent-stiffness materials with another design field. Notably, this framework accommodates design dependent loads, has the ability to introduce holes, and ensures the satisfaction of optimality criteria. It builds upon the fictitious domain, ersatz material, material interpolation and level-set methods. Additionally, it also borrows from parameterized density-based topology optimization methods. Since analytical sensitivities can be computed, we use efficient nonlinear programming algorithms to update the design instead of the Hamilton–Jacobi’s scheme of level-set methods. We illustrate the features of our framework by designing a cantilever beam with octet truss microlattice, a dam with design-dependent loads, and a composite clevis plate.

42 ENGINEERING↗
DOE OSTI2020

Topology optimization of multiple deformable bodies in contact with large deformations

Previous works in topology optimization of structures with contact boundary conditions have concentrated on the two-dimensional rigid obstacle problem. This is because the contact analysis of multiple three-dimensional deformable bodies with meshes that are non-matching across the contact interface requires computationally complex contact algorithms beyond the scope of previous optimization investigations. Here, our research is devoted to addressing topology design problems with multiple deformable three-dimensional components in contact using state-of-the-art contact algorithms.

42 ENGINEERING↗