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26 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Global stellarator coil optimization with quadratic constraints and objectives

Most present stellarator designs are produced by costly two-stage optimization: the first for an optimized equilibrium, and the second for a coil design reproducing its magnetic configuration. Few proxies for coil complexity and forces exist at the equilibrium stage. Rapid initial state finding for both stages is a topic of active research. Most present convex coil optimization codes use the least square winding surface method by Merkel (NESCOIL), with recent improvements in conditioning, regularization, sparsity, and physics objectives. While elegant, the method is limited to modeling the norms of linear functions in coil current. We present QUADCOIL, a global coil optimization method that targets combinations of linear and quadratic functions of the current. It can directly constrain and/or minimize a wide range of physics objectives unavailable in NESCOIL and REGCOIL, including the Lorentz force, magnetic energy, curvature, field-current alignment, and the maximum density of a dipole array. QUADCOIL requires no initial guess and runs nearly $10$ 2 x faster than filament optimization. Integrating it in the equilibrium optimization stage can potentially exclude equilibria with difficult-to-design coils, without significantly increasing the computation time per iteration. QUADCOIL finds the exact, global minimum in a large parameter space when possible, and otherwise finds a well-performing approximate global minimum. It supports most regularization techniques developed for NESCOIL and REGCOIL. We demonstrate QUADCOIL’s effectiveness in coil topology control, minimizing non-convex penalties, and predicting filament coil complexity with three numerical examples.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

A Fast Temporal Decomposition Procedure for Long-Horizon Nonlinear Dynamic Programming

We propose a fast temporal decomposition procedure for solving long-horizon nonlinear dynamic programs. The core of the procedure is sequential quadratic programming (SQP) that utilizes a differentiable exact augmented Lagrangian as the merit function. Within each SQP iteration, we approximately solve the Newton system using an overlapping temporal decomposition strategy. We show that the approximate search direction is still a descent direction of the augmented Lagrangian provided the overlap size and penalty parameters are suitably chosen, which allows us to establish the global convergence. Moreover, we show that a unit step size is accepted locally for the approximate search direction and further establish a uniform, local linear convergence over stages. This local convergence rate matches the rate of the recent Schwarz scheme (Na et al. 2022). However, the Schwarz scheme has to solve nonlinear subproblems to optimality in each iteration, whereas we only perform a single Newton step instead. Numerical experiments validate our theories and demonstrate the superiority of our method.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1978

Differential encoding for multiple amplitude and phase shift keying systems

Because of the symmetry in most two-dimensional signal constellations, ambiguities exist at the receiver as to the exact phase orientation of the received signal set. In PSK systems, this ambiguity is resolved by the use of differential encoding. This paper presents differential encoding techniques which can be used with a variety of symmetric signal sets to remove their phase ambiguity. While not proven to be optimum, the techniques do have low performance penalties relative to the uncoded performance. The key to reducing the performance penalty is to use the minimum amount of differential encoding necessary to resolve the ambiguity. Examples of encoding techniques for several common signal constellations are given, including their performance penalties.

Weber, W. J., III↗
NASA NTRS1999

Optimization of Aerospace Structure Subject to Damage Tolerance Criteria

The objective of this cooperative agreement was to seek computationally efficient ways to optimize aerospace structures subject to damage tolerance criteria. Optimization was to involve sizing as well as topology optimization. The work was done in collaboration with Steve Scotti, Chauncey Wu and Joanne Walsh at the NASA Langley Research Center. Computation of constraint sensitivity is normally the most time-consuming step of an optimization procedure. The cooperative work first focused on this issue and implemented the adjoint method of sensitivity computation in an optimization code (runstream) written in Engineering Analysis Language (EAL). The method was implemented both for bar and plate elements including buckling sensitivity for the latter. Lumping of constraints was investigated as a means to reduce the computational cost. Adjoint sensitivity computation was developed and implemented for lumped stress and buckling constraints. Cost of the direct method and the adjoint method was compared for various structures with and without lumping. The results were reported in two papers. It is desirable to optimize topology of an aerospace structure subject to a large number of damage scenarios so that a damage tolerant structure is obtained. Including damage scenarios in the design procedure is critical in order to avoid large mass penalties at later stages. A common method for topology optimization is that of compliance minimization which has not been used for damage tolerant design. In the present work, topology optimization is treated as a conventional problem aiming to minimize the weight subject to stress constraints. Multiple damage configurations (scenarios) are considered. Each configuration has its own structural stiffness matrix and, normally, requires factoring of the matrix and solution of the system of equations. Damage that is expected to be tolerated is local and represents a small change in the stiffness matrix compared to the baseline (undamaged) structure. The exact solution to a slightly modified set of equations can be obtained from the baseline solution economically without actually solving the modified system. Sherrnan-Morrison-Woodbury (SMW) formulas are matrix update formulas that allow this. SMW formulas were therefore used here to compute adjoint displacements for sensitivity computation and structural displacements in damaged configurations.

Akgun, Mehmet A.↗
NASA NTRS2000

Adjoint Techniques for Topology Optimization of Structures Under Damage Conditions

The objective of this cooperative agreement was to seek computationally efficient ways to optimize aerospace structures subject to damage tolerance criteria. Optimization was to involve sizing as well as topology optimization. The work was done in collaboration with Steve Scotti, Chauncey Wu and Joanne Walsh at the NASA Langley Research Center. Computation of constraint sensitivity is normally the most time-consuming step of an optimization procedure. The cooperative work first focused on this issue and implemented the adjoint method of sensitivity computation (Haftka and Gurdal, 1992) in an optimization code (runstream) written in Engineering Analysis Language (EAL). The method was implemented both for bar and plate elements including buckling sensitivity for the latter. Lumping of constraints was investigated as a means to reduce the computational cost. Adjoint sensitivity computation was developed and implemented for lumped stress and buckling constraints. Cost of the direct method and the adjoint method was compared for various structures with and without lumping. The results were reported in two papers (Akgun et al., 1998a and 1999). It is desirable to optimize topology of an aerospace structure subject to a large number of damage scenarios so that a damage tolerant structure is obtained. Including damage scenarios in the design procedure is critical in order to avoid large mass penalties at later stages (Haftka et al., 1983). A common method for topology optimization is that of compliance minimization (Bendsoe, 1995) which has not been used for damage tolerant design. In the present work, topology optimization is treated as a conventional problem aiming to minimize the weight subject to stress constraints. Multiple damage configurations (scenarios) are considered. Each configuration has its own structural stiffness matrix and, normally, requires factoring of the matrix and solution of the system of equations. Damage that is expected to be tolerated is local and represents a small change in the stiffness matrix compared to the baseline (undamaged) structure. The exact solution to a slightly modified set of equations can be obtained from the baseline solution economically without actually solving the modified system.. Shennan-Morrison-Woodbury (SMW) formulas are matrix update formulas that allow this (Akgun et al., 1998b). SMW formulas were therefore used here to compute adjoint displacements for sensitivity computation and structural displacements in damaged configurations.

Akgun, Mehmet A.↗
NASA NTRS1994

Accurate interlaminar stress recovery from finite element analysis

The accuracy and robustness of a two-dimensional smoothing methodology is examined for the problem of recovering accurate interlaminar shear stress distributions in laminated composite and sandwich plates. The smoothing methodology is based on a variational formulation which combines discrete least-squares and penalty-constraint functionals in a single variational form. The smoothing analysis utilizes optimal strains computed at discrete locations in a finite element analysis. These discrete strain data are smoothed with a smoothing element discretization, producing superior accuracy strains and their first gradients. The approach enables the resulting smooth strain field to be practically C1-continuous throughout the domain of smoothing, exhibiting superconvergent properties of the smoothed quantity. The continuous strain gradients are also obtained directly from the solution. The recovered strain gradients are subsequently employed in the integration o equilibrium equations to obtain accurate interlaminar shear stresses. The problem is a simply-supported rectangular plate under a doubly sinusoidal load. The problem has an exact analytic solution which serves as a measure of goodness of the recovered interlaminar shear stresses. The method has the versatility of being applicable to the analysis of rather general and complex structures built of distinct components and materials, such as found in aircraft design. For these types of structures, the smoothing is achieved with 'patches', each patch covering the domain in which the smoothed quantity is physically continuous.

Tessler, Alexander↗
DOE OSTI2022

A fourth-order phase-field fracture model: Formulation and numerical solution using a continuous/discontinuous Galerkin method

Modeling crack initiation and propagation in brittle materials is of great importance to be able to predict sudden loss of load-carrying capacity and prevent catastrophic failure under severe dynamic loading conditions. Second-order phase-field fracture models have gained wide adoption given their ability to capture the formation of complex fracture patterns, e.g. via crack merging and branching, and their suitability for implementation within the context of the conventional finite element method. Higher-order phase-field models have also been proposed to increase the regularity of the exact solution and thus increase the spatial convergence rate of its numerical approximation. However, they require special numerical techniques to enforce the necessary continuity of the phase field solution. In this paper, we derive a fourth-order phase-field model of fracture in two independent ways; namely, from Hamilton’s principle and from a higher-order micromechanics-based approach. The latter approach is novel, and provides a physical interpretation of the higher-order terms in the model. In addition, we propose a continuous/discontinuous Galerkin (C/DG) method for use in computing the approximate phase-field solution. This method employs Lagrange polynomial shape functions to guarantee -continuity of the solution at inter-element boundaries, and enforces the required regularity with the aid of additional variational and interior penalty terms in the weak form. Finally, the phase-field equation is coupled with the momentum balance equation to model dynamic fracture problems in hyper-elastic materials. Two benchmark problems are presented to compare the numerical behavior of the C/DG method with mixed finite element methods.

42 ENGINEERING↗
NASA NTRS2000

Mission Design Overview for Mars 2003/2005 Sample Return Mission

In May 2003, a new and exciting chapter in Mars exploration will begin with the launch of the first of three spacecraft that will collectively contribute toward the goal of delivering samples from the Red Planet to Earth. This mission is called Mars Sample Return (MSR) and will utilize both the 2003 and 2005 launch opportunities with an expected sample return in October 2008. NASA and CNES are major partners in this mission. The baseline mission mode selected for MSR is Mars orbit rendezvous (MOR), analogous in concept to the lunar orbit rendezvous (LOR) mode used for Apollo in the 1960s. Specifically, MSR will employ two NASA-provided landers of nearly identical design and one CNES-provided orbiter carrying a NASA payload of rendezvous sensors, orbital capture mechanisms, and an Earth entry vehicle (EEV). The high-level concept is that the landers will launch surface samples into Mars orbit, and the orbiter will retrieve the samples in orbit and then carry them back to Earth. The first element to depart for Mars will be one of the two landers. Currently, it is proposed that an intermediate class launch vehicle, such as the Boeing Delta 3 or Lockheed Martin Atlas 3A, will launch this 1800-kg lander from Cape Canaveral during the May 2003 opportunity. The lander will utilize a Type-1 transfer trajectory with an arrival at Mars in mid-December 2003. Landing will be aided by precision approach navigation and a guided hypersonic entry to achieve a touchdown accuracy of 10 km or better. Although the exact landing site has not yet been determined, it is estimated that lander resource constraints will limit the site to between 15 degrees north and south latitudes. Following touchdown, the lander will deploy a six-wheeled, 60-kg rover carrying an extensive suite of instruments designed to aid in the analysis of the local terrain and collection of core samples from selected rocks. The surface mission is currently designed around a concept called the surface traverse. Each traverse will involve the rover exploring a selected area of terrain up to 100 meters from the lander, the collection of rock core samples, and the delivery of the samples from the traverse back to a sample canister on the lander. Planning estimates indicate that up to three traverses may be possible during the expected 90-sol lifetime of the lander. The canister that will receive the samples from the rover will be attached to the top stage of a small solid-fueled rocket mounted to the deck of the lander. This rocket is called the Mars Ascent Vehicle (MAV) and consists of three stages weighing a total of about 140 kg. After the conclusion of the surface mission, the MAV will lift-off and insert the sample canister into a near-circular orbit with an altitude of about 600 km and inclination of 45 degrees. The sample canister will wait in this orbit until it is retrieved by the orbiter sometime in early 2007. In August 2005, the second lander and a CNES-provided orbiter weighing 2700 kg will depart for Mars. Currently, it is proposed that a single Ariane 5 provided by CNES will launch both of these two elements onto a Type-2 transfer trajectory. Although the orbiter and lander will be launched together, they will separate shortly after injection and will fly to Mars as two independent spacecraft. However, both spacecraft will perform a maneuver between 10 and 15 days after launch so that their arrival times at Mars differ by between 12 and 24 hours. This scheme will reduce the operational complexity at the encounter date. A set of four 60-kg surface probes will ride piggyback on the orbiter to Mars. These CNES-provided probes are called Netlanders and will serve as surface stations for scientific investigations independent of the Mars Sample Return goals. Starting approximately one month prior to arrival at Mars, the orbiter will begin to release the Netlanders one at a time. Each release cycle will take several days, and will include time for precision navigation to execute one or two maneuvers that will target the Netlanders to their proper landing site. All four deployment cycles will be completed prior to 10 days before arrival. Both the orbiter and lander will arrive in late-July 2006. Upon arrival, the lander will perform a precision landing and surface mission similar in concept to the one that was executed during the 2003 opportunity. Although the landing site for the 2005 opportunity has not been selected, it is expected to be different from the 2003 site to enhance the diversity of the collected samples. The orbiter's arrival at Mars will be highlighted by the first use of aerocapture to insert a spacecraft into a capture orbit around another planet. The choice of aerocapture, as opposed to a propulsive orbit insertion, was considered mission enabling due to a reduction of over 2000 m/s in mission AV. Aerocapture will be targeted to produce a 250 km x 1400 km capture orbit with an inclination of 45 degrees. Current analysis indicates that achieving this goal will require approximately six minutes of flight deep in the atmosphere with a targeted periapsis of approach of about 43 km. After factoring into account the penalty for carrying a heat shield to survive aerocapture, the net savings compared to a propulsive orbital insertion amounts to several hundred kilograms.

Lee, Wayne J.↗