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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 379 records · Page 21
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Optimization-based algorithms for nonlinear mechanics and frictional contact

An optimization-based strategy for solving nonlinear mechanics problems is proposed. In contrast to typical nonlinear equation solver algorithms that aim to find zeros in the residual force function, we minimize an energy (or energy-like) function to encourage solutions which are locally stable equilibria. These smooth and potentially non-convex objective functions are minimized using a preconditioned conjugate-gradient trust-region algorithm. Contact is formulated as an inequality constrained minimization problem, and is solved with an augmented Lagrangian algorithm. Friction is included in the approach via a regularized quasi-potential energy, and other dissipative behavior is included through the use of variational constitutive updates. Finally, to accelerate convergence rates for the Lagrange multipliers, we propose a novel multiplier update algorithm utilizing the Fischer-Burmeister function, and demonstrate super-linear solver convergence for some applications.

42 ENGINEERING↗
NASA NTRS1994

(abstract) Optimal Low Thrust Trajectories Using Differential Inclusion Concepts

Low thrust propulsion systems typically have their greatest benefit for high energy missions or missions with large post-launch maneuver requirements. Missions which have been examined include main belt asteroid rendezvous, comet rendezvous, outer planet and Mercury orbiters, Pluto flyby, and solar probe missions. Low thrust mission design software used to determine these trajectories is based on two distinct formulations of the optimal control problem: the indirect and direct methods. The traditional approach (indirect) is to use the calculus of variations to obtain first order necessary conditions on the states and costates. In contrast, direct methods are conceptually different in that no explicit integration takes place. A direct method based on differential inclusion concepts has been developed and successfully used to compute low thrust trajectories. This new approach removes explicit control dependence from the problem thereby reducing the dimension of the parameter space for the nonlinear programming problem. Also when compared to other direct methods, fewer nonlinear constraints are required to represent the dynamics of the problem.

low↗
NASA NTRS1991

A geometric nonlinear degenerated shell element using a mixed formulation with independently assumed strain fields

A mixed formulation is chosen to overcome deficiencies of the standard displacement-based shell model. Element development is traced from the incremental variational principle on through to the final set of equilibrium equations. Particular attention is paid to developing specific guidelines for selecting the optimal set of strain parameters. A discussion of constraint index concepts and their predictive capability related to locking is included. Performance characteristics of the elements are assessed in a wide variety of linear and nonlinear plate/shell problems. Despite limiting the study to geometric nonlinear analysis, a substantial amount of additional insight concerning the finite element modeling of thin plate/shell structures is provided. For example, in nonlinear analysis, given the same mesh and load step size, mixed elements converge in fewer iterations than equivalent displacement-based models. It is also demonstrated that, in mixed formulations, lower order elements are preferred. Additionally, meshes used to obtain accurate linear solutions do not necessarily converge to the correct nonlinear solution. Finally, a new form of locking was identified associated with employing elements designed for biaxial bending in uniaxial bending applications.

Graf, Wiley E.↗
DOE OSTI2023

On unifying randomized methods for inverse problems

This work unifies the analysis of various randomized methods for solving linear and nonlinear inverse problems with Gaussian priors by framing the problem in a stochastic optimization setting. By doing so, we show that many randomized methods are variants of a sample average approximation (SAA). More importantly, we are able to prove a single theoretical result that guarantees the asymptotic convergence for a variety of randomized methods. Additionally, viewing randomized methods as an SAA enables us to prove, for the first time, a single non-asymptotic error result that holds for randomized methods under consideration. Another important consequence of our unified framework is that it allows us to discover new randomization methods. Here, we present various numerical results for linear, nonlinear, algebraic, and PDE-constrained inverse problems that verify the theoretical convergence results and provide a discussion on the apparently different convergence rates and the behavior for various randomized methods.

42 ENGINEERING↗
NASA NTRS2004

A Study of Penalty Function Methods for Constraint Handling with Genetic Algorithm

COMETBOARDS (Comparative Evaluation Testbed of Optimization and Analysis Routines for Design of Structures) is a design optimization test bed that can evaluate the performance of several different optimization algorithms. A few of these optimization algorithms are the sequence of unconstrained minimization techniques (SUMT), sequential linear programming (SLP) and the sequential quadratic programming techniques (SQP). A genetic algorithm (GA) is a search technique that is based on the principles of natural selection or "survival of the fittest". Instead of using gradient information, the GA uses the objective function directly in the search. The GA searches the solution space by maintaining a population of potential solutions. Then, using evolving operations such as recombination, mutation and selection, the GA creates successive generations of solutions that will evolve and take on the positive characteristics of their parents and thus gradually approach optimal or near-optimal solutions. By using the objective function directly in the search, genetic algorithms can be effectively applied in non-convex, highly nonlinear, complex problems. The genetic algorithm is not guaranteed to find the global optimum, but it is less likely to get trapped at a local optimum than traditional gradient-based search methods when the objective function is not smooth and generally well behaved. The purpose of this research is to assist in the integration of genetic algorithm (GA) into COMETBOARDS. COMETBOARDS cast the design of structures as a constrained nonlinear optimization problem. One method used to solve constrained optimization problem with a GA to convert the constrained optimization problem into an unconstrained optimization problem by developing a penalty function that penalizes infeasible solutions. There have been several suggested penalty function in the literature each with there own strengths and weaknesses. A statistical analysis of some suggested penalty functions is performed in this study. Also, a response surface approach to robust design is used to develop a new penalty function approach. This new penalty function approach is then compared with the other existing penalty functions.

Ortiz, Francisco↗
NASA NTRS1968

Solving nonlinear heat transfer constant area fin problems

Tables and graphs were compiled for solving nonlinear heat transfer constant area fin problems. The differential equation describing one-dimensional steady-state temperature distribution and heat flow under three modes of heat transfer with heat generation was investigated.

Source record↗
NASA NTRS1990

Discrete approximations to optimal trajectories using direct transcription and nonlinear programming

A recently developed method for solving optimal trajectory problems uses a piecewise-polynomial representation of the state and control variables, enforces the equations of motion via a collocation procedure, and thus approximates the original calculus-of-variations problem with a nonlinear-programming problem, which is solved numerically. This paper identifies this method as a direct transcription method and proceeds to investigate the relationship between the original optimal-control problem and the nonlinear-programming problem. The discretized adjoint equation of the collocation method is found to have deficient accuracy, and an alternate scheme which discretizes the equations of motion using an explicit Runge-Kutta parallel-shooting approach is developed. Both methods are applied to finite-thrust spacecraft trajectory problems, including a low-thrust escape spiral, a three-burn rendezvous, and a low-thrust transfer to the moon.

Enright, Paul J.↗
DOE OSTI2020

A Nonlinear Regression Method for Composite Protection Modeling of Induction Motor Loads

Protection equipment are used to prevent damages to induction motor loads by isolating those from the power network in the event of severe faults. Modeling the response of induction motor loads and their protection is vital for power system planning and operation, especially in understanding system's response moments after a fault has occurred. This article proposes an optimization based framework to generate composite protection models for commercial building motor loads. Introducing a mathematical abstraction, the task of finding a suitable (simplified) model of the composite protection scheme is formulated as a nonlinear regression problem. Numerical examples are provided to illustrate the application of the framework.

Kundu, Soumya↗
NASA NTRS1989

Assessment of structural analysis technology for elastic shell collapse problems

The prediction of the ultimate load carrying capability for compressively loaded shell structures is a challenging nonlinear analysis problem. Selected areas of finite element technology research and nonlinear solution technology are assessed. Herein, a finite element analysis procedure is applied to four shell collapse problems which have been used by computational structural mechanics researchers in the past. This assessment will focus on a number of different shell element formulations and on different approaches used to account for geometric nonlinearities. The results presented confirm that these aspects of nonlinear shell analysis can have a significant effect on the predicted nonlinear structural response. All analyses were performed using the CSM Testbed software system which allowed a convenient assessment of different element formulations with a consistent approach to solving the discretized nonlinear equations.

Knight, N. F., Jr.↗
NASA NTRS1980

Hybrid-finite-element analysis of some nonlinear and 3-dimensional problems of engineering fracture mechanics

In this paper, efficient numerical methods for the analysis of crack-closure effects on fatigue-crack-growth-rates, in plane stress situations, and for the solution of stress-intensity factors for arbitrary shaped surface flaws in pressure vessels, are presented. For the former problem, an elastic-plastic finite element procedure valid for the case of finite deformation gradients is developed and crack growth is simulated by the translation of near-crack-tip elements with embedded plastic singularities. For the latter problem, an embedded-elastic-singularity hybrid finite element method, which leads to a direct evaluation of K-factors, is employed.

Atluri, S. N.↗
NASA NTRS1987

Acoustic gravity waves: A computational approach

This paper discusses numerical solutions of a hyperbolic initial boundary value problem that arises from acoustic wave propagation in the atmosphere. Field equations are derived from the atmospheric fluid flow governed by the Euler equations. The resulting original problem is nonlinear. A first order linearized version of the problem is used for computational purposes. The main difficulty in the problem as with any open boundary problem is in obtaining stable boundary conditions. Approximate boundary conditions are derived and shown to be stable. Numerical results are presented to verify the effectiveness of these boundary conditions.

Hariharan, S. I.↗
NASA NTRS1988

Acoustic gravity waves - A computational approach

This paper discusses numerical solutions of a hyperbolic initial boundary value problem that arises from acoustic wave propagation in the atmosphere. Field equations are derived from the atmospheric fluid flow governed by the Euler equations. The resulting original problem is nonlinear. A first order linearized version of the problem is used for computational purposes. The main difficulty in the problem as with any open boundary problem is in obtaining stable boundary conditions. Approximate boundary conditions are derived and shown to be stable. Numerical results are presented to verify the effectiveness of these boundary conditions.

Hariharan, S. I.↗
NASA NTRS1993

A global approach to kinematic path planning to robots with holonomic and nonholonomic constraints

Robots in applications may be subject to holonomic or nonholonomic constraints. Examples of holonomic constraints include a manipulator constrained through the contact with the environment, e.g., inserting a part, turning a crank, etc., and multiple manipulators constrained through a common payload. Examples of nonholonomic constraints include no-slip constraints on mobile robot wheels, local normal rotation constraints for soft finger and rolling contacts in grasping, and conservation of angular momentum of in-orbit space robots. The above examples all involve equality constraints; in applications, there are usually additional inequality constraints such as robot joint limits, self collision and environment collision avoidance constraints, steering angle constraints in mobile robots, etc. The problem of finding a kinematically feasible path that satisfies a given set of holonomic and nonholonomic constraints, of both equality and inequality types is addressed. The path planning problem is first posed as a finite time nonlinear control problem. This problem is subsequently transformed to a static root finding problem in an augmented space which can then be iteratively solved. The algorithm has shown promising results in planning feasible paths for redundant arms satisfying Cartesian path following and goal endpoint specifications, and mobile vehicles with multiple trailers. In contrast to local approaches, this algorithm is less prone to problems such as singularities and local minima.

Divelbiss, Adam↗
NASA NTRSDate not supplied

Analytical Partial Derivatives of the Q-Law Guidance Algorithm

One method of producing low-thrust trajectories is the closed-loop Q-Law guidance algorithm. This work wraps Q-Law inside a nonlinear programming problem to search for locally optimal gain combinations and enforce nonlinear constraints on the initial state. Gradient-based trajectory optimization has been shown to benefit greatly when analytical partial derivatives are supplied to the optimizer. This paper presents the Q-Law optimization problem setup and derives the Q-Law thrust vector partial derivatives for the State Transition Matrix required by standard nonlinear optimization software.

Jackson L Shannon↗