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At least 73 records · Page 4

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NASA NTRS1990

Application of optimization methods to helicopter rotor blade design

A procedure for the minimum weight design of helicopter rotor blades with constraints on multiple coupled flap-lag natural frequencies, autorotational inertia, and centrifugal stress is presented. Optimum designs are obtained for blades with both rectangular and tapered planforms and are compared within a reference blade. The effects of higher-frequency constraints and stress constraints on the optimum blade designs are assessed. The results indicate that there is an increase in blade weight and a significant change in the design variable distributions with an increase in the number of frequency constraints. The inclusion of stress constraints has different effects on the wall thickness distributions of rectangular and tapered blades, but tends to increase the magnitude of the nonstructural segment weight distributions for both blade types.

Chattopadhyay, A.↗

DOE OSTI2021

Imposing equilibrium on experimental 3-D stress fields using Hodge decomposition and FFT-based optimization

Here, we present a methodology to impose micromechanical constraints, i.e. stress equilibrium at grain and sub-grain scale, to an arbitrary (non-equilibrated) voxelized stress field obtained, for example, by means of synchrotron X-ray diffraction techniques. The method consists in finding the equilibrated stress field closest (in L 2 -norm sense) to the measured non-equilibrated stress field, via the solution of an optimization problem. The extraction of the divergence-free (equilibrated) part of a general (non-equilibrated) field is performed using the Hodge decomposition of a symmetric matrix field, which is the generalization of the Helmholtz decomposition of a vector field into the sum of an irrotational field and a solenoidal field. The combination of: a) the Euler–Lagrange equations that solve the optimization problem, and b) the Hodge decomposition, gives a differential expression that contains the bi-harmonic operator and two times the curl operator acting on the experimental stress field. These high-order derivatives can be efficiently performed in Fourier space. The method is applied to filter the non-equilibrated parts of a synthetic piecewise constant stress fields with a known ground truth, and stress fields in Gum Metal, a beta-Ti-based alloy measured in-situ using Diffraction Contrast Tomography (DCT). In both cases, the largest corrections were obtained near grain boundaries.

36 MATERIALS SCIENCE↗

NASA NTRS1977

Inclusion of explicit thermal requirements in optimum structural design

A finite-element based procedure is described for obtaining minimum mass designs of structures subjected to combined thermal and mechanical loading and both strength and thermal constraints. The procedure is based on a mathematical programming method using the Sequence of Unconstrained Minimizations Technique (SUMT) in which design requirements are incorporated by an exterior penalty function. The procedure is limited to steady-state temperatures which are controlled by structural sizing only. The optimization procedure is demonstrated by the design of a structural wing box with both mechanical loading and external heating, subject to design constraints on stress, minimum gage, and temperature. The final design for these conditions is compared with a corresponding design in which temperature constraints are omitted.

Adelman, H. M.↗

NASA NTRS1985

Large scale structural synthesis

A general purpose optimization program is coupled to a large scale finite element program to provide an efficient tool for structural synthesis. The resulting interface program may be used to design structures for minimum weight, subject to constraints on stress, displacement, and vibration frequencies. A variety of state-of-the-art techniques are employed, including design variable linking, constraint deletion, reciprocal variables, and formal approximations. The capability is demonstrated with the design of a gear housing using 30 design variables and over 5000 nonlinear inequality constraints. The finite element model consists of over 1600 elements and 7000 displacement degrees of freedom. The design required six detailed finite element analyses and approximately one hour on a Cray-1s supercomputer. It is concluded that structures of practical size and complexity can be efficiently designed using numerical optimization.

Vanderplaats, G. N.↗

NASA NTRS1993

Merits and limitations of optimality criteria method for structural optimization

The merits and limitations of the optimality criteria (OC) method for the minimum weight design of structures subjected to multiple load conditions under stress, displacement, and frequency constraints were investigated by examining several numerical examples. The examples were solved utilizing the Optimality Criteria Design Code that was developed for this purpose at NASA Lewis Research Center. This OC code incorporates OC methods available in the literature with generalizations for stress constraints, fully utilized design concepts, and hybrid methods that combine both techniques. Salient features of the code include multiple choices for Lagrange multiplier and design variable update methods, design strategies for several constraint types, variable linking, displacement and integrated force method analyzers, and analytical and numerical sensitivities. The performance of the OC method, on the basis of the examples solved, was found to be satisfactory for problems with few active constraints or with small numbers of design variables. For problems with large numbers of behavior constraints and design variables, the OC method appears to follow a subset of active constraints that can result in a heavier design. The computational efficiency of OC methods appears to be similar to some mathematical programming techniques.

Patnaik, Surya N.↗

DOE OSTI2020

Shear Thickening and Jamming of Dense Suspensions: The "Roll" of Friction.

Particle-based simulations of discontinuous shear thickening (DST) and shear jamming (SJ) suspensions are used to study the role of stress-activated constraints, with an emphasis on resistance to gearlike rolling. Rolling friction decreases the volume fraction required for DST and SJ, in quantitative agreement with real-life suspensions with adhesive surface chemistries and "rough" particle shapes. It sets a distinct structure of the frictional force network compared to only sliding friction, and from a dynamical perspective leads to an increase in the velocity correlation length, in part responsible for the increased viscosity. The physics of rolling friction is thus a key element in achieving a comprehensive understanding of strongly shear-thickening materials.

Singh, Abhinendra↗

NASA NTRS1972

Minimum weight design of structures via optimality criteria

The state of the art of automated structural design through the use of optimality criteria, with emphasis on aerospace applications is reviewed. Constraints on stresses, displacements, and buckling strengths under static loading, as well as lower bound limits on natural frequencies and flutter speeds are presented. It is presumed that the reader is experienced in finite element methods of analysis, but is not familiar with optimal design techniques.

Kiusalaas, J.↗

NASA NTRS2001

A Review of the CTOA/CTOD Fracture Criterion: Why it Works

The CTOA/CTOD fracture criterion is one of the oldest fracture criteria applied to fracture of metallic materials with cracks. During the past two decades, the use of elastic-plastic finite-element analyses to simulate fracture of laboratory specimens and structural components using the CTOA criterion has expanded rapidly. But the early applications were restricted to two-dimensional analyses, assuming either plane-stress or plane-strain behavior, which lead to generally non-constant values of CTOA, especially in the early stages crack extension. Later, the non-constant CTOA values were traced to inappropriate state-of-stress (or constraint) assumptions in the crack-front region and severe crack tunneling in thin-sheet materials. More recently, the CTOA fracture criterion has been used with three-dimensional analyses to study constraint effects, crack tunneling, and the fracture process. The constant CTOA criterion (from crack initiation to failure) has been successfully applied to numerous structural applications, such as aircraft fuselages and pipelines. But why does the "constant CTOA" fracture criterion work so well? This paper reviews the results from several studies, discusses the issues of why CTOA works, and discusses its limitations.

Newman, J. C., Jr.↗

NASA NTRS2011

A New Aerodynamic Data Dispersion Method for Launch Vehicle Design

A novel method for implementing aerodynamic data dispersion analysis is herein introduced. A general mathematical approach combined with physical modeling tailored to the aerodynamic quantity of interest enables the generation of more realistically relevant dispersed data and, in turn, more reasonable flight simulation results. The method simultaneously allows for the aerodynamic quantities and their derivatives to be dispersed given a set of non-arbitrary constraints, which stresses the controls model in more ways than with the traditional bias up or down of the nominal data within the uncertainty bounds. The adoption and implementation of this new method within the NASA Ares I Crew Launch Vehicle Project has resulted in significant increases in predicted roll control authority, and lowered the induced risks for flight test operations. One direct impact on launch vehicles is a reduced size for auxiliary control systems, and the possibility of an increased payload. This technique has the potential of being applied to problems in multiple areas where nominal data together with uncertainties are used to produce simulations using Monte Carlo type random sampling methods. It is recommended that a tailored physics-based dispersion model be delivered with any aerodynamic product that includes nominal data and uncertainties, in order to make flight simulations more realistic and allow for leaner spacecraft designs.

Pinier, Jeremy T.↗

NASA NTRS1992

Truss topology optimization with simultaneous analysis and design

Strategies for topology optimization of trusses for minimum weight subject to stress and displacement constraints by Simultaneous Analysis and Design (SAND) are considered. The ground structure approach is used. A penalty function formulation of SAND is compared with an augmented Lagrangian formulation. The efficiency of SAND in handling combinations of general constraints is tested. A strategy for obtaining an optimal topology by minimizing the compliance of the truss is compared with a direct weight minimization solution to satisfy stress and displacement constraints. It is shown that for some problems, starting from the ground structure and using SAND is better than starting from a minimum compliance topology design and optimizing only the cross sections for minimum weight under stress and displacement constraints. A member elimination strategy to save CPU time is discussed.

Sankaranarayanan, S.↗

NASA NTRS2019

Level Set Topology Optimization of Load Carrying Heat Dissipation Devices

In this paper, we introduce a level set method topology optimization method of structures subjected to coupled mechanical and thermal loads. Different examples considering compliance minimization and stress minimization under temperature and volume constraints, and mass minimization under stress and temperature constraints, are presented. The p-norm of the stress field and temperature field is used to approximate the maximum stress and temperature, respectively. The developed method is applied in the design of an L-bracket and a battery package. The results show that designs obtained by ignoring the thermal or structural constraints can result in high values of temperature or stress, respectively.

Kambampati, Sandilya↗

NASA NTRS1993

Three-dimensional elastic-plastic finite-element analyses of constraint variations in cracked bodies

Three-dimensional elastic-plastic (small-strain) finite-element analyses were used to study the stresses, deformations, and constraint variations around a straight-through crack in finite-thickness plates for an elastic-perfectly plastic material under monotonic and cyclic loading. Middle-crack tension specimens were analyzed for thicknesses ranging from 1.25 to 20 mm with various crack lengths. Three local constraint parameters, related to the normal, tangential, and hydrostatic stresses, showed similar variations along the crack front for a given thickness and applied stress level. Numerical analyses indicated that cyclic stress history and crack growth reduced the local constraint parameters in the interior of a plate, especially at high applied stress levels. A global constraint factor alpha(sub g) was defined to simulate three-dimensional effects in two-dimensional crack analyses. The global constraint factor was calculated as an average through-the-thickness value over the crack-front plastic region. Values of alpha(sub g) were found to be nearly independent of crack length and were related to the stress-intensity factor for a given thickness.

Newman, J. C., Jr.↗

NASA NTRS1999

Analyses of Fatigue Crack Growth and Closure Near Threshold Conditions for Large-Crack Behavior

A plasticity-induced crack-closure model was used to study fatigue crack growth and closure in thin 2024-T3 aluminum alloy under constant-R and constant-K(sub max) threshold testing procedures. Two methods of calculating crack-opening stresses were compared. One method was based on a contact-K analyses and the other on crack-opening-displacement (COD) analyses. These methods gave nearly identical results under constant-amplitude loading, but under threshold simulations the contact-K analyses gave lower opening stresses than the contact COD method. Crack-growth predictions tend to support the use of contact-K analyses. Crack-growth simulations showed that remote closure can cause a rapid rise in opening stresses in the near threshold regime for low-constraint and high applied stress levels. Under low applied stress levels and high constraint, a rise in opening stresses was not observed near threshold conditions. But crack-tip-opening displacement (CTOD) were of the order of measured oxide thicknesses in the 2024 alloy under constant-R simulations. In contrast, under constant-K(sub max) testing the CTOD near threshold conditions were an order-of-magnitude larger than measured oxide thicknesses. Residual-plastic deformations under both constant-R and constant-K(sub max) threshold simulations were several times larger than the expected oxide thicknesses. Thus, residual-plastic deformations, in addition to oxide and roughness, play an integral part in threshold development.

Newman, J. C., Jr.↗

NASA NTRS1976

Optimization of multi-constrained structures based on optimality criteria

A weight-reduction algorithm is developed for the optimal design of structures subject to several multibehavioral inequality constraints. The structural weight is considered to depend linearly on the design variables. The algorithm incorporates a simple recursion formula derived from the Kuhn-Tucker necessary conditions for optimality, associated with a procedure to delete nonactive constraints based on the Gauss-Seidel iterative method for linear systems. A number of example problems is studied, including typical truss structures and simplified wings subject to static loads and with constraints imposed on stresses and displacements. For one of the latter structures, constraints on the fundamental natural frequency and flutter speed are also imposed. The results obtained show that the method is fast, efficient, and general when compared to other competing techniques. Extensions to the generality of the method to include equality constraints and nonlinear merit functions is discussed.

Rizzi, P.↗

NASA NTRS1999

Sensitivity of Lumped Constraints Using the Adjoint Method

Adjoint sensitivity calculation of stress, buckling and displacement constraints may be much less expensive than direct sensitivity calculation when the number of load cases is large. Adjoint stress and displacement sensitivities are available in the literature. Expressions for local buckling sensitivity of isotropic plate elements are derived in this study. Computational efficiency of the adjoint method is sensitive to the number of constraints and, therefore, the method benefits from constraint lumping. A continuum version of the Kreisselmeier-Steinhauser (KS) function is chosen to lump constraints. The adjoint and direct methods are compared for three examples: a truss structure, a simple HSCT wing model, and a large HSCT model. These sensitivity derivatives are then used in optimization.

Akgun, Mehmet A.↗

NASA NTRS1990

Weight minimization of a support structure

This paper addresses the weight minimization of a circular plate-like structure which resulted in a 26 percent weight reduction. The optimization was performed numerically with the COPES/ADS program using the modified method of feasible directions. Design parameters were the inner thickness and outer thickness of the plate with constraints on maximum yield stress and maximum transverse displacement. Also, constraints were specified for the upper and lower bounds of the fundamental frequency and plate thicknesses. The MSC/NASTRAN finite element program was used for the evaluation of response variables. Original and final designs of the plate were tested using an Instron tension-compression machine to compare finite element results to measured strain data. The difference between finite element strain components and measured strain data was within engineering accuracy.

Kluberdanz, Donald J.↗

DOE OSTI2022

Stress-constrained topology optimization of lattice-like structures using component-wise reduced order models

We report lattice-like structures can provide a combination of high stiffness with light weight that is useful in many applications, but a resolved finite element mesh of such structures results in a computationally expensive discretization. This computational expense may be particularly burdensome in many-query applications, such as optimization. We develop a stress-constrained topology optimization method for lattice-like structures that uses component-wise reduced order models as a cheap surrogate, providing accurate computation of stress fields while greatly reducing run time relative to a full order model. We demonstrate the ability of our method to produce large reductions in mass while respecting a constraint on the maximum stress in a pair of test problems. The ROM methodology provides a speedup of about 150x in forward solves compared to full order static condensation and provides a relative error of less than 5% in the relaxed stress.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

On the flow-stress model of Preston, Tonks, and Wallace - Observations, parameter constraints, and implementations (Rev. 1)

A detailed discussion about the PTW flow-stress model has been presented, including theoretical considerations, model calibrations to experimental data, and model implementations in LANL ASC hydro-codes. The main findings are: In order to reproduce the intended behavior of the PTW model at high strain rates, the following conditions on the model parameters need to be valid: y 1 ≥ s 0 and y 2 ≥ β ; When the conditions above are not satisfied, PTW and PTW_Mod1 have slightly different behavior in the phonon-drag regime, and should be treated as different models. PTW exhibits a discontinuity above the critical strain rate. PTW_Mod1 does not show such a discontinuity but implies a different strain-rate dependence at high strain rates. Examples of this behavior include older calibrations for stainless steel and depleted uranium; In the thermal-activation regime, some flexibility was introduced in the original PTW model to allow for different rate-dependent behaviors at intermediate strain rates. Example: copper. However, many material calibrations do not require this extra flexibility, and the complexity and ambiguity of the intended behavior can be partially blamed for the inconsistent model implementations across ASC codes; The limit for the material constant p going to zero is well defined and leads to a simplified flow-stress equation, discontinuity free; Modern calibrations of the PTW parameters are done using Impala. Constraints on the PTW parameters are enforced; Implementation of the PTW model in LANL ASC hydro-codes suffered of several shortcom ings. At the time of writing, FLAG and xRAGE contain consistent and correct implemen tations of the PTW and PTW_Mod1 models. Corresponding changes to Pagosa have been suggested.

36 MATERIALS SCIENCE↗