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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 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Chain rigidity controlled aggregation ability and solid-state microstructures for efficient stretchable conjugated polymer films

Stretchable conjugated polymer films with good electrical performance under mechanical deformation are highly desirable for soft electronics. However, the mechanical and electrical properties of these films, particularly in conjugated polymer:elastomer blends, are not fully understood at molecular level. Here, this study explores the relationships among molecular structure, aggregation ability, film microstructure, and the electrical/mechanical properties of three diketopyrrolopyrrole-based conjugated polymers (P1, P2, P3) with decreasing backbone rigidity and their corresponding polymer:elastomer blends. The most flexible polymer P3 shows strong aggregation, which forms highly crystalline fibers to produce fragile neat film and produces large isolated crystallites restricting charge transport in blend film. As chain rigidity increases, the P1 and P2 polymers show weaker aggregation, and produce smaller crystallites in neat films with enhanced ductility. P1 and P2 based blend films display nanocrystallites polymer networks with dispersed elastomer domains. As a result, we achieved near-constant charge mobility before and after stretching under 50 % strain for P2-based blend films with well-controlled pathways for both charge transport and energy dissipation. This study demonstrates the critical role of backbone rigidity in regulating the properties of stretchable conjugated polymer films, paving the way for more reliable and deformable materials in soft electronics.

36 MATERIALS SCIENCE↗
NASA NTRS1993

Parallel O(log n) algorithms for open- and closed-chain rigid multibody systems based on a new mass matrix factorization technique

In this paper, parallel O(log n) algorithms for computation of rigid multibody dynamics are developed. These parallel algorithms are derived by parallelization of new O(n) algorithms for the problem. The underlying feature of these O(n) algorithms is a drastically different strategy for decomposition of interbody force which leads to a new factorization of the mass matrix (M). Specifically, it is shown that a factorization of the inverse of the mass matrix in the form of the Schur Complement is derived as M(exp -1) = C - B(exp *)A(exp -1)B, wherein matrices C, A, and B are block tridiagonal matrices. The new O(n) algorithm is then derived as a recursive implementation of this factorization of M(exp -1). For the closed-chain systems, similar factorizations and O(n) algorithms for computation of Operational Space Mass Matrix lambda and its inverse lambda(exp -1) are also derived. It is shown that these O(n) algorithms are strictly parallel, that is, they are less efficient than other algorithms for serial computation of the problem. But, to our knowledge, they are the only known algorithms that can be parallelized and that lead to both time- and processor-optimal parallel algorithms for the problem, i.e., parallel O(log n) algorithms with O(n) processors. The developed parallel algorithms, in addition to their theoretical significance, are also practical from an implementation point of view due to their simple architectural requirements.

Fijany, Amir↗
NASA NTRS1989

A unifying framework for rigid multibody dynamics and serial and parallel computational issues

A unifying framework for various formulations of the dynamics of open-chain rigid multibody systems is discussed. Their suitability for serial and parallel processing is assessed. The framework is based on the derivation of intrinsic, i.e., coordinate-free, equations of the algorithms which provides a suitable abstraction and permits a distinction to be made between the computational redundancy in the intrinsic and extrinsic equations. A set of spatial notation is used which allows the derivation of the various algorithms in a common setting and thus clarifies the relationships among them. The three classes of algorithms viz., O(n), O(n exp 2) and O(n exp 3) or the solution of the dynamics problem are investigated. Researchers begin with the derivation of O(n exp 3) algorithms based on the explicit computation of the mass matrix and it provides insight into the underlying basis of the O(n) algorithms. From a computational perspective, the optimal choice of a coordinate frame for the projection of the intrinsic equations is discussed and the serial computational complexity of the different algorithms is evaluated. The three classes of algorithms are also analyzed for suitability for parallel processing. It is shown that the problem belongs to the class of N C and the time and processor bounds are of O(log2/2(n)) and O(n exp 4), respectively. However, the algorithm that achieves the above bounds is not stable. Researchers show that the fastest stable parallel algorithm achieves a computational complexity of O(n) with O(n exp 4), respectively. However, the algorithm that achieves the above bounds is not stable. Researchers show that the fastest stable parallel algorithm achieves a computational complexity of O(n) with O(n exp 2) processors, and results from the parallelization of the O(n exp 3) serial algorithm.

Fijany, Amir↗
DOE OSTI2026

Influence of Rigidity–Hydration Coupling on Size-Dependent Diffusion in Hydrated Polymer Membranes

Selective ion transport in polymer membranes depends critically on how penetrant motion couples to polymer dynamics and hydration. Yet, the mechanistic interplay between polymer rigidity, water content, and penetrant size remains poorly understood, especially in the regime where the penetrant diameter, polymer Kuhn length, and correlation length are comparable. Here, we employ coarse-grained molecular dynamics simulations to systematically investigate penetrant diffusion in hydrated polymer networks across a broad range of water volume fractions, chain rigidities, and penetrant sizes. The results reveal a transition from a decoupled regime, where small penetrants diffuse nearly independently of polymer relaxation, to a coupled regime in which large penetrants require cooperative polymer motion for transport. Increasing polymer rigidity amplifies the sensitivity of diffusivity to hydration, particularly at low water content, leading to pronounced deviations from Stokes−Einstein scaling. Comparison with scaling theories and free-volume models shows that classical nanoparticle-based frameworks fail to capture this intermediate regime. To address this gap, we extend the Yasuda model to incorporate polymer rigidity through a single parameter that quantifies the dynamic contribution of chain stiffness to free-volume fluctuations. The resulting model collapses diffusivity data across all sizes, water contents, and rigidities, providing a unified description of penetrant transport in hydrated polymer matrices. Furthermore, these findings establish polymer rigidity as a key, tunable determinant of diffusion and offer a framework for interpreting size-dependent transport in ion-selective membranes.

diffusion↗
DOE OSTI2026

Computationally designed coiled coil ‘bundlemers’ as model colloidal nanoparticles for solution assembly and materials design (Final Report)

As a collaborative team at the University of Delaware and the University of Pennsylvania, Kloxin, Pochan and Saven designed new biomimetic nanomaterials de novo, leveraging a variety of complementary areas of expertise: computational design of biopolymers (Saven at the University of Pennsylvania), and synthesis and characterization (Kloxin and Pochan at the University of Delaware). Overall activities included: sequence-specific peptide synthesis; covalent crosslinking; noncovalent assembly; site-specific functionalization; and nanostructural characterization using electron microscopy and solution-phase (x-ray and neutron) scattering. Using natural and non-natural amino acids, the team created modular, functional peptide building blocks for elaboration of new nanostructured materials. Ultimately, the development of robust peptide-based, building blocks provides tools for researchers to readily produce complex nanomaterial structures in a wide range of applications. The project had three, interconnecting goals in an effort to provide the broader scientific community with a new peptide-based paradigm for materials design and characterization. First, we further developed the coiled-coil bundle-based toolbox (otherwise known as the ‘bundlemer’ toolbox) via computational design with experimental bundle assembly verification. Second, we developed new uses of covalent interactions, in addition to desired physical (noncovalent) interactions, to assemble bundlemers into 1-D polymer chains with targeted chain rigidity, length, and dispersity. Thirds, we used the above designs to experimentally realize (physical or covalent) polymers to target the creation of liquid crystals or to realize interparticle assembly into nanoporous lattices. The close integration of the three groups was instrumental in success of the biomolecular materials design, formation, and understanding for future designs.

36 MATERIALS SCIENCE↗
NASA NTRS1994

Negative birefringent polyimide films

A negative birefringent film, useful in liquid crystal displays, and a method for controlling the negative birefringence of a polyimide film is disclosed which allows the matching of an application to a targeted amount of birefringence by controlling the degree of in-plane orientation of the polyimide by the selection of functional groups within both the diamine and dianhydride segments of the polyimide which affect the polyimide backbone chain rigidity, linearity, and symmetry. The higher the rigidity, linearity and symmetry of the polyimide backbone, the larger the value of the negative birefringence of the polyimide film.

Harris, Frank W.↗
NASA NTRSDate not supplied

Physics and Modeling of Quasi-Steady and Forced Shock Trains

The dual-mode scramjet is a propulsive concept for contemporary hypersonic vehicles promising flight cruise speeds upwards of Mach 5. Despite decades of development and a recent resurgence in interest, such engines are not routinely deployed for commercial or military purposes. Instead, they have been confined to the realm of ground-test research and limited one-off flight test missions. One of the key stumbling blocks on the critical path to deployment of a dual-mode scramjet is the optimal design and stable operation of the isolator, a typically constant area duct that separates the scramjet inlet from the combustor. During ramjet mode at Mach numbers from 3 to 5 and during the transition to scramjet mode at higher Mach numbers, the isolator contains the pseudo-shock. Necessary to meet the back-pressure in the combustor, the pseudo-shock is typically divided into a shock dominated shock train region followed by a turbulence driven mixing region. Fluctuations in combustor pressure due to vehicle maneuvering, throttling, or combustion instabilities drive the shock train to shift streamwise within the isolator. In response to sharp pressure fluctuations, the shock train is unable to stabilize within the isolator, and the scramjet unstarts by ejecting the shock train out the inlet. This work addresses three key gaps in understanding of the isolator pseudo-shock. The phenomenon is studied in three experimental facilities to investigate the quasi-steady and unsteady fluid dynamics of the shock train in fueled and un-fueled test conditions. The strong link between boundary layer morphology and shock train structure is studied in detail and used as a tool to evaluate the state-of-the-art definitions and models of the pseudo-shock. Identifying the limitations of these models, a new process driven flux-conserved pseudo-shock model is proposed. This provides a computationally efficient model grounded in the fluid dynamic mechanisms of the pseudo-shock with better predictive capability than the current state-of-the-art across all facilities tested. The unsteady behavior of the shock train is further investigated to identify and understand two distinct forced dynamic modes: mechanically induced, low-rate forcing and high-rate combustion driven unsteadiness that sheds upstream propagating shocks. The proposed process driven model is found to be effective in the the limiting case of high-rate combustion driven unsteadiness by evaluating the model in a shock stationary reference frame. Further analysis identifies the approximately rigid chain motion of the shock train structure to mechanically induced forcing. The time delay between the onset of forced dynamics is found to saturate to a constant value and maximum shock train speed along the isolator with respect to the perturbation rate of change. The result of this work provides dual-mode scramjet designers with improved tools and physical understanding to develop more efficient, robust, and capable propulsion systems for hypersonic vehicles.

JAXA↗
NASA NTRS1989

Recursive multibody dynamics and discrete-time optimal control

A recursive algorithm is developed for the solution of the simulation dynamics problem for a chain of rigid bodies. Arbitrary joint constraints are permitted, that is, joints may allow translational and/or rotational degrees of freedom. The recursive procedure is shown to be identical to that encountered in a discrete-time optimal control problem. For each relevant quantity in the multibody dynamics problem, there exists an analog in the context of optimal control. The performance index that is minimized in the control problem is identified as Gibbs' function for the chain of bodies.

Deleuterio, G. M. T.↗
NASA NTRS1989

Simulation of spacecraft attitude dynamics using TREETOPS and model-specific computer Codes

The simulation of spacecraft attitude dynamics and control using the generic, multi-body code called TREETOPS and other codes written especially to simulate particular systems is discussed. Differences in the methods used to derive equations of motion--Kane's method for TREETOPS and the Lagrangian and Newton-Euler methods, respectively, for the other two codes--are considered. Simulation results from the TREETOPS code are compared with those from the other two codes for two example systems. One system is a chain of rigid bodies; the other consists of two rigid bodies attached to a flexible base body. Since the computer codes were developed independently, consistent results serve as a verification of the correctness of all the programs. Differences in the results are discussed. Results for the two-rigid-body, one-flexible-body system are useful also as information on multi-body, flexible, pointing payload dynamics.

Cochran, John E.↗
NASA NTRS1999

Dynamics of Single Chains of Suspended Ferrofluid Particles

We present an experimental study of the dynamics of isolated chains made of super-paramagnetic particles under the influence of a magnetic field. The motivation of this work is to understand if the chain fluctuations exist and, if it does, how does the fluctuation affect chain aggregation. We find that single chains strongly fluctuate and that the characteristic frequency of their fluctuations is inversely proportional to the magnetic field strength. The higher the field the lower the characteristic frequency of the chain fluctuations. In the high magnetic field limit, chains behave like rigid rods without any internal motions. In this work, we used ferrofluid particles suspended in water. These particles do not have any intrinsic magnetization. Once a magnetic field is applied, a dipole moment is induced in each particle, proportional to the magnetic field. A dipolar magnetic interaction then occurs between particles. If dipole-dipole magnetic energy is higher than the thermal energy, the result is a structure change inside the dipolar fluid. The ratio of these two energies is expressed by a coupling constant lambda as: lambda = (pi(a(exp 3))(chi(exp 2))(mu(sub 0))(H(sub 0))(exp 2))/18kT Where a is the particle radius, mu(sub 0) is the vacuum magnetic permeability, H(sub 0) the applied magnetic field, k the Boltzmann constant and T the absolute temperature. If lambda > 1, magnetic particles form chains along the field direction. The lateral coalescence of several chains may form bigger aggregates especially if the particle volume fraction is high. While many studies and applications deal with the rheological properties and the structural changes of these dipolar fluids, this work focuses on the understanding of the chain dynamics. In order to probe the chain dynamics, we used dynamic light scattering (DLS) in self-beating mode as our experimental technique. The experimental geometry is such that the scattering plane is perpendicular to the magnetic field. Therefore, only motions in this plane are probed. A very dilute sample of a ferrofluid emulsion with a particle volume fraction of 10(exp -5) is used in this experiment. We chose such a low volume fraction to avoid multiple light scattering as well as lateral chain-chain aggregation. DLS measures the dynamic structure factor S(q,t) of the sample (q is the scattering wave vector, t is the time). In the absence of the magnetic field, identical particles of ferrofluid droplets are randomly distributed and S(q,t) reduces to exp(-q(exp 2)2D(sub 0)t). D(sub 0)=(kT/(6(pi)(eta)(a)) is the diffusion coefficient of Brownian particles (where Xi = (6(pi)(eta)(a)) is the Stokes frictional coefficient of a spherical particle in a fluid of viscosity eta). If interactions or polydispersity can not be ignored, an effective diffusion coefficient is introduced. Formally, D(sub eff) is defined as: D(sub eff) = - q(exp -2) partial derivative of (ln(S(q,t)) with respect to time, as t goes to 0. D(sub eff) reduces to D(sub 0) if no interactions and only a few particles size are present. Therefore, we can use DLS to measure particle size. The particle radius was found to be a=0.23 mu m with 7% of polydispersity. In this case, if we vary the scattering angle theta (and so q) we do not have any change in the measured diffusion coefficient: it is q-independent. When a magnetic field is applied, particles aggregate into chains if lambda > 1. We first studied the kinetics of the chain formation when lambda = 406. At a fixed scattering angle, we measured diffusion coefficient D(sub eff) as a function of time. Experimentally, we find that D(sub eff) decreases monotonously with time. Physically, this means that chains are becoming longer and longer. Since we are only sensitive to motions in the scattering plane and since chains have their main axis perpendicular to this plane, the measured diffusion coefficient is the trans-verse diffusion coefficient. We can relate D(sub eff) to the mean number of particles per chain N(t) at a given time and to the diffusion coefficient of an isolated particle D(sub 0) as D(sub eff)=f(N(t))D(sub 0). Since f(N) is known from other recent work, N can be expressed as a function of the time. We found a square root dependency: N(t) proportional to the square root of t. As expected for very low volume fraction, this behavior is characteristic of a diffusion-limited aggregation as suggested by several authors and by our previous work. In this study, we focus on the dependence of the effective diffusion coefficient on the scattering angle and the magnetic field strength. After the magnetic field is applied (lambda = 406) for a long time, typically 6 hours, kinetics of chain formation becomes very slow. Chain size does not vary much over the next hour period. Thus, we can perform different interesting experiments. First, at a fixed magnetic field, we measure the effective diffusion coefficient as a function of the scattering angle (from 5 to 130 deg). Our results show that the measured diffusion coefficient increases linearly with the scattering angle: D(sub eff) proportional to q. If we do the same experiment for different lambda values, D(sub eff) depends on lambda as D(sub eff) proportional to lambda(exp -1/2). We also find for different lambda values that the same asymptotic D(sub eff) value is obtained when q approaches zero. The angle dependency of D(sub eff) suggests that an additional motion exists besides chain drifting. Chain size is constant during experiment, which was verified by measuring the same diffusion coefficient at the beginning and at the end of the angle switching. If chains are rigid, D(sub eff) is independent of q. Therefore, we found that D(sub eff) not only measures the motion of the entire chain but also its internal fluctuations. These internal motions are the fluctuations of the particles in the chain. To understand the q dependency of D(sub eff), let us look at the probing length used. In our study, the characteristic length scale probed is l=2pi/q which is in the range of 0.9<l/a<20. When l is much larger than the particle radius (l/a going to infinity) we are mainly sensitive to the center of mass diffusion of the chain. D(sub eff) is then the diffusion of the entire chain and depends only on N but not on q and lambda. The value D(sub eff) allows us to obtain the number of particles per chain N. In the opposite limit (i.e. l/a < 1), we are sensitive to motions on the size of individual particles. The main contributions to the measured diffusion coefficient come from internal motions of the chains (i.e. particles' fluctuations inside the chain). We investigated also the effect of the chain size on D(sub eff). For the same value of the magnetic interaction lambda and different chain sizes, we found that the slope of D(sub eff) versus q decreases when N increases as a power law D(sub eff) proportional to N(exp -0.7). This is an important behavior because this means that the longer the chain the slower its internal fluctuations besides the whole chain motion.

Cutillas, S.↗
NASA NTRS2005

Momentum-Based Dynamics for Spacecraft with Chained Revolute Appendages

An efficient formulation is presented for a sub-class of multi-body dynamics problems that involve a six degree-of-freedom base body and a chain of N rigid linkages connected in series by single degree-of-freedom revolute joints. This general method is particularly well suited for simulations of spacecraft dynamics and control that include the modeling of an orbiting platform with or without internal degrees of freedom such as reaction wheels, dampers, and/or booms. In the present work, particular emphasis is placed on dynamic simulation of multi-linkage robotic manipulators. The differential equations of motion are explicitly given in terms of linear and angular momentum states, which can be evaluated recursively along a serial chain of linkages for an efficient real-time solution on par with the best of the O(N3) methods.

Queen, Steven↗
NASA NTRS2002

Rotationally Molded Liquid Crystalline Polymers

Rotational molding is a unique process for producing hollow plastic parts. Rotational molding offers advantages of low cost tooling and can produce very large parts with complicated shapes. Products made by rotational molding include water tanks with capacities up to 20,000 gallons, truck bed liners, playground equipment, air ducts, Nylon fuel tanks, pipes, toys, stretchers, kayaks, pallets, and many others. Thermotropic liquid crystalline polymers are an important class of engineering resins employed in a wide variety of applications. Thermotropic liquid crystalline polymers resins are composed of semi-rigid, nearly linear polymeric chains resulting in an ordered mesomorphic phase between the crystalline solid and the isotropic liquid. Ordering of the rigid rod-like polymers in the melt phase yields microfibrous, self-reinforcing polymer structures with outstanding mechanical and thermal properties. Rotational molding of liquid crystalline polymer resins results in high strength and high temperature hollow structures useful in a variety of applications. Various fillers and reinforcements can potentially be added to improve properties of the hollow structures. This paper focuses on the process and properties of rotationally molded liquid crystalline polymers.

Rogers, Martin↗
NASA NTRS1995

Resistance to Rolling in the Adhesive Contact of Two Elastic Spheres

For the stability of agglomerates of micron sized particles it is of considerable importance to study the effects of tangential forces on the contact of two particles. If the particles can slide or roll easily over each other, fractal structures of these agglomerates will not be stable. We use the description of contact forces by Johnson, Kendall and Roberts, along with arguments based on the atomic structure of the surfaces in contact, in order to calculate the resistance to rolling in such a contact. It is shown that the contact reacts elastically to torque forces up to a critical bending angle. Beyond that, irreversible rolling occurs. In the elastic regime, the moment opposing the attempt to roll is proportional to the bending angle and to the pull-off force P(sub c). Young's modulus of the involved materials has hardly any influence on the results. We show that agglomerates of sub-micron sized particles will in general be quite rigid and even long chains of particles cannot be bent easily. For very small particles, the contact will rather break than allow for rolling. We further discuss dynamic properties such as the possibility of vibrations in this degree of freedom and the typical amount of rolling during a collision of two particles.

Dominik, C.↗
NASA NTRS1995

Resistance to Rolling in the Adhesive Contact of Two Elastic Spheres

For the stability of agglomerates of micron sized particles it is of considerable importance to study the effects of tangential forces on the contact of two particles. If the particles can slide or roll easily over each other, fractal structures of these agglomerates will not be stable. We use the description of contact forces by Johnson, Kendall and Roberts, along with arguments based on the atomic structure of the surfaces in contact, in order to calculate the resistance to rolling in such a contact. It is shown that the contact reacts elastically to torque forces up to a critical bending angle. Beyond that, irreversible rolling occurs. In the elastic regime, the moment opposing the attempt to roll is proportional to the bending angle and to the pull-off force P(sub c). Young's modulus of the involved materials has hardly any influence on the results. We show that agglomerates of sub-micron sized particles will in general be quite rigid and even long chains of particles cannot be bent easily. For very small particles, the contact will rather break than allow for rolling. We further discuss dynamic properties such as the possibility of vibrations in this degree of freedom and the typical amount of rolling during a collision of two particles.

Dominik, C.↗
NASA NTRS1999

Chain Dynamics in Magnetorheological Suspensions

Magnetorheological (MR) suspensions are composed of colloidal particles which acquire dipole moments when subjected to an external magnetic field. At sufficient field strengths and concentrations, the dipolar particles rapidly aggregate to form long chains. Subsequent lateral cross-linking of the dipolar chains is responsible for a rapid liquid-to-solid-like rheological transition. The unique, magnetically-activated rheological properties of MR suspensions make them ideal for interfacing mechanical systems to electronic controls. Additionally, the ability to experimentally probe colloidal suspensions interacting through tunable anisotropic potentials is of fundamental interest. Our current experimental work has focused on understanding the fluctuations of dipolar chains. It has been proposed by Halsey and Toor (HT) that the strong Landau-Peierls thermal fluctuations of dipolar chains could be responsible for long-range attractions between chains. Such interactions will govern the long-time relaxation of MR suspensions. We have synthesized monodisperse neutrally buoyant MR suspensions by density matching stabilized ferrofluid emulsion droplets with D2O. This allows us to probe the dynamics of the dipolar chains using light scattering without gravitational, interfacial, and polydispersity effects to resolve the short-wavelength dynamics of the dipolar chains. We used diffusing wave spectroscopy to measure these dynamics. The particle displacements at short times that show an independence to the field strength, but at long times exhibit a constrained, sub-diffusive motion that slows as the dipole strength is increased. The experiments are in good qualitative agreement with Brownian dynamics simulations of dipolar chains. Although there have been several important and detailed studies of the structure and interactions in MR suspensions, there has not been conclusive evidence that supports or contradicts the HT model prediction that long-range interactions exist between fluctuating chains of dipolar particles. Resolving this issue would contribute greatly to the understanding of these interesting and important materials. We have begun to test the predictions of the HT model by both examining the dynamics of individual chains and by measuring the forces between dipolar chains directly to accurately and quantitatively assess the interactions that they experience. To do so, we employ optical trapping techniques and video-microscopy to manipulate and observe our samples on the microscopic level. With these techniques, it is possible to observe chains that are fluctuating freely in three-dimensions, independent of interfacial effects. More importantly, we are able to controllably observe the interactions of two chains at various separations to measure the force-distance profile. The techniques also allow us to study the mechanical properties of individual chains and chain clusters. Our work to this point has focused on reversibly-formed dipolar chains due to field induced dipoles where the combination of this chaining, the dipolar forces, and the hydrodynamic interactions that dictate the rheology of the suspensions. One can envision, however, many situations where optical, electronic, or rheological behavior may be optimized with magneto-responsive anisotropic particles. Chains of polarizable particles may have the best properties as they can coil and flex in the absence of a field and stiffen and orient when a field is applied. We have recently demonstrated a synthesis of stable, permanent paramagnetic chains by both covalently and physically linking paramagnetic colloidal particles. The method employed allows us to create monodisperse chains of controlled length. We observed the stability, field-alignment, and rigidity of this new class of materials. The chains may exhibit unique rheological properties in an applied magnetic field over isotropic suspensions of paramagnetic particles. They are also useful rheological models as bead-spring systems. These chains form the basis for our current experiments with optical traps.

Gast, A. P.↗
NASA NTRS1989

Nonlinear strain-displacement relations and flexible multibody dynamics

Dynamics of chains of flexible bodies undergoing large rigid body motions, but small elastic deflections are considered. The role of nonlinear strain-displacement relations in the development of the motion equations correct to first order in elastic deflections is investigated. The general form of these equations linearized only in the small elastic deflections is presented, and the relative significance of various nonlinear terms is studied both analytically and through the use of the numerical simulations. Numerical simulations are performed for a two link chain constrained to move in the plane, subject to hinge torques. Each link is modeled as a thin beam. Slew maneuver simulation results are compared for models with and without properly modeled kinematics of deformation. The goal of this case study is to quantify the importance of the terms in the equations of motion which arise from the inclusion of nonlinear strain-displacement relations. It is concluded that unless the consistently linearized equations in elastic deflections and speeds are available and necessary, the inconsistently (prematurely) linearized equations should be replaced in all cases by ruthlessly linearized equations: equations in which all nonlinear terms involving the elastic deflections and speeds are ignored.

Padilla, Carlos E.↗
NASA NTRS1993

Stress stiffening and approximate equations in flexible multibody dynamics

A useful model for open chains of flexible bodies undergoing large rigid body motions, but small elastic deformations, is one in which the equations of motion are linearized in the small elastic deformations and deformation rates. For slow rigid body motions, the correctly linearized, or consistent, set of equations can be compared to prematurely linearized, or inconsistent, equations and to 'oversimplified,' or ruthless, equations through the use of open loop dynamic simulations. It has been shown that the inconsistent model should never be used, while the ruthless model should be used whenever possible. The consistent and inconsistent models differ by stress stiffening terms. These are due to zeroth-order stresses effecting virtual work via nonlinear strain-displacement terms. In this paper we examine in detail the nature of these stress stiffening terms and conclude that they are significant only when the associated zeroth-order stresses approach 'buckling' stresses. Finally it is emphasized that when the stress stiffening terms are negligible the ruthlessly linearized equations should be used.

Padilla, Carlos E.↗