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A continuous beam model is developed for approximate analysis of a large, slender, beam-like truss. The model is incorporated in a multi-level optimization scheme for the weight minimization of such trusses. This scheme is tested against traditional optimization procedures for savings in computational cost. Results from both optimization methods are presented for comparison.
It is clear that computer software is needed to assist in the generation of the equations of motion for complex, flexible spacecraft. Daniel Poelaert of ESTEC has developed the software DISTEL with which he has modeled the structural dynamics for different satellites. He is interested in expanding the capabilities of DISTEL to include structural damping and control systems. Unfortunately, the software has not been released. The author has developed similar software, PDEMOD, which has been used to model the Spacecraft control Laboratory Experiment (SCOLE), the Solar Array Flight Experiment (SAFE), the Mini-MAST truss, and the LACE satellite. PDEMOD has been used also for optimal parameter estimation and integrated control-structures design. PDEMOD is also being extended to include structural damping and control systems which are imbedded into the same equations for the structural dynamics. This paper will address the formulation of the equations for the structural dynamics of spacecraft structures which are constructed of a 3-dimensional arrangement of rigid bodies and flexible beam elements. Control system dynamics are imbedded into the same equations so that model order reduction approximations are not necessary. The input data consists of the physical data of the elements and the topological information describing how the elements are connected. PDEMOD accomplishes the following: (1) automatically assembles the equations of motion for the entire structural model; (2) calculates the modal frequencies; (3) calculates the mode shapes; (4) generates perspective views of the mode shapes; and (5) forms selected transfer functions. The software PDEMOD continues to be developed to provide additional features to assist in analyzing and synthesizing control and structural systems for flexible spacecraft.
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The Space Shuttle External Tank is covered with rigid polymeric closed-cell foam insulation to prevent ice formation, protect the metallic tank from aerodynamic heating, and control the breakup of the tank during re-entry. The cryogenic state of the tank, as well as the ascent into a vacuum environment, places this foam under significant stress. Because the loss of the foam during ascent poses a critical risk to the shuttle orbiter, there is much interest in understanding the stress state in the foam insulation and how it may contribute to fracture and debris loss. Several foam applications on the external tank have been analyzed using finite element methods. This presentation describes the approach used to model the foam material behavior and compares analytical results to experiments.
This document is a viewgraph presentation reporting on work in modeling the foam insulation of the Space Shuttle External Tank. An analytical understanding of foam mechanics is required to design against structural failure. The Space Shuttle External Tank is covered primarily with closed cell foam to: Prevent ice, Protect structure from ascent aerodynamic and engine plume heating, and Delay break-up during re-entry. It is important that the foam does not shed unacceptable debris during ascent environment. Therefore a modeling of the foam insulation was undertaken.
The behavior of arrays of coupled oscillators has been previously studied by computatinal solution of a set of non-linear differential equations describing the time dependence of each oscillator in the presence of signals coupled from neighboring oscillators.
A multiscale modeling methodology that combines the predictive capability of discrete dislocation plasticity and the computational efficiency of continuum crystal plasticity is developed. Single crystal configurations of different grain sizes modeled with periodic boundary conditions are analyzed using discrete dislocation plasticity (DD) to obtain grain size-dependent stress-strain predictions. These relationships are mapped into crystal plasticity parameters to develop a multiscale DD/CP model for continuum level simulations. A polycrystal model of a structurally-graded microstructure is developed, analyzed and used as a benchmark for comparison between the multiscale DD/CP model and the DD predictions. The multiscale DD/CP model follows the DD predictions closely up to an initial peak stress and then follows a strain hardening path that is parallel but somewhat offset from the DD predictions. The difference is believed to be from a combination of the strain rate in the DD simulation and the inability of the DD/CP model to represent non-monotonic material response.
A continuum model for the SCOLE configuration has been derived using transfer matrices. Controller designs for distributed parameter systems have been analyzed. Pole-assignment controller design is considered easy to implement but stability is not guaranteed. An explicit transfer function of dynamic controllers has been obtained and no model reduction is required before the controller is realized. One specific LQG controller for continuum models had been derived, but other optimal controllers for more general performances need to be studied.
Continuum Damage Mechanics (CDM) based progressive damage and failure analysis (PDFA) methods have demonstrated success in a variety of finite element analysis (FEA) implementations. However, the technical maturity of CDM codes has not yet been proven for the full design space of composite materials in aerospace applications. CDM-based approaches represent the presence of damage by changing the local material stiffness definitions and without updating the original mesh or element integration schemes. Without discretely representing cracks and their paths through the mesh, damage in models with CDM-based materials is often distributed in a region of partially damaged elements ahead of stress concentrations. Having a series of discrete matrix cracks represented by a softened region may affect predictions of damage propagation and, thus, structural failure. This issue can be mitigated by restricting matrix damage development to discrete, fiber-aligned rows of elements; hence CDM-based matrix cracks can be implemented to be more representative of discrete matrix cracks. This paper evaluates the effect of restricting CDM matrix crack development to discrete, fiber-aligned rows where the spacing of these rows is controlled by a user-defined crack spacing parameter. Initially, the effect of incrementally increasing matrix crack spacing in a unidirectional center notch coupon is evaluated. Then, the lessons learned from the center notch specimen are applied to open-hole compression finite element models. Results are compared to test data, and the limitations, successes, and potential of the matrix crack spacing approach are discussed.
Creep crack growth tests have been carried out in compact type specimens of INCO 718 at 1200 F (649 C). Theoretical creep crack growth predictions have been carried out by incorporating a unified viscoplastic constitutive model and a continuum damage model into the ARAQUS nonlinear finite element program. Material constants for both the viscoplastic model and the creep continuum damage model were determined from tests carried out on uniaxial bar specimens of INCO 718 at 1200 F (649 C). A comparison of the theoretical creep crack growth rates obtained from the finite element predictions with the experimentally observed creep crack growth rates indicates that the viscoplastic/continuum damage model can be used to successfully predict creep crack growth in compact type specimens using material constants obtained from uniaxial bar specimens of INCO 718 at 1200 F (649 C).
A parameterized orthogonal tight-binding mathematical model of the quantum electronic structure of the bismuth telluride molecule has been devised for use in conjunction with a semiclassical transport model in predicting the thermoelectric properties of doped bismuth telluride. This model is expected to be useful in designing and analyzing Bi2Te3 thermoelectric devices, including ones that contain such nano - structures as quantum wells and wires. In addition, the understanding gained in the use of this model can be expected to lead to the development of better models that could be useful for developing other thermoelectric materials and devices having enhanced thermoelectric properties. Bi2Te3 is one of the best bulk thermoelectric materials and is widely used in commercial thermoelectric devices. Most prior theoretical studies of the thermoelectric properties of Bi2Te3 have involved either continuum models or ab-initio models. Continuum models are computationally very efficient, but do not account for atomic-level effects. Ab-initio models are atomistic by definition, but do not scale well in that computation times increase excessively with increasing numbers of atoms. The present tight-binding model bridges the gap between the well-scalable but non-atomistic continuum models and the atomistic but poorly scalable ab-initio models: The present tight-binding model is atomistic, yet also computationally efficient because of the reduced (relative to an ab-initio model) number of basis orbitals and flexible parameterization of the Hamiltonian.
Ranges of validity for the continuum-beam model, the length-scale effects and continuum assumptions are analyzed in the framework of scaling analysis of NT structure. Two coupled criteria for the applicability of the continuum model are presented. Scaling analysis of NT buckling and geometric parameters (e.g., diameter and length) is carried out to determine the key non-dimensional parameters that control the buckling strains and modes of NT buckling. A model applicability map, which represents two classes of NTs, is constructed in the space of non-dimensional parameters. In an analogy with continuum mechanics, a mechanical law of geometric similitude is presented for two classes of beam-like NTs having different geometries. Expressions for the critical buckling loads and strains are tailored for the distinct groups of NTs and compared with the data provided by the molecular dynamics simulations. Implications for molecular dynamics simulations and the NT-based scanning probes are discussed.
Although significant advances have been made in modeling and controlling flexible systems, there remains a need for improvements in model accuracy and in control performance. The finite element models of flexible systems are unduly complex and are almost intractable to optimum parameter estimation for refinement using experimental data. Distributed parameter or continuum modeling offers some advantages and some challenges in both modeling and control. Continuum models often result in a significantly reduced number of model parameters, thereby enabling optimum parameter estimation. The dynamic equations of motion of continuum models provide the advantage of allowing the embedding of the control system dynamics, thus forming a complete set of system dynamics. There is also increased insight provided by the continuum model approach.
A continuum modeling approach by self-consistently coupling plasma dynamics and gas flow will be presented for the analysis of high density plasma reactors. Experimental data shows that gas flow distribution affects the etch rate uniformity even at low pressures (6-20 mTorr) and flow rates (20-70 sccm). This study will investigate the effects of gas flow and gas energy on bulk plasma densities and temperatures using a continuum model. The model solves multidimensional equations of mass balance for neutrals and ions, gas momentum, separate energy equations for electrons and neutrals and Maxwell's equations for power coupling. A test case of N2 plasma in a 300mm TCP etch reactor, for which hybrid model and Langmuir probe data are available, is chosen for this analysis. Our preliminary results show that modeling gas flow and energy improves the predictions of electron density and its spatial variation in the reactor when compared with the experimental data. The aim of this study is to identify the operating conditions for the TCP reactor when a self-consistent modeling of gas flow is important.
Limitations in the validity of the continuum beam model for carbon nanotubes (NTs) and nanorods are examined. Applicability of all assumptions used in the model is restricted by the two criteria for geometric parameters that characterize the structure of NTs. The key non-dimensional parameters that control the NT buckling behavior are derived via dimensional analysis of the nanomechanical problem. A mechanical law of geometric similitude for NT buckling is extended from continuum mechanics for different molecular structures. A model applicability map, where two classes of beam-like NTs are identified, is constructed for distinct ranges of non-dimensional parameters. Expressions for the critical buckling loads and strains are tailored for two classes of NTs and compared with the data provided by the molecular dynamics simulations. copyright 2001 Elsevier Science Ltd. All rights reserved.
Advances in continuum modeling, progress in reduction methods, and analysis and modeling needs for large space structures are covered with specific attention given to repetitive lattice trusses. As far as continuum modeling is concerned, an effective and verified analysis capability exists for linear thermoelastic stress, birfurcation buckling, and free vibration problems of repetitive lattices. However, application of continuum modeling to nonlinear analysis needs more development. Reduction methods are very effective for bifurcation buckling and static (steady-state) nonlinear analysis. However, more work is needed to realize their full potential for nonlinear dynamic and time-dependent problems. As far as analysis and modeling needs are concerned, three areas are identified: loads determination, modeling and nonclassical behavior characteristics, and computational algorithms. The impact of new advances in computer hardware, software, integrated analysis, CAD/CAM stems, and materials technology is also discussed.
In April, 1989, a workshop on constitutive relationships and models in continuum theories of multiphase flows was held at NASA's Marshall Space Flight Center. Topics of constitutive relationships for the partial or per phase stresses, including the concept of solid phase pressure are discussed. Models used for the exchange of mass, momentum, and energy between the phases in a multiphase flow are also discussed. The program, abstracts, and texts of the presentations from the workshop are included.
The paper presents an application of adaptive finite element methods to the modeling of low-cycle continuum damage and life prediction of high-temperature components. The major objective is to provide automated and accurate modeling of damaged zones through adaptive mesh refinement and adaptive time-stepping methods. The damage modeling methodology is implemented in an usual way by embedding damage evolution in the transient nonlinear solution of elasto-viscoplastic deformation problems. This nonlinear boundary-value problem is discretized by adaptive finite element methods. The automated h-adaptive mesh refinements are driven by error indicators, based on selected principal variables in the problem (stresses, non-elastic strains, damage, etc.). In the time domain, adaptive time-stepping is used, combined with a predictor-corrector time marching algorithm. The time selection is controlled by required time accuracy. In order to take into account strong temperature dependency of material parameters, the nonlinear structural solution a coupled with thermal analyses (one-way coupling). Several test examples illustrate the importance and benefits of adaptive mesh refinements in accurate prediction of damage levels and failure time.