An automatic node-relabeling scheme for bandwidth minimization of stiffness matrices.
Stiffness matrices bandwidth minimization by automatic node relabeling in equilibrium problems of lumper-parameter systems
Akyuz, F. A.↗
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Buckling and vibration of any prismatic assembly of shear and compression loaded anisotropic plates with an arbitrary supporting structure
The computer program designated 'VIPASA', which accurately treats buckling and vibration in prismatic plate assemblies with a response that varies sinusoidally in the longitudinal direction, has been found to be limited by the production of an in-plane shear loading of component plates that produces skewed mode shapes. These do not conform to desired support conditions. This problem is presently overcome through a coupling of the VIPASA stiffness matrices for different wavelength responses by means of the Lagrangian Multipliers method. The theory extends to supports at arbitrary locations, and even to the support provided by any elastic structure. The generality and capabilities of VIPASA have been retained in the computer program designated 'VICON', which permits constraints and a supporting structure consisting of any number of transverse beam columns.
Anderson, M. S.↗
Vibrating Beam With Spatially Periodic Stiffness
Report presents theoretical analysis of vibrations of simply supported beam, bending stiffness varying about steady value, sinusoidally with position along length. Problem of practical importance because related to vibrations of twisted-pair electric-power transmission lines. Twists promote nonuniform shedding of vortexes and prevents resonant accumulation of vibrational energy from wind.
Townsend, John S.↗
Hybrid Upwind Splitting (HUS) by a Field-by-Field Decomposition
We introduce and develop a new approach for upwind biasing: the hybrid upwind splitting (HUS) method. This original procedure is based on a suitable hybridization of current prominent flux vector splitting (FVS) and flux difference splitting (FDS) methods. The HUS method is designed to naturally combine the respective strengths of the above methods while excluding their main deficiencies. Specifically, the HUS strategy yields a family of upwind methods that exhibit the robustness of FVS schemes in the capture of nonlinear waves and the accuracy of some FDS schemes in the resolution of linear waves. We give a detailed construction of the HUS methods following a general and systematic procedure directly performed at the basic level of the field by field (i.e. waves) decomposition involved in FDS methods. For such a given decomposition, each field is endowed either with FVS or FDS numerical fluxes, depending on the nonlinear nature of the field under consideration. Such a design principle is made possible thanks to the introduction of a convenient formalism that provides us with a unified framework for upwind methods. The HUS methods we propose bring significant improvements over current methods in terms of accuracy and robustness. They yield entropy-satisfying approximate solutions as they are strongly supported in numerical experiments. Field by field hybrid numerical fluxes also achieve fairly simple and explicit expressions and hence require a computational effort between that of the FVS and FDS. Several numerical experiments ranging from stiff 1D shock-tube to high speed viscous flows problems are displayed, intending to illustrate the benefits of the present approach. We assess in particular the relevance of our HUS schemes to viscous flow calculations.
Coquel, Frederic↗
A Six-Node Curved Triangular Element and a Four-Node Quadrilateral Element for Analysis of Laminated Composite Aerospace Structures
Mathematical development and some computed results are presented for Mindlin plate and shell elements, suitable for analysis of laminated composite and sandwich structures. These elements use the conventional 3 (plate) or 5 (shell) nodal degrees of freedom, have no communicable mechanisms, have no spurious shear energy (no shear locking), have no spurious membrane energy (no membrane locking) and do not require arbitrary reduction of out-of-plane shear moduli or under-integration. Artificial out-of-plane rotational stiffnesses are added at the element level to avoid convergence problems or singularity due to flat spots in shells. This report discusses a 6-node curved triangular element and a 4-node quadrilateral element. Findings show that in regular rectangular meshes, the Martin-Breiner 6-node triangular curved shell (MB6) is approximately equivalent to the conventional 8-node quadrilateral with integration. The 4-node quadrilateral (MB4) has very good accuracy for a 4-node element, and may be preferred in vibration analysis because of narrower bandwidth. The mathematical developments used in these elements, those discussed in the seven appendices, have been applied to elements with 3, 4, 6, and 10 nodes and can be applied to other nodal configurations.
Martin, C. Wayne↗
Validating Finite Element Models of Assembled Shell Structures
The validation of finite element models of assembled shell elements is presented. The topics include: 1) Problems with membrane rotations in assembled shell models; 2) Penalty stiffness for membrane rotations; 3) Physical stiffness for membrane rotations using shell elements with 6 dof per node; and 4) Connections avoiding rotations.
membrane rotations↗
Description and use of LSODE, the Livermore Solver for Ordinary Differential Equations
LSODE, the Livermore Solver for Ordinary Differential Equations, is a package of FORTRAN subroutines designed for the numerical solution of the initial value problem for a system of ordinary differential equations. It is particularly well suited for 'stiff' differential systems, for which the backward differentiation formula method of orders 1 to 5 is provided. The code includes the Adams-Moulton method of orders 1 to 12, so it can be used for nonstiff problems as well. In addition, the user can easily switch methods to increase computational efficiency for problems that change character. For both methods a variety of corrector iteration techniques is included in the code. Also, to minimize computational work, both the step size and method order are varied dynamically. This report presents complete descriptions of the code and integration methods, including their implementation. It also provides a detailed guide to the use of the code, as well as an illustrative example problem.
Radhakrishnan, Krishnan↗
Spline-based distributed system identification with application to large space antennas
A parameter and state estimation technique for distributed models is demonstrated through the solution of a problem generic to large space antenna system identification. Assuming the position of the reflective surface of the maypole (hoop/column) antenna to be approximated by the static two-dimensional, stretched-membrane partial differential equation with variable-stiffness coefficient functions, a spline-based approximation procedure is described that estimates the shape and stiffness functions from data set observations. For given stiffness functions, the Galerkin projection with linear spline-based functions is applied to project the distributed problem onto a finite-dimensional subspace wherein algebraic equations exist for determining a static shape (state) prediction. The stiffness functions are then parameterized by cubic splines and the parameters estimated by an output error technique. Numerical results are presented for data descriptive of a 100-m-diameter maypole antenna.
Banks, H. T.↗
An Elasticity-Based Mesh Scheme Applied to the Computation of Unsteady Three-Dimensional Spoiler and Aeroelastic Problems
This paper presents a modification of the spring analogy scheme which uses axial linear spring stiffness with selective spring stiffening/relaxation. An alternate approach to solving the geometric conservation law is taken which eliminates the need for storage of metric Jacobians at previous time steps. Efficiency and verification are illustrated with several unsteady 2-D airfoil Euler computations. The method is next applied to the computation of the turbulent flow about a 2-D airfoil and wing with two and three- dimensional moving spoiler surfaces, and the results compared with Benchmark Active Controls Technology (BACT) experimental data. The aeroelastic response at low dynamic pressure of an airfoil to a single large scale oscillation of a spoiler surface is computed. This study confirms that it is possible to achieve accurate solutions with a very large time step for aeroelastic problems using the fluid solver and aeroelastic integrator as discussed in this paper.
Bartels, Robert E.↗
Multi-frequency General Relativistic Radiation-hydrodynamics with M 1 Closure
We report on recent upgrades to our general relativistic radiation-magnetohydrodynamics code, Cosmos++ , which expands the two-moment, M 1 , radiation treatment from gray to multi-frequency transport, including Doppler and gravitational frequency shifts. The solver accommodates either photon (Bose–Einstein) or neutrino (Fermi–Dirac) statistical distribution functions with absorption, emission, and elastic scattering processes. An implicit scheme is implemented to simultaneously solve the primitive inversion problem together with the radiation–matter coupling source terms, providing stability over a broad range of opacities and optical depths where the interaction terms can be stiff. We discuss our formulations and numerical methods, and validate our methods against a wide variety of test problems spanning optically thin to thick regimes in flat, weakly curved, and strongly curved spacetimes.
79 ASTRONOMY AND ASTROPHYSICS↗
Precise control of flexible manipulators
The design and experimental testing of end point position controllers for a very flexible one link lightweight manipulator are summarized. The latest upgraded version of the experimental set up, and the basic differences between conventional joint angle feedback and end point position feedback are described. A general procedure for application of modern control methods to the problem is outlined. The relationship between weighting parameters and the bandwidth and control stiffness of the resulting end point position closed loop system is shown. It is found that joint rate angle feedback in addition to the primary end point position sensor is essential for adequate disturbance rejection capability of the closed loop system. The use of a low order multivariable compensator design computer code; called Sandy is documented. A solution to the problem of control mode switching between position sensor sets is outlined. The proof of concept for endpoint position feedback for a one link flexible manipulator was demonstrated. The bandwidth obtained with the experimental end point position controller is about twice as fast as the beam's first natural cantilevered frequency, and comes within a factor of four of the absolute physical speed limit imposed by the wave propagation time of the beam.
Cannon, R. H., Jr.↗
Numerical analysis of stiffened shear webs in the postbuckling range
The postbuckling behavior of shear webs divided into rectangular panels by stiffeners (uprights) was studied numerically, using the STAGS program in which two-dimensional finite differences are used to solve buckling and nonlinear problems. Universal nondimensional parameters, suggested by linear buckling data, are found to hold for the postbuckling range. Results indicate that the postbuckling stiffness of shear webs with isotropic panels is roughly two thirds of the prebuckling stiffness. The postbuckling behavior of shear webs with isotropic and orthotropic material properties is compared. Some practical aspects of solving nonlinear problems of this type by the numerical method employed are examined.
Stein, M.↗
Application of symbolic and algebraic manipulation software in solving applied mechanics problems
As its name implies, symbolic and algebraic manipulation is an operational tool which not only can retain symbols throughout computations but also can express results in terms of symbols. This report starts with a history of symbolic and algebraic manipulators and a review of the literatures. With the help of selected examples, the capabilities of symbolic and algebraic manipulators are demonstrated. These applications to problems of applied mechanics are then presented. They are the application of automatic formulation to applied mechanics problems, application to a materially nonlinear problem (rigid-plastic ring compression) by finite element method (FEM) and application to plate problems by FEM. The advantages and difficulties, contributions, education, and perspectives of symbolic and algebraic manipulation are discussed. It is well known that there exist some fundamental difficulties in symbolic and algebraic manipulation, such as internal swelling and mathematical limitation. A remedy for these difficulties is proposed, and the three applications mentioned are solved successfully. For example, the closed from solution of stiffness matrix of four-node isoparametrical quadrilateral element for 2-D elasticity problem was not available before. Due to the work presented, the automatic construction of it becomes feasible. In addition, a new advantage of the application of symbolic and algebraic manipulation found is believed to be crucial in improving the efficiency of program execution in the future. This will substantially shorten the response time of a system. It is very significant for certain systems, such as missile and high speed aircraft systems, in which time plays an important role.
Tsai, Wen-Lang↗
The crack and wedging problem for an orthotropic strip
The plane elasticity problem for an orthotropic strip containing a crack parallel to its boundaries is considered. The problem is formulated under general mixed mode loading conditions. The stress intensity factors depend on two dimensionless orthotropic constants only. For the crack problem the results are given for a single crack and two collinear cracks. The calculated results show that of the two orthotropic constants the influence of the stiffness ratio on the stress intensity factors is much more significant than that of the shear parameter. The problem of loading the strip by a rigid rectangular lengths continuous contact is maintained along the wedge strip interface; at a certain critical wedge length the separation starts at the midsection of the wedge, and the length of the separation zone increases rapidly with increasing wedge length.
Cinar, A.↗
The crack and wedging problem for an orthotropic strip
The plane elasticity problem for an orthotropic strip containing a crack parallel to its boundaries is considered. The problem is formulated under general mixed mode loading conditions. The stress intensity factors depend on two dimensionless orthotropic constants only. For the crack problem the results are given for a single crack and two collinear cracks. The calculated results show that of the two orthotropic constants the influence of the stiffness ratio on the stress intensity factors is much more significant than that of the shear parameter. The problem of loading the strip by a rigid rectangular lengths continuous contact is maintained along the wedge strip interface; at a certain critical wedge length the separation starts at the midsection of the wedge, and the length of the separation zone increases rapidly with increasing wedge length. Previously announced in STAR as N82-26707
Cinar, A.↗
A penny shaped crack in a filament-reinforced matrix. 2: The crack problem
The elastostatic interaction problem between a penny-shaped crack and a slender inclusion or filament in an elastic matrix was formulated. For a single filament as well as multiple identical filaments located symmetrically around the crack the problem is shown to reduce to a singular integral equation. The solution of the problem is obtained for various geometries and filament-to-matrix stiffness ratios, and the results relating to the angular variation of the stress intensity factor and the maximum filament stress are presented.
Pacella, A. H.↗
Space Station alpha joint bearing
Perhaps the most critical structural system aboard the Space Station is the Solar Alpha Rotary Joint which helps align the power generation system with the sun. The joint must provide structural support and controlled rotation to the outboard transverse booms as well as power and data transfer across the joint. The Solar Alpha Rotary Joint is composed of two transition sections and an integral, large diameter bearing. Alpha joint bearing design presents a particularly interesting problem because of its large size and need for high reliability, stiffness, and on orbit maintability. The discrete roller bearing developed is a novel refinement to cam follower technology. It offers thermal compensation and ease of on-orbit maintenance that are not found in conventional rolling element bearings. How the bearing design evolved is summarized. Driving requirements are reviewed, alternative concepts assessed, and the selected design is described.
Everman, Michael R.↗
Influence of time domain unsteady aerodynamics on coupled flap-lag-torsional aeroelastic stability and response of rotor blades
This paper describes the incorporation of finite-state, time-domain aerodynamics in a flag-lag-torsional aeroelastic stability and response analysis in forward flight. Improvements to a previous formulation are introduced which eliminate spurious singularities. The methodology for solving the aeroelastic stability and response problems with augmented states, in the time domain, is presented using an implicit formulation. Results describing the aeroelastic behavior of soft and stiff in-plane hingeless rotor blades, in forward flight, are presented to illustrate the sensitivity of both the stability and response problems to time domain unsteady aerodynamics.
Friedmann, P. P.↗