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A nonconforming finite method is described for treating linear equilibrium problems, and a convergence proof showing second order accuracy is given. The close relationship to a related compact finite difference scheme due to Phillips and Rose is examined. A condensation technique is shown to preserve the compactness property and suggests an approach to a certain type of homogenization.
A series of impact problems were analyzed using the Eulerian hydrocode CTH. The objective was to quantify the amount of energy dissipated locally by a projectile-infinite plate impact. A series of six impact problems were formulated such that the mass and speed of each projectile were varied in order to allow for increasing speed with constant kinetic energy. The properties and dimensions of the plate were the same for each projectile impact. The resulting response of the plate was analyzed for global Kinetic Energy, global momentum, and local maximum shear stress. The percentage of energy dissipated by the various hypervelocity impact phenomena appears as a relative change of shear stress at a point away from the impact in the plate.
Application to the simulation of idealized spacecraft are considered both for multiple-rigid-body models and for models consisting of combination of rigid bodies and elastic bodies, with the elastic bodies being defined either as continua, as finite-element systems, or as a collection of given modal data. Several specific examples are developed in detail by alternative methods of analytical mechanics, and results are compared to a Newton-Euler formulation. The following methods are developed from d'Alembert's principle in vector form: (1) Lagrange's form of d'Alembert's principle for independent generalized coordinates; (2) Lagrange's form of d'Alembert's principle for simply constrained systems; (3) Kane's quasi-coordinate formulation of D'Alembert's principle; (4) Lagrange's equations for independent generalized coordinates; (5) Lagrange's equations for simply constrained systems; (6) Lagrangian quasi-coordinate equations (or the Boltzmann-Hamel equations); (7) Hamilton's equations for simply constrained systems; and (8) Hamilton's equations for independent generalized coordinates.
Equivalent equations which govern deformations of self-gravitating elastic bodies of nonuniform internal temperature
Spinning body with rigid and elastic parts, using Liapunov direct method for attitude stability analysis
This paper discusses theoretical foundations of quantitative image-based measurements for extracting and reconstructing geometric, kinematic and dynamic properties of observed objects. New results are obtained by using a combination of methods in perspective geometry, differential geometry. radiometry, kinematics and dynamics. Specific topics include perspective projection transformation. perspective developable conical surface, perspective projection under surface constraint, perspective invariants, the point correspondence problem. motion fields of curves and surfaces. and motion equations of image intensity. The methods given in this paper arc useful for determining morphology and motion fields of deformable bodies such as elastic bodies. viscoelastic mediums and fluids.
Thermodynamic properties of inhomogeneous elastic bodies
Problems of elasticity associated with the behavior of free surfaces of elastic bodies are reviewed with particular reference to the propagation of characteristic waves and the criteria of wrinkling of free surfaces. All transformations are given for the case when a free surface of an elastic body is streamlined by the flow of inviscid fluid. The wrinkling phenomenon is illustrated by example.
The indicator is characterized by an elongated elastic body having extended from the opposite ends of threaded shanks adapted to selected tension members. A pair of external shoulders, one of which is axially displaceable relative to the other, and a rigid tubular sleeve interposed between said shoulders are included. Tension is applied to the elastic body for imparting strain. The movable shoulder can be advanced into abutting engagement with the sleeve, whereby the sleeve is placed in compression once the tensile forces are removed from the shanks. A reapplication of tensile forces equal to the initially applied tensile forces removes the sleeve from compression, whereby the sleeve is freed for rotation for thus indicating the magnitude of the applied tensile forces.
Computational Fluid Dynamics combined with a Discrete Element Method is one of the computational methods that can be used to model multiphase flows. In this method various phases, gas and liquid or solid, are present in the same computational domain. The local averaged Navier–Stokes equations determine the flow of the continuous phase fluid and are solved using the traditional CFD finite volume approach. DEM is based on a Lagrangian formulation, which solves the equations of motion, expressed in ordinary differential equations, for representative particles as they move in space and time. The interactions between the continuous fluid phase and discrete solid phase are modeled with the use of Newton’s laws of motion via drag force. The particles interact with each other and with the boundaries of the fluid continuum, and the resulting contact forces are included in the equations of motion. The properties of solid particles and boundaries are treated as elastic bodies, with specified density, elastic modulus, and Poisson’s ratio. Particle shapes may vary from single spherical particles to more complex-shaped composite particles. The particles may be introduced into the domain by random or structured injection at a point, surface, or volume, depending on the application. More details on the formulation can be found in the Simcenter STAR-CCM+ User’s Manual and OpenFOAM website.
Dynamic stability analysis of liquid filled rigid bodies and liquid filled elastic bodies
System of differential equations that reflects interrelationships of deformation, diffusion, and thermoconductivity used to study stress concentration around holes in elastic body
The effects of pin elasticity, pin/hole friction, and pin/hole clearance on the stresses around a hole in a pin-loaded orthotropic plate were studied. The problem was modeled as a planar problem, the pin and plate being two elastic bodies interacting through contact. Complex variable elasticity, a collocation scheme to enforce the pin/hole boundary conditions, and an iteration procedure to find the contact, slip, and no-slip regions were used to obtain numerical results. The results indicate that pin elasticity is not as important a variable as friction and clearance are. A rigid pin assumption, as opposed to the popular cosinusoidal radial traction, can be used without much error but clearance and friction should not be ignored.
Approximate analytic and numerical theories are developed with which to model, and compare with laboratory measurements, the diffuse ultrasonic field transmitted from one elastic body to another through a resonant coupling. Particular focus is on the sensitivity of the transmitted field to perturbations in the natural frequency of the coupling, and on the manifestation of such perturbations as time delays in the second body. Immediate application is to measurements of slow dynamic elastic nonlinearity. It is found that the developed approximate theories do a good job of predicting the time dependence of mean square transmitted signal and signal spectra. They also predict the time delays, both their erratic character and their means. Analytic dependence of these time shifts on the fractional frequency perturbation df/f is derived.
A variational formulation is given for the equations of motion for an unconstrained elastic body, and Hamilton's principle is used to derive the equations of motion and deformation of the body. Finite-element approximations are developed for these dynamical equations with respect to a body axis system satisfying the mean axis conditions. The free-body influence matrix for the body then is developed in terms of the finite-element model parameters.
The equations of motion for an arbitrarily interconnected collection of substructures are derived. The substructures are elastic bodies which may be idealized as finite element assemblies and are subject to small deformations relative to a nominal state. Interconnections between the elastic substructures permit large relative translations and rotations between substructures, governed by Pfaffian constraints describing the connections. Screw connections (permitting rotation about and translation along a single axis) eliminate constraint forces and incorporate modal coupling. The problem of flexible spacecraft simulation is discussed. Hurty's component mode approach is extended by permitting interconnected elastic substructures large motions relative to each other and relative to inertial space. The hybrid coordinate methods are generalized by permitting all substructures to be flexible (rather than only the terminal members of a topological tree of substructures). The basic relationships of continuum mechanics are developed.
A nonlinear simulation is developed to model the longitudinal motion of a vehicle in hypersonic flight. The equations of motion pertinent to this study are presented. Analytic expressions for the aerodynamic forces acting on a hypersonic vehicle which were obtained from Newtonian Impact Theory are further developed. The control surface forces are further examined to incorporate vehicle elastic motion. The purpose is to establish feasible equations of motion which combine rigid body, elastic, and aeropropulsive dynamics for use in nonlinear simulations. The software package SIMULINK is used to implement the simulation. Also discussed are issues needing additional attention and potential problems associated with the implementation (with proposed solutions).
Two approaches are developed to analyze the dynamic behavior of flexible multibody systems. In the first approach each body is modeled with a modal methodology in a local non-inertial frame of reference, whereas in the second approach, each body is modeled with a finite element methodology in the inertial frame. In both cases, the interaction among the various elastic bodies is represented by constraint equations. The two approaches were compared for accuracy and efficiency: the first approach is preferable when the nonlinearities are not too strong but it becomes cumbersome and expensive to use when many modes must be used. The second approach is more general and easier to implement but could result in high computation costs for a large system. The constraints should be enforced in a time derivative fashion for better accuracy and stability.