An analysis of statically indeterminate trusses having members stressed beyond the proportional limit
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Results from NASA/HBCU Grant No. NAG-1-1125 are summarized. Designs developed for model fabrication, exploratory concepts drafted, interface of computer with robot and end-effector, and capability enhancement are discussed.
A new Potential Fields approach to the robotic path planning problem is proposed and implemented. Our approach, which is based on one originally proposed by Munger, computes an incremental joint vector based upon attraction to a goal and repulsion from obstacles. By repetitively adding and computing these 'steps', it is hoped (but not guaranteed) that the robot will reach its goal. An attractive force exerted by the goal is found by solving for the the minimum norm solution to the linear Jacobian equation. A repulsive force between obstacles and the robot's links is used to avoid collisions. Its magnitude is inversely proportional to the distance. Together, these forces make the goal the global minimum potential point, but local minima can stop the robot from ever reaching that point. Our approach improves on a basic, potential field paradigm developed by Munger by using an active, adaptive field - what we will call a 'flexible' potential field. Active fields are stronger when objects move towards one another and weaker when they move apart. An adaptive field's strength is individually tailored to be just strong enough to avoid any collision. In addition to the local planner, a global planning algorithm helps the planner to avoid local field minima by providing subgoals. These subgoals are based on the obstacles which caused the local planner to fail. A best-first search algorithm A* is used for graph search.
A new approach to find homogeneous models for beam-like repeated flexible structures is proposed which conceptually involves two steps. The first step involves the approximation of 3-D non-homogeneous model by a 1-D periodic beam model. The structure is modeled as a 3-D non-homogeneous continuum. The displacement field is approximated by Taylor series expansion. Then, the cross sectional mass and stiffness matrices are obtained by energy equivalence using their additive properties. Due to the repeated nature of the flexible bodies, the mass, and stiffness matrices are also periodic. This procedure is systematic and requires less dynamics detail. The first step involves the homogenization from a 1-D periodic beam model to a 1-D homogeneous beam model. The periodic beam model is homogenized into an equivalent homogeneous beam model using the additive property of compliance along the generic axis. The major departure from previous approaches in literature is using compliance instead of stiffness in homogenization. An obvious justification is that the stiffness is additive at each cross section but not along the generic axis. The homogenized model preserves many properties of the original periodic model.
A deterministic methodology is presented for developing closed-form deflection equations for two-dimensional and three-dimensional lattice structures. Four types of lattice structures are studied: beams, plates, shells and soft lattices. Castigliano's second theorem, which entails the total strain energy of a structure, is utilized to generate highly accurate results. Derived deflection equations provide new insight into the bending and shear behavior of the four types of lattices, in contrast to classic solutions of similar structures. Lattice derivations utilizing kinetic energy are also presented, and used to examine the free vibration response of simple lattice structures. Derivations utilizing finite element theory for unique lattice behavior are also presented and validated using the finite element analysis code EAL.
The subject grant was in effect from 7/l/99 to 10/31/99. The objective of this grant was to complete a strut-braced wing study which began, which was in effect from 6/27/96 until 9/15/99. While the initial grant was on-going, we were also under subcontract to Lockheed-Martin, Aerospace Systems Division, Marietta, GA to do additional studies related to the strut-braced wing grant "A Structural and Aerodynamic Investigation of a Strut-Braced Wing Transonic Aircraft Concept", 4/l/98-11/15/98. Lockheed-Martin was under contract to NASA Langley. Finally the research under this grant has led to a joint proposal from NASA Langley, Locheed-Martin, Virginia Tech and NASA Dryden to develop a transonic strut-braced wing demonstration aircraft in response to Flight Research for Revolutionary Aeronautical Concepts (REVCON). This final report summarizes the research done, augmented by the additional concommitant research projects mentioned above.
Rigorous analysis of geometrically nonlinear structures demands creating mathematical models that accurately include loading and support conditions and, more importantly, model the stiffness and response of the structure. Nonlinear geometric structures often contain critical points with snap-through behavior during the response to large loads. Studying the post buckling behavior during a portion of a structure's unstable load history may be necessary. Primary structures made from ductile materials will stretch enough prior to failure for loads to redistribute producing sudden and often catastrophic collapses that are difficult to predict. The responses and redistribution of the internal loads during collapses and possible sharp snap-back of structures have frequently caused numerical difficulties in analysis procedures. The presence of critical stability points and unstable equilibrium paths are major difficulties that numerical solutions must pass to fully capture the nonlinear response. Some hurdles still exist in finding nonlinear responses of structures under large geometric changes. Predicting snap-through and snap-back of certain structures has been difficult and time consuming. Also difficult is finding how much load a structure may still carry safely. Highly geometrically nonlinear responses of structures exhibiting complex snap-back behavior are presented and analyzed with a finite element approach. The arc-length method will be reviewed and shown to predict the proper response and follow the nonlinear equilibrium path through limit points.
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Global astrometry is the measurement of stellar positions and motions. These are typically characterized by five parameters, including two position parameters, two proper motion parameters, and parallax. The Space Interferometry Mission (SIM) will derive these parameters for a grid of approximately 1300 stars covering the celestial sphere to an accuracy of approximately 4uas, representing a two orders of magnitude improvement over the most precise current star catalogues. Narrow angle astrometry will be performed to a 1uas accuracy. A wealth of scientific information will be obtained from these accurate measurements encompassing many aspects of both galactic (and extragalactic science. SIM will be subject to a number of instrument errors that can potentially degrade performance. Many of these errors are systematic in that they are relatively static and repeatable with respect to the time frame and direction of the observation. This paper and its companion define the modeling of the, contributing factors to these errors and the analysis of how they impact SIM's ability to perform astrometric science.
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The present invention provides an aircraft having variable airframe geometry for accommodating efficient flight. The aircraft includes an elongated fuselage, an oblique wing pivotally connected with said fuselage, a wing pivoting mechanism connected with said oblique wing and said fuselage, and a brace operably connected between said oblique wing and said fuselage. The present invention also provides an aircraft having an elongated fuselage, an oblique wing pivotally connected with said fuselage, a wing pivoting mechanism connected with said oblique wing and said fuselage, a propulsion system pivotally connected with said oblique wing, and a brace operably connected between said propulsion system and said fuselage.
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The second Interferometry Program Experiment (IPEX-2) is a technology demonstration precursor to the Space Interferometry Mission, a 10-meter baseline space-based interferometer scheduled for launch in 2005.
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