Search

Guideline for design of adaptive structures specifies active members should be located at positions of maximum strain energy. Equations of motion of flexible structures formulated in terms of kinetic energies, strain energies, and direct measurements of forces. Maintaining precise dimensional control during assembly essential to assembly without large external loads or to prevent jamming of substructure preventing successful deployment. Active members used to prevent "binding" during deployment of structure. Then structure adjusted to precision shape requirement and adjusted during operation as required.

In this article, the vibration control of adaptive truss structures, where the control actuation is provided by length adjustable active members, is formulated as a direct output feedback control problem. A control method named Model Truncated Output Feedback (MTOF) is presented. The method allows the control feedback gain to be determined in a decoupled and truncated modal space in which only the critical vibration modes are retained. The on-board computation required by MTOF is minimal; thus, the method is favorable for the applications of vibration control of large scale structures. The truncation of the modal space inevitably introduces spillover effect during the control process. In this article, the effect is quantified in terms of active member locations, and it is shown that the optimal placement of active members, which minimizes the spillover effect (and thus, maximizes the control performance) can be sought. The problem of optimally selecting the locations of active members is also treated.

This paper describes the optimal location selection of actuators for vibration control in prestressed adaptive trusses. Since prestressed adaptive trusses are statically indeterminate, the actuators to be used for vibration control purposes must work against (1) existing static axial prestressing forces, (2) static axial forces caused by the actuation, and (3) dynamic axial forces caused by the motion of the mass. In statically determinate adaptive trusses (1) and (2) are non - existing. The actuator placement problem in statically indeterminate trusses is therefore governed by the actuation energy and the actuator strength requirements. Assuming output feedback type control of selected vibration modes in autonomous systems, a procedure is given for the placement of vibration controlling actuators in prestressed adaptive trusses.

In this work vibration control of statically indeterminate adaptive truss structures is investigated. Here, the actuators (i.e., length adjusting devices) that are used for vibration control, work against the axial forces caused by the inertial forces. In statically determinate adaptive trusses no axial force is induced by the actuation. The control problem in statically indeterminate trusses may be dominated by the actuation-induced axial element forces. The creation of actuation-induced axial forces puts the system to a higher energy state, thus aggravates the controls. It is shown that by the usage of sufficient number of slave actuators in addition to the actual control actuators, the actuation-induced axial element forces can be nullified, and the control problem of the statically indeterminate adaptive truss problem is reduced to that of a statically determinate one. It is also shown that the usage of slave actuators saves a great amount of control energy and provides robustness for the controls.

In this work the actuator placement problem for the precision control in prestressed adaptive space trusses is studied. These structures cannot be statically determinate, implying that the length-adjusting actuators have to work against the existing prestressing forces, and also against the stresses caused by the actuation. This type of difficulties does not exist in statically determinate adaptive trusses where, except for overcoming the friction, the actuators operate under zero axial force, and require almost no energy. The actuator placement problem in statically inderterminate trusses is, therefore, governed seriously by the energy and the strength requirements. The paper provides various methodologies for the actuator placement problem in prestressed space trusses.

Proposed here is a method of vibration control based on limiting the maximum axial forces in the active members of an adaptive truss. The actuators simulate elastic rigid-plastic behavior and consume the vibrational energy as work. The method is applicable to both statically determinate as well as indeterminate truss structures. However, for energy efficient control of statistically indeterminate trusses extra actuators may be provided on the redundant bars. An energy formulation relating the various control parameters is derived to get an estimate of the control time. Since the simulation of elastic rigid-plastic behavior requires a piecewise linear control law, a general analytical solution is not possible. Numerical simulation by step-by-step integration is performed to simulate the control of an example truss structure. The problems of application to statically indeterminate trusses and optimal actuator placement are identified for future work.

The application of adaptive structures to the structural design of space structures is examined with attention given to facilitating their construction in space and enhancing reliability. A modified approach based on traditional techniques is presented which incorporates the loads analysis by Wada (1979) and the application of adaptive structures to control structural motion. An analytical technique is described for the deployment/construction of the structure in which each step of the assembly sequence is analyzed. The use of adaptive structures is shown to permit the static adjustment of the structure after assembly in its operational environment. The concepts presented to incorporate adaptive structures in the deployment of large space structures are expected to improve the reliability and reduce the cost of the total systems.

The natural vibration frequencies of a structure can be affected by inducing stress in the structure. The success of this kind of control of the resonant frequencies of a truss structure depends on the geometry of the structure. It is shown that in adaptive truss structures the method is effective for vibrations in less stiff directions, such as the normal direction of the plane containing all of the bars of a node, suggesting its applicability for cable, membrane, and thin plate and shell structures.

Prospective NASA space efforts will require submicron dimensional-precision structures of 10-50 m and 20-30 year service lives, such as the 20 m-diameter Large Deployable Reflector; in most such designs, truss structures are selected due to their deployability and assemblability in space. An account is presently given of the critical role played by adaptive-structure concepts. A major aspect of these development efforts involves the use of the smallest feasible set of active members for the required functions; these can preload the structure, eliminate joint gaps, and adjust precision degrees-of-freedom.

Effect of imperfections in the joints of an adaptive structure on its slow (no inertia forces) motion along a prescribed trajectory as a space crane is studied. Two mathematical models to predict the effect of joint imperfections are proposed. The two models are used to obtain estimates of the deviations of the node of the space crane to which the end-effector is attached, from its prescribed trajectory. An application of the models to a two-section space crane is given.

Thermal stresses developed in a dendritic silicon crystal ribbon have been shown to cause plastic deformation and residual stresses in the ribbon. This paper presents an implementation of a numerical model proposed for thermoelastoplastic behavior of a material. The model has been used to study the effects of plasticity of silicon on the residual stresses. The material properties required to implement this model are all assumed, and the response of the material to the variations in these assumed parameters of the constitutive law and in the finite element mesh is investigated. The steady state growth process is observed to be periodic with nonzero residual stresses. Numerical difficulties are also encountered in the computer solution process, resulting in sharp jumps and large oscillations in the stress responses.

Report discusses application of Cholesky factorization algorithm to positive definite, banded Hermitian matrices. Begins by extending Cholesky factorization algorithm to cover uniformly-partitioned, banded, positive definite matrices of rank n that is real symmetric or Hermitian. Then two stratagems given for use of algorithm in concurrent-processing system in which N less than it has to be to enable factorization of matrix in as few serial steps as possible and where uniformly high efficiency expected from all processing elements. One of major purposes of this and related studies to maximize speedup and efficiency in system of concurrent-data-processing elements.

The linear optimal control problem of an nth-order time-invariant dynamic system with a quadratic performance functional is usually solved by the Hamilton-Jacobi approach. This leads to the solution of the differential matrix Riccati equation with a terminal condition. The bulk of the computation for the optimal control problem is related to the solution of this equation. There are various algorithms in the literature for solving the matrix Riccati equation. However, computational complexities and storage requirements as a function of numbers of state variables, control variables, and sensors are not available for all these algorithms. In this work, the computational complexities and storage requirements for some of these algorithms are given. These expressions show the immensity of the computational requirements of the algorithms in solving the Riccati equation for large-order systems such as the control of highly flexible space structures. The expressions are also needed to compute the speedup and efficiency of any implementation of these algorithms on concurrent machines.

Cost of computation appears competitive with other methods. Problem to compute optimal control of forced response of structure with n degrees of freedom identified in terms of smaller number, r, of vibrational modes. Article begins with Hamilton-Jacobi formulation of mechanics and use of quadratic cost functional. Complexity reduced by alternative approach in which quadratic cost functional expressed in terms of control variables only. Leads to iterative solution of second-order time-integral matrix Volterra equation of second kind containing optimal control vector. Cost of algorithm, measured in terms of number of computations required, is of order of, or less than, cost of prior algoritms applied to similar problems.

Mathematical model includes nonlinear effects. In development simulates growth of silicon ribbon from melt. Takes account of entire temperature and stress history of ribbon. Numerical simulations performed with new model helps in search for temperature distribution, pulling speed, and other conditions favoring growth of wide, flat, relatively defect-free silicon ribbons for solar photovoltaic cells at economically attractive, high production rates. Also applicable to materials other than silicon.

Mathematical model represents thermomechanical behavior of solid web of rectangular cross section as pulled from melt of same material. Intended for application to growth of silicon webs or ribbons, model general enough to be applicable to other materials as well. Shows suitable temperature distribution results in stress-free ribbon. Conceptual ribbon of rectangular cross section pulled from melt. Simplified configuration used to calculate thermal conditions for stress-free ribbon.

Thermal stresses developed during the growth of silicon crystal ribbon have been shown to be negligible, thus eliminating residual stresses and dislocations, if the temperature profile satisfies a second-order partial differential equation inside the ribbon. This has been numerically verified through a finite element model, an outline of which is presented here. This model shows that, for homogeneous isotropic material with temperature independent thermal expansion coefficients, thermal stresses will vanish if the temperature profile satisfies the Laplacian. A comparison of stresses due to uniform and nonuniform temperature gradients in the plane of the ribbon is also presented. The strategies employed to control the round-off error and to validate the computer model are discussed.