Engineering Papers⌕ Search

Engineering topics

Haftka, Raphael T.

Publications and source records attributed to Haftka, Raphael T..

108 records · Page 6
All sourcesNASA NTRSDOE OSTI
NASA NTRS1987

Survey of methods for calculating sensitivity of general eigenproblems

A survey of methods for sensitivity analysis of the algebraic eigenvalue problem for non-Hermitian matrices is presented. In addition, a modification of one method based on a better normalizing condition is proposed. Methods are classified as Direct or Adjoint and are evaluated for efficiency. Operation counts are presented in terms of matrix size, number of design variables and number of eigenvalues and eigenvectors of interest. The effect of the sparsity of the matrix and its derivatives is also considered, and typical solution times are given. General guidelines are established for the selection of the most efficient method.

Murthy, Durbha V.↗
NASA NTRS1987

Sensitivity derivatives and optimization of nodal point locations for vibration reduction

A method is developed for sensitivity analysis and optimization of nodal point locations in connection with vibration reduction. A straightforward derivation of the expression for the derivative of nodal locations is given, and the role of the derivative in assessing design trends is demonstrated. An optimization process is developed which uses added lumped masses on the structure as design variables to move the node to a preselected location; for example, where low response amplitude is required or to a point which makes the mode shape nearly orthogonal to the force distribution, thereby minimizing the generalized force. The optimization formulation leads to values for added masses that adjust a nodal location while minimizing the total amount of added mass required to do so. As an example, the node of the second mode of a cantilever box beam is relocated to coincide with the centroid of a prescribed force distribution, thereby reducing the generalized force substantially without adding excessive mass. A comparison with an optimization formulation that directly minimizes the generalized force indicates that nodal placement gives essentially a minimum generalized force when the node is appropriately placed.

Pritchard, Jocelyn I.↗
NASA NTRS1987

Effect of sensor and actuator errors on static shape control for large space structures

An analytical study was performed to predict and assess the effect of actuator and sensor errors on the performance of a shape control procedure for flexible space structures using applied temperatures. Approximate formulas were derived for the expected value and variance of the rms distortion ratio (ratio of rms distortions with and without corrections) based on the assumption of zero-mean normally distributed random errors in measured distortions and actuator output temperatures. Studies were carried out for a 55-meter radiometer antenna reflector distorted from its ideal parabolic shape by nonuniform orbital heating. The first study consisted of varying the sensor and actuator errors for the case of 12 actuators and computing the distortion ratio. In the second study, sensor and actuator errors were prescribed and the effect of increasing the number of actuators was evaluated.

Haftka, Raphael T.↗
NASA NTRS1987

Efficient single-level solution of hierarchical problems in structural optimization

A demonstration is made of the use of single-level hierarchical solution techniques for engineering design, which, unlike the formulation stage-applied multilevel techniques, are applied at the solution stage. A single-level decomposition technique is developed which reduces computational costs and memory requirements without incurring the disadvantages of multilevel optimization. Savings of 75 percent are obtained in a case involving 500 design variables and 2408 constraints.

Thareja, Rajiv R.↗
NASA NTRS1987

Simultaneous analysis and design for eigenvalue maximization

A simultaneous analysis and design approach to the maximization of buckling or vibration eigenvalues is presented. Both unimodal and bimodal optimum solutions are considered. A discretization of the structure and response is used to obtain sets of nonlinear algebraic equations which are solved numerically. The formulation is applied to the solution of the optimum design of a beam-column supported by an elastic foundation for maximum buckling load. Two cases are considered: the optimum design of the column for a given foundation and the optimum design of the foundation for a given column. Results are compared to published solutions when possible.

Plaut, Raymond H.↗
NASA NTRS1987

Simultaneous structure/control optimization of large flexible spacecraft

This paper presents an approach to the simultaneous optimal design of a structure and control system for large flexible spacecrafts based on realistic objective function and constraints. The weight or total cost of structure and control system is minimized subject to constraints on the magnitude of response to a given disturbance involving both rigid-body and elastic modes. A nested optimization technique is developed to solve the combined problem. As an example, simple beam-like spacecraft under a steady-state white-noise disturbance force is investigated and some results of optimization are presented. In the numerical examples, the stiffness distribution, the location of controller and the control gains are optimized. Direct feedback control and linear quadratic optimal control laws are used with both inertial and non-inertial disturbing force. It is shown that the total cost is sensitive to the overall structural stiffness so that a simultaneous optimization of the structure and control system is indeed useful.

Onoda, Junjiro↗
NASA NTRS1987

Physically based sensitivity derivatives for finite-element programs

Attention is given to a virtual-work approach to the definition of sensitivity in terms of physical quantities; sensitivity fields are treated as a solution to loadings that consist of body forces, initial strains, and initial stresses. The method can accordingly be implemented in a finite element package, with only minimal knowledge of its programming detail and without access to its source code. The application of the approach to one- and two-dimensional problems is demonstrated. The sensitivity of the structural response for truss structures was computed with respect to the cross-sectional areas of the members.

Barthelemy, Bruno↗
NASA NTRS1987

A comparison of active vibration control techniques - Output feedback vs optimal control

The paper presents analytical and experimental comparison of two control laws for a laboratory structure designed to simulate large space structures. The first control law is the standard linear quadratic law, which is optimal but requires model reduction for practical implementation. The second control law is a new simple direct feedback control law designed to minimize control forces while guaranteeing stability. The optimal control law was found to be only slightly better than the direct feedback law even in terms of the quadratic performance index. Moreover, the optimal control law provided almost no margin of stability for the unmodeled modes while the direct feedback law provided significant stability margins to all modes. The above results were verified experimentally using a digital implementation of the control laws. Excellent agreement between the analytical prediction and experimental measurements was observed.

Martinovic, Zoran N.↗
NASA NTRS1987

Accuracy of derivatives of control performance using a reduced structural model

The sensitivity of control system performance to structural changes is calculated for a multi-span beam with direct-rate feedback vibration control. Reduced models based on the natural modes of the structure are formed and derivatives of the damping ratios of the closed-loop eigenvalues are calculated. The convergence of the derivatives of the damping ratios with increasing number of modes is shown to be slower than the convergence of the damping ratios themselves. In particular, in some cases the convergence of finite-element approximations to the derivatives is much faster than the convergence of the modal approximations. The results indicate that the use of reduced models based on natural vibration modes may be ill-advised for calculating the sensitivity of control system performance to changes in the controlled structure.

Sandridge, Chris A.↗
NASA NTRS1987

Approximations to eigenvalues of modified general matrices

The reanalysis of non-self-adjoint dynamic models is computationally very expensive in design optimization applications. This paper describes several approximations that can be applied to eigenvalues of non-hermitian matrices to reduce that computational cost. Approximations based on eigenvalue derivatives, generalized Rayleigh quotient and the trace theorem are presented and their accuracy and computational cost are estimated. The accuracy and cost estimates are verified by applying the approximations to random matrices and matrices arising in flutter analysis of compressor blades. Recommendations are made for selection of the best approximation when the derivatives are available and when they are not. In particular, it is concluded that the quadratic approximation for eigenvalues should never be used as higher order approximations are always more accurate as well as more efficient.

Murthy, Durbha V.↗
NASA NTRS1987

An analytical and experimental investigation of output feedback vs. linear quadratic regulator

This paper presents analytical and experimental comparison of three control laws for a laboratory structure designed to simulate large space structures. The first control law is the standard time invariant linear quadratic regulator with state estimation, which requires model reduction for practical implementation. This model reduction is associated with the so-called spillover instability. Two new simple direct output feedback control laws guaranteeing stability are proposed. One minimizes the maximum control force, and the other minimizes the same quadratic performance index as the linear quadratic regulator. The three control laws are found to give comparable performance for the modes retained in the reduced model. However, the standard linear quadratic regulator with state estimation provides almost no margin of stability for the unmodeled modes, while the simpler direct feedback laws provide significant stability margins to all modes. The analytical results were verified experimentally using a digital implementation of the control laws. Good agreement between the analytical predictions and experimental measurements was observed.

Martinovic, Zoran N.↗
NASA NTRS1987

An evaluation of higher-order modal methods for calculating transient structural response

The present study evaluates a higher-order modal method proposed by Leung for transient structural analysis entitled the force-derivative method. This method repeatedly integrates by parts with respect to time the convolution-integral form of the structural response to produce successively better approximations to the contribution of the higher modes which are neglected in the modal summation. Comparisons are made of the force-derivative, the mode-displacement, and the mode-acceleration methods for several numerical example problems for various times, levels of damping, and forcing functions. The example problems include a tip-loaded cantilevered beam and a simply-supported multispan beam. The force-derivative method is shown to converge to an accurate solution in fewer modes than either the mode-displacement or the mode-acceleration methods. In addition, for problems in which there are a large number of closely-spaced frequencies whose mode shapes have a negligible contribution to the response, the force derivative method is very effective in representing the effect of the important, but otherwise neglected, higher modes.

Camarda, Charles J.↗
NASA NTRS1987

Interdisciplinary and multilevel optimum design

Interactions among engineering disciplines and subsystems in engineering system design are surveyed and specific instances of such interactions are described. Examination of the interactions that a traditional design process in which the numerical values of major design variables are decided consecutively is likely to lead to a suboptimal design. Supporting numerical examples are a glider and a space antenna. Under an alternative approach introduced, the design and its sensitivity data from the subsystems and disciplines are generated concurrently and then made available to the system designer enabling him to modify the system design so as to improve its performance. Examples of a framework structure and an airliner wing illustrate that approach.

Sobieszczanski-Sobieski, Jaroslaw↗
NASA NTRS1986

Interdisciplinary and multilevel optimum design

Interactions among engineering disciplines and subsystems in engineering system design are surveyed and specific instances of such interactions are described. Examination of the interactions that a traditional design process in which the numerical values of major design variables are decided consecutively is likely to lead to a suboptimal design. Supporting numerical examples are a glider and a space antenna. Under an alternative approach introduced, the design and its sensitivity data from the subsystems and disciplines are generated concurrently and then made available to the system designer enabling him to modify the system design so as to improve its performance. Examples of a framework structure and an airliner wing illustrate that approach.

Sobieszczanski-Sobieski, Jaroslaw↗
NASA NTRS1986

Evaluation of several modal methods for transient structural analysis

The convergence properties of three modal methods for solving structural transient response (STR) problems are examined by comparing the accuracy of the total number of modes used to represent the responses. The goal is to identify a method which involves as few degrees of freedom as possible. Two mode superposition methods, the mode displacement method (MDM) and the mode acceleration method (MAM), are fitted with equivalent expressions for damped response. An error norm is employed to compare the accuracies of the methods in calculating displacements, moments, and shear forces for a viscously-damped cantilevered beam experiencing several dynamic loading conditions and levels of damping. The MAM converges quicker and uses fewer dof, mainly because it has a pseudo-static response term which accounts for some of the flexibility of higher modes. A third method, which integrates the convolution integral iteratively over time, generates a higher order approximation to the STR with a reduced number of modes. It converges fastest among the three, but requires definition of an appropriate forcing function. Finally, the MAM and MDM models are applied to study the effects of the forcing frequency and the initial conditions.

Camarda, Charles J.↗
NASA NTRS1986

Interdisciplinary optimum design

Problems related to interdisciplinary interactions in the design of a complex engineering systems are examined with reference to aerospace applications. The interdisciplinary optimization problems examined include those dealing with controls and structures, materials and structures, control and stability, structure and aerodynamics, and structure and thermodynamics. The discussion is illustrated by the following specific applications: integrated aerodynamic/structural optimization of glider wing; optimization of an antenna parabolic dish structure for minimum weight and prescribed emitted signal gain; and a multilevel optimization study of a transport aircraft.

Sobieszczanski-Sobieski, Jaroslaw↗
NASA NTRS1985

A compressive failure model for anisotropic plates with a cutout under compressive and shear loads

Failure models for the prediction of compressive strength of plates with a hole are investigated. One of the models is based on the strength failure of the fibers that leads to fiber kinking failure. A different version is developed for cases where shear failure of the fibers is expected to be a dominate failure mode. Both models are capable of including the effects of combined shearing and compressive stresses around a hole in a plate and, therefore, are expected to be applicable to plates under combined shearing and compressive loadings, as well as anisotropic plates.

Guerdal, Zafer↗