Computational aspects of sensitivity calculations in transient structural analysis

A key step in the application of formal automated design techniques to structures under transient loading is the calculation of sensitivities of response quantities to the design parameters. This paper considers structures with general forms of damping acted on by general transient loading and addresses issues of computational errors and computational efficiency. The equations of motion are reduced using the traditional basis of vibration modes and then integrated using a highly accurate, explicit integration technique. A critical point constraint formulation is used to place constraints on the magnitude of each response quantity as a function of time. Three different techniques for calculating sensitivities of the critical point constraints are presented. The first two are based on the straightforward application of the forward and central difference operators, respectively. The third is based on explicit differentiation of the equations of motion. Condition errors, finite difference truncation errors, and modal convergence errors for the three techniques are compared by applying them to a simple five-span-beam problem. Sensitivity results are presented for two different transient loading conditions and for both damped and undamped cases

Reducing distortion and internal forces in truss structures by member exchanges

Manufacturing errors in the length of members or joint diameters of large truss reflector backup structures may result in unacceptable large distortion errors or member forces. However, it may be possible to accurately measure these length or diameter errors. The present work suggests that a member and joint placement strategy may be used to reduce distortion errors and internal member forces. A member and joint exchange algorithm is used to demonstrate the potential of this approach on several 102-member and 660-member truss reflector structures. It is shown that it is possible to simultaneously reduce the rms of the surface error and the rms of member forces by two orders of magnitude by member and joint exchanges

Marginal Effects in the Bivariate Probit Model

This paper derives the marginal effects for a conditional mean function in the bivariate probit model. A general expression is given for a model which allows for sample selectivity and heteroscedasticity. The computations are illustrated using microeconomic data from a study on credit scoring

Do Undergraduate Majors or Ph.D. Students Affect Faculty Size?

Regression analysis using panel data for 42 colleges and universities over 14 years suggests that the economics faculty size of universities offering a Ph.D. in economics is determined primarily by the long-run average number of Ph.D. degrees awarded annually; the number of full-time faculty increases at almost a one-for-one pace as the average number of Ph.D.s grows. Faculty size at Ph.D. granting universities is largely unresponsive to changes in the contemporaneous number of undergraduate economics degrees awarded at those institutions. Similarly, faculty size at colleges where a bachelor’s is the highest degree awarded is responsive to the long and short term average number of economics degrees awarded but not the annual changes in BS and BA degrees awarded in economics.faculty size, student body, Ph.D. degrees, bachelor degrees

Does Teaching Load Affect Faculty Size?

Random effects estimates using panel data for 42 colleges and universities over 16 years reveal that the economics faculty size of universities offering a Ph.D. in economics is determined primarily by the long-run average number of Ph.D. degrees awarded annually; the number of full-time faculty increases at almost a one-for-one pace as the average number of Ph.D.s grows. Faculty size at Ph.D. granting universities is largely unresponsive to changes in the number of undergraduate economics degrees awarded at those institutions. In contrast, faculty size at colleges where a bachelor's is the highest degree awarded is responsive to the average number of economics degrees awarded annually, growing by about one for each additional eleven graduating economics majors.student body, faculty size, Ph.D. degrees, bachelor degrees

Structural analysis of a thermal insulation retainer assembly

In January 1989 an accident occurred in the National Transonic Facility wind tunnel at NASA Langley Research Center that was believed to be caused by the failure of a thermal insulation retainer. A structural analysis of this retainer assembly was performed in order to understand the possible failure mechanisms. Two loading conditions are important and were considered in the analysis. The first is the centrifugal force due to the fact that this retainer is located on the fan drive shaft. The second loading is a differential temperature between the retainer assembly and the underlying shaft. Geometrically nonlinear analysis is required to predict the stiffness of this component and to account for varying contact regions between various components in the assembly. High, local stresses develop in the band part of the assembly near discontinuities under both the centrifugal and thermal loadings. The presence of an aluminum ring during a portion of the part's operating life was found to increase the stresses in other regions of the band. Under the centrifugal load, high bending stresses develop near the intersection of the band with joints in the assembly. These high bending stresses are believed to be the most likely cause for failure of the assembly

Computational Aspects of Sensitivity Calculations in Linear Transient Structural Analysis

A study has been performed focusing on the calculation of sensitivities of displacements, velocities, accelerations, and stresses in linear, structural, transient response problems. One significant goal was to develop and evaluate sensitivity calculation techniques suitable for large-order finite element analyses. Accordingly, approximation vectors such as vibration mode shapes are used to reduce the dimensionality of the finite element model. Much of the research focused on the accuracy of both response quantities and sensitivities as a function of number of vectors used. Two types of sensitivity calculation techniques were developed and evaluated. The first type of technique is an overall finite difference method where the analysis is repeated for perturbed designs. The second type of technique is termed semianalytical because it involves direct, analytical differentiation of the equations of motion with finite difference approximation of the coefficient matrices. To be computationally practical in large-order problems, the overall finite difference methods must use the approximation vectors from the original design in the analyses of the perturbed models

Inflation as a Probe of Short Distance Physics

We show that a string-inspired Planck scale modification of general relativity can have observable cosmological effects. Specifically, we present a complete analysis of the inflationary perturbation spectrum produced by a phenomenological Lagrangian that has a standard form on large scales but incorporates a string-inspired short distance cutoff, and find a deviation from the standard result. We use the de Sitter calculation as the basis of a qualitative analysis of other inflationary backgrounds, arguing that in these cases the cutoff could have a more pronounced effect, changing the shape of the spectrum. Moreover, the computational approach developed here can be used to provide unambiguous calculations of the perturbation spectrum in other heuristic models that modify trans-Planckian physics and thereby determine their impact on the inflationary perturbation spectrum. Finally, we argue that this model may provide an exception to constraints, recently proposed by Tanaka and Starobinsky, on the ability of Planck-scale physics to modify the cosmological spectrum.Comment: revtex, 8 pages, eps figures included, references adde