Thesis (Sc.D.)--Massachusetts Institute of Technology, Dept. of Civil Engineering, 1980. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING. / Bibliography: leaves 180-184. / by Hooshang Banon. / Sc.D.

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The semi-analytical method, widely used for calculating derivatives of static response with respect to design variables for structures modeled by finite elements, is studied in this research. The research shows that the method can have serious accuracy problems for shape design variables in structures modeled by beam, plate, truss, frame, and solid elements. Local and global indices are developed to test the accuracy of the semi-analytical method. The local indices provide insight into the problem of large errors for the semi-analytical method. Local error magnification indices are developed for beam and plane truss structures, and several examples showing the severity of the problem are presented. The global index provides us with a general method for checking the accuracy of the semi-analytical method for any type of model. It characterizes the difference in errors between a general finite-difference method and the semi-analytical method. Moreover, a method improving the accuracy of the semi-analytical method (when possible) is provided. Examples are presented showing the use of the global index. / Ph. D.

The method of dimensional analysis has been used for almost a century with experimental methods to obtain, among other things, prediction equations in the physical sciences and engineering. Only recently has the method been considered in the statistical sense. A thorough literature research is presented, including history, method and theory, problems, and disadvantages of dimensional analysis. The dimensional analysis preliminary model is transformed into a multiple linear regression model and is compared to a quadratic regression model with respect to prediction of a single variable in some practical examples. Whereas dimensions are the main consideration in the dimensional analysis model, they are ignored in the quadratic regression model. Two sets of experimental data were used, each set on both models, and the respective residual sum of squares and multiple correlation coefficients compared. The results were similar in both cases. The correlation coefficients of the quadratic model were higher than those of the dimensional analysis model and the residual sum of squares were lower for the quadratic than for the dimensional analysis model. / M.S.

Master of Science

The first experiment consisted of the making and testing of a cardboard model of a beam fixed at both ends. The results obtained from the model compared very favorably with the mathematical solution as there was a variation of only 1.8 percent. The second experiment was performed with a cardboard model of a bent fixed at both supports. The results from the model as compared to the mathematical solution could not be made to check very closely. There was a variation up to 10 percent in the influence lines for moment for horizontal loads, and a difference as high as 50 percent for vertical loads. It was found after the experiment was performed that the modulus of elasticity of the columns was about four times as great as the modulus in the girder. Then after making the correction in the mathematical solution for the difference in the modulus of elasticity there were only three points that showed a variation of over six percent, and most of the points were under 3½ percent. / M.S.

Moment Distribution Method was modified so that simple techniques applicable to symmetrical and anti-symmetrical frames may be applied to non-symmetrical rigid frames consisting of prismatic members. This approach simplifies considerably the calculations. Using the above approach, two different "Simplified Moment Distribution Methods" were introduced. Method No. l, an “exact” method, makes it possible to execute moment distribution in a single cycle. The “exact" values of the unknown moments are obtained by solving a set of simultaneous equations. This method is applicable to single-bay frames having an arbitrary number of stories. In the solution there is one unknown moment and one equation for each story. Method No. 2 simplifies the analysis of multiple-bay, multiple-story frames. It is a modified version of the standard moment distribution. Only half of the total number of joints has to be considered in this analysis and the convergence of the iteration process is accelerated. The presentation of the theory is preceded by the definition of a set of modified constants pertinent to the two methods. Illustrative examples for the analysis of single-bay as well as multiple-bay frames are included. / Master of Science

Experiments were conducted to measure the three-dimensional static and free vibrational response of two graphite-epoxy, thin-walled, open section frames. The frames are semi-circular with a radius of three feet, and one specimen has an I cross section and the other has a channel cross section. The flexibility influence coefficients were measured in static tests for loads applied at midspan with the ends of the specimens clamped. Natural frequencies and modes were determined from vibrational tests for free and clamped end conditions. The experimental data is used to evaluate a new finite element which was developed specifically for the analysis of curved, thin-walled structures. The formulation of the element is based on a Vlaysov-type, thin-walled, curved beam theory. The predictions from the finite element program generally correlated well with the experimental data for the symmetric I-specimen. Discrepancies in some of the data were found to be due to flexibility in the â clamped' end conditions. With respect to the data for the channel specimen, the correlation was less satisfactory. The finite element analysis predicted the out-of-plane response of the channel specimen reasonably well, but large discrepancies occurred between the predicted in-plane response and the experimental data. The analysis predicted a much more compliant in-plane response then was observed in the experiments. / Master of Science

With a great amount of research currently being aimed towards dynamic analysis and control of very large, flexible structures, the need for accurate knowledge of the properties of a structure in terms of the mass, damping, and stiffness matrices is of extreme importance. Typical problems associated with existing structural model identification methods are: (i) non-unique solutions may be obtained when utilizing only free-response measurements (unless some parameters are fixed at their nominal values), (ii) convergence may be difficult to achieve if the initial estimate of the parameters is not "close" to the truth, (iii) physically unrealistic coupling in the system matrices may occur as a consequence of the identification process, (iv) large, highly redundant parameter sets may be required to characterize the system, and (v) large measurement sets may be required. To overcome these problems, a novel identification technique is developed in this dissertation to determine the mass, damping, and stiffness matrices of an undamped, lightly damped, or significantly damped structure from a small set of measurements of both free-response data (natural frequencies, damping factors) and forced-response data (frequency response functions). The identification method is first developed for undamped structures. Through use of the spectral decomposition of the frequency response matrix and the orthogonality properties of the mode shapes, a unique identification of the mass and stiffness matrices is obtained. The method is also shown to be easily incorporated into a substructure synthesis package for identifying high-order systems. The method is then extended to include viscous damped structures. A matrix perturbation approach is developed for lightly damped structures, in which the mass and stiffness matrices are identified using the imaginary components of the measured eigenvalues and, as a post-processor, the damping matrix is obtained from the real components of the measured eigenvalues. For significantly damped structures, the mass, dauping, and stiffness matrices are identified simultaneously. A simple, practical method is also developed for identification of the time-varying relaxation modulus associated with a viscoelastic structure. By assuming time-localized elastic behavior, the relaxation modulus is determined from a series of identification tests performed at various times throughout the response history. Many interesting examples are presented throughout the dissertation to illustrate the applicability and potential of the identification method. It is observed from the numerical results that the uniquely identified structure agrees with simulated measurements of both free and forced·response records. / Ph. D.

Thesis (Ph. D.)--University of Canterbury, 2009. / Typescript (photocopy). "July 2009." Includes bibliographical references. Also available via the World Wide Web.