Many structures are sensitive to initial imperfections, sometimes leading to a great decrease in buckling load. Koiter showed that the effect of initial imperfections is largely determined by the initial post-buckling behavior of the perfect structure. The present work seeks to implement Koiter’s method of asymptotic post-buckling analysis on a finite element program Engineering Analysis Language (EAL). EAL is based on engineering strain measures. It is shown via examples that the predicted post-buckling behavior of a structure for engineering strain measure is approximately the same as that for Green’s strain measure provided the strains are small. To characterize the post-buckling behavior by Koiter’s method in the finite element form, the linear and incremental stiffness matrices are required. These matrices comprise the tangent stiffness matrix. As EAL uses the modified Newton-Raphson procedure to solve nonlinear structures, it calculates the tangent stiffness. The first and second order incremental stiffnesses are extracted by partial differentiation of the tangent stiffness using a second order central difference scheme. The linear stiffness is directly given by the EAL processor ”K”. These stiffnesses are then used to get the post-buckling load-displacement behavior close to the bifurcation point. Numerical results for the initial post-buckling behavior are obtained for truss and frame structures using the Koiter’s analysis procedure on EAL. It is compared to the nonlinear load-displacement behavior of the structures with small initial imperfections. The post-buckling load-displacement behavior for a knee frame is also compared to the behavior obtained experimentally by Roorda [19] and analytically by Koiter [13]. The asymptotic analysis procedure has given good asymptotic post-buckling results. / Master of Science

The buckling constant for neutron moderators in the shape of an elliptic cylinder, hemisphere, and"piggy-back" cylinder has been determined by experimental measurements using paraffin as a moderator. The pulsed neutron sources technique was used throughout the work; a fast neutron burst of short duration was injected into regular paraffin shapes (cylinders with diameter and height ratio equal approximately to one). An empirical curve of decay constant of the neutron population versus the buckling was obtained. The measured decay constant, λ, was fitted by the method of least square to a parabola in B² of the form: λ=Σ_av+ B²D - CB⁴ where λ= the decay constant B² = the buckling constant Σ_a = the macroscopic absorption cross section v = the neutron velocity D = diffusion coefficient C = diffusion cooling coefficient The resulting values of the diffusion parameters are: Σ_a v = 4858 ± 162 sec⁻¹ D = 25911 ± 202 sec⁻¹ cm² C = 1186 ± 2558 sec⁻¹ cm⁴ By measuring the decay constant, the buckling of the moderators with irregular shapes were determined from the above parameters. The result was in general accord with the theoretical approximations for such shapes. / Master of Science

The first purpose of the present paper is to provide an elastic theory from which problems involving coupling may be approached. Potential energy and equilibrium expressions will be derived for these are the components of the theory which are lacking. The potential energy expression may be used either in small- or large-deflection analysis. Equations of equilibrium are presented for both small- and large-deflection theory. The second purpose of the present paper is to determine the effect of coupling on deflections and buckling of a simple supported anisotropic plate in compression. A small deflection analysis of this problem is made using the theory presented herein. No large deflection analysis is attempted; however, an estimation of the large deflection effect of coupling is made. The electric theory presented herein forms a basis from which problems involving coupling may be treated. The significance of coupling is most apparent in problems which would involve stability considerations in the absence of coupling. The presence of deflections due to coupling prior to reaching the uncoupled buckling load forces the problem to be treated asa one of deflections rather than stability. Coupling has a general detrimental effect upon this type of problem in that it lowers the load at which deflections grow rapidly (that is, buckling in the uncoupled case). The effect of coupling on the buckling of plates of equal bending stiffnesses in their two orthogonal directions becomes negligible as the aspect ratio of the plate becomes large. Some lateral deflection prior to buckling will occur, however, even for large aspect ratios. The general anisotropic plate is considered in the small-deflections solution to the differential equation of equilibrium. Computations were made for cases in which the bending stiffness were equal. The equations and methods are applicable to cases in which the bending stiffness are not equal. / Master of Science

Typescript (photocopy). / Digitized by Kansas Correctional Industries

Thesis. 1975. M.S.--Massachusetts Institute of Technology. Dept. of Ocean Engineering. / Includes bibliographical references. / M.S.

Digitized by Kansas Correctional Industries

Thesis. 1978. Ph.D.--Massachusetts Institute of Technology. Dept. of Ocean Engineering. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING. / Includes bibliographical references. / Ph.D.

Abstract not available

This thesis investigates the effects of elastic restraint at the supports on the behaviour of shallow concrete arches, and the time-dependent effects of shrinkage and creep of concrete on the nonlinear behaviour of shallow arches. The nonlinear behaviour of shallow circular arches with elastic rotational restraints at each support and subjected to a uniformly distributed radial load is firstly investigated. A virtual work formulation is used to establish both the nonlinear equilibrium equations and the buckling equilibrium equation for shallow arches. The analytical results show that the effects of the stiffness of the rotational restraints on the prebuckling and buckling response are significant. An analytical model is developed for the in-plane elastic stability analysis of shallow parabolic arches with horizontal spring supports subjected to a uniformly distributed vertical load. A parametric study is undertaken using the proposed analytical model. It is found that the effects of the stiffness of the horizontal springs on the prebuckling response, buckling load and buckling behaviour of arches are significant. An analytical model is developed to simulate the time-dependent behaviour of shallow concrete parabolic arches with horizontal spring supports subjected to a sustained loading, and in particular to investigate creep buckling. The time-dependent buckling load and the critical time (or age) of the arches are calculated by using an iterative process based on the proposed model. A systematic parametric study is undertaken, and the results show that the various parameters have a profound effect on the time-dependent buckling load and the prebuckling life of arches. Both short-term and long-term experimental investigations of shallow parabolic tied concrete arches are described and used to validate the analytical models. For the short-term tests, three concrete arches were subjected to a uniformly distributed vertical load and were loaded to failure. For the long-term tests, seven concrete arches were subjected to sustained service loads. The instantaneous and time-dependent deflections were recorded throughout the period of loading, together with the distribution of the horizontal thrust at the supports. Comparisons between the experimental results and the analytical predictions using the analytical models are made to verify the accuracy of the theoretical models.

Thesis (Ph. D.)--Virginia Polytechnic Institute and State University, 1991. / Vita. Abstract. Includes bibliographical references (leaves 154-158). Also available via the Internet.