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    <copyright>Copyright © 2026. National Academy of Sciences. All rights reserved.</copyright>
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    <managingEditor>tris-trb@nas.edu (Bill McLeod)</managingEditor>
    <webMaster>tris-trb@nas.edu (Bill McLeod)</webMaster>
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      <title>On the Mathematical Theory of Vehicular Traffic Flow II: Discrete Velocity Kinetic Models</title>
      <link>https://trid.trb.org/View/840492</link>
      <description><![CDATA[This paper discusses the modeling of vehicle traffic flow by using discrete mathematical kinetic theory.  The authors use a discretization developed in the velocity space by a grid adapted to the local density.  This discretization can overcome, at least in part, some technical difficulties related to the selection of the correct representation scale.  The adaptive grid allows an improved description of various phenomena related to vehicular traffic flow.  The authors propose specific models and use qualitative and computer analysis to show the properties of the models, including their abilities to describe real flow conditions.]]></description>
      <pubDate>Wed, 28 Nov 2007 08:26:39 GMT</pubDate>
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      <title>NEW APPROACH TO THE ANALYSIS OF SHELLS, PLATES AND MEMBRANES WITH FINITE DEFLECTIONS</title>
      <link>https://trid.trb.org/View/40072</link>
      <description><![CDATA[This paper presents a new perturbation method of analysis applicable to a class of geometrically non-linear problems of shells, plates, and membranes with translationally restrained edges.  The perturbation parameter is a linear function of Poisson's ratio.  The convergence of successive perturbations (i.e., approximations) is independent of the magnitudes of deflections.  Several solutions and results are obtained for the purposes of illustration and discussion.  Whenever possible, calculated values are compared with results obtained by other means.]]></description>
      <pubDate>Wed, 13 Aug 1975 00:00:00 GMT</pubDate>
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      <title>MULTIPLE BUCKLED STATES OF RECTANGULAR PLATES</title>
      <link>https://trid.trb.org/View/24864</link>
      <description><![CDATA[The article considers the buckling of a simply supported plate subjected to a constant edge thrust.  A study of the nonlinear static problem indicates that there are nine possible equilibrium states.  One of these corresponds to the unbuckled state while the remaining eight represent buckled states.  A linear stability analysis and a calculation of the potential energy of each of the static solutions indicates that four of the solutions are stable and five are unstable.]]></description>
      <pubDate>Tue, 31 Dec 1974 00:00:00 GMT</pubDate>
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      <title>NON-LINEAR SHALLOW WATER THEORY</title>
      <link>https://trid.trb.org/View/20089</link>
      <description><![CDATA[The equations controlling the three dimensional motion of a viscous, incompressible fluid in shallow water, are derived for use in any orthogonal coordinate system. Simplified equations for two dimensional motion are also developed.  The equations are developed in terms of special coordinate dependent functions.]]></description>
      <pubDate>Sat, 05 Oct 1974 00:00:00 GMT</pubDate>
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      <title>STABILITY OF WHIRLING SHAFTS WITH INTERNAL AND EXTERNAL DAMPING</title>
      <link>https://trid.trb.org/View/18407</link>
      <description><![CDATA[Necessary and sufficient conditions for the stability of motion of whirling shafts are established using the direct method of Lyapunov.  The non-linear mathematical model employed is based on the work of V.V. Bolotin and includes the effects of both internal and external damping.  A coordinate transformation is used to facilitate the analysis.  In effect, this transformation establishes a mathematical equivalence between the governing equations for a whirling shaft with both internal and external damping, and the governing equations for a whirling shaft with internal damping only.]]></description>
      <pubDate>Thu, 28 Feb 1974 00:00:00 GMT</pubDate>
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