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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>Minimization of the Linear Functional</title>
      <link>https://trid.trb.org/View/1124165</link>
      <description><![CDATA[This paper presents some numerical methods for minimization problems as Variational Inequalities of Elliptic (IVE). The numerical analysis, which is obtained based on abstract algorithms and concrete numerical algorithms, is described by software (in Pascal).]]></description>
      <pubDate>Thu, 29 Dec 2011 07:47:46 GMT</pubDate>
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      <title>DIFFRACTION OF ANTI-PLANE SH WAVES BY A SEMI-CIRCULAR CYLINDRICAL HILL WITH AN INSIDE CONCENTRIC SEMI-CIRCULAR TUNNEL</title>
      <link>https://trid.trb.org/View/755519</link>
      <description><![CDATA[An important problem in earthquake engineering and seismology is to explain the amplification or deamplification effects to earthquake responses by surface and subsurface topography.  This article presents a closed-form analytic solution of two-dimensional scattering and diffraction of plane SH waves by a semi-cylindrical hill with a semi-cylindrical concentric tunnel inside an elastic half-space; the authors use the cylindrical wave functions expansion method.  The solution is reduced to solving a set of infinite linear algebraic equations. Fourier expansion theorem with the form of complex exponential function and cosine function is used. Numerical solutions are obtained by truncation of the infinite equations. The authors conclude that the amplification of surface displacement amplitudes at some points around a hill can be as high as two times the free-field motions.  The utilization of complex exponential and cosine forms of Fourier expansion theorem can improve the efficiency and precision of mixed boundary problems.]]></description>
      <pubDate>Mon, 02 May 2005 00:00:00 GMT</pubDate>
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      <title>ANALYSIS OF MULTIBEAM BRIDGES WITH BEAM ELEMENTS OF SLAB AND BOX SECTION</title>
      <link>https://trid.trb.org/View/105338</link>
      <description><![CDATA[SINGLE-SPAN, RIGHT, MULTIBEAM BRIDGES HAVING BEAM ELEMENTS OF SOLID OR HOLLOW SECTION ARE ANALYZED. THE ANALYSIS TREATS THE BEAMS AS INDIVIDUAL ELEMENTS, CONNECTED TO ONE ANOTHER BY FRICTIONLESS HINGES WHICH SIMULATE THE SHEAR KEY AND TRANSVERSE RODS CONNECTING THE BEAMS. THE LONGITUDINAL, VERTICAL, AND TRANSVERSE JOINT FORCES AT EACH HINGE ARE TAKEN AS THE UNKNOWN FUNCTIONS. THE COMPATIBILITY CONDITIONS FOR THE DISPLACEMENTS AT EACH HINGE PROVIDE BASIC EQUATIONS FOR FINDING THE JOINT FORCES. SINCE THE BEAMS ARE ELASTIC AND SIMPLY SUPPORTED AT THEIR ENDS, FOURIER SERIES EXPANSIONS OF ALL THE FORCES AND DISPLACEMENTS ARE USED TO REDUCE THE PROBLEM TO THE SOLUTION OF SETS OF SIMULTANEOUS LINEAR ALGEBRAIC EQUATIONS. SINCE THE FOURIER SERIES FOR THE JOINT FORCES EITHER DO NOT CONVERGE OR ELSE CONVERGE TOO SLOWLY FOR PRACTICAL USE, A METHOD OF ACCELERATING THE CONVERGENCE OF THE FOURIER SERIES FOR THE JOINT FORCES IS PRESENTED, BASED ON A STUDY OF THE ASYMPTOTIC BEHAVIOR OF THE COEFFICIENTS OF THE FOURIER SERIES. THIS METHOD IS COMPUTATIONALLY PRACTICAL AND LEADS TO THE EXPLICIT DETERMINATION OF THE MOST IMPORTANT CHARACTERISTICS OF THE JOINT FORCES. RESULTS FOR THE JOINT FORCE DISTRIBUTIONS AND THE SHEARS AND MOMENTS IN THE BEAMS ARE PRESENTED IN TABLES FOR SELECTED, PRACTICAL MULTIBEAM BRIDGES COMPOSED OF FOUR AND EIGHT BEAMS. /AUTHOR/]]></description>
      <pubDate>Mon, 13 Jun 1994 00:00:00 GMT</pubDate>
      <guid>https://trid.trb.org/View/105338</guid>
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      <title>MATRIX MODEL FOR THE DETERMINATION OF CONSTITUENT TRAFFIC STREAMS FROM POINT MEASUREMENTS</title>
      <link>https://trid.trb.org/View/226162</link>
      <description><![CDATA[No abstract provided.]]></description>
      <pubDate>Thu, 31 Jul 1986 00:00:00 GMT</pubDate>
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