(************** Content-type: application/mathematica ************** CreatedBy='Mathematica 4.2' Mathematica-Compatible Notebook This notebook can be used with any Mathematica-compatible application, such as Mathematica, MathReader or Publicon. The data for the notebook starts with the line containing stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). 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For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. *******************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 39628, 885]*) (*NotebookOutlinePosition[ 40292, 908]*) (* CellTagsIndexPosition[ 40248, 904]*) (*WindowFrame->Normal*) Notebook[{ Cell["16.21 Techniques of structural analysis and design", "Title", TextAlignment->Center, FontSize->18], Cell["\<\ Home assignment 6 \ \>", "Subtitle", TextAlignment->Center, FontSize->18], Cell["\<\ Question 5 a: Problem 7.36 a from textbook\ \>", "Subtitle"], Cell[BoxData[ \(Clear["\"]; Off[General::spell, General::spell1];\)], "Input",\ FontSize->24], Cell["\<\ Simply supported beam on an elastic foundation under uniform \ distributed load. \ \>", "Title", FontSize->24], Cell["1) Seek approximate solutions of the form:", "Subtitle", FontSize->24], Cell[BoxData[{ \(Ck[n_] := \ Table[ck[i], {i, n}]\), "\[IndentingNewLine]", \(\[Phi]k[n_]\ := \ Table[Sin[\((2\ i - 1)\)\ \[Pi]\ x\/L], {i, n}]\), "\[IndentingNewLine]", \(w[n_]\ := \ Ck[n] . \[Phi]k[n]\)}], "Input", FontSize->24], Cell[CellGroupData[{ Cell[BoxData[ \(w[2]\)], "Input", FontSize->24], Cell[BoxData[ \(ck[1]\ Sin[\(\[Pi]\ x\)\/L] + ck[2]\ Sin[\(3\ \[Pi]\ x\)\/L]\)], "Output"] }, Open ]], Cell["\<\ 2) Define the approximate potential \[CapitalPi](Ck) for this \ problem\ \>", "Subtitle", FontSize->24], Cell[BoxData[ RowBox[{"\[IndentingNewLine]", RowBox[{ RowBox[{ StyleBox["\[CapitalPi]", FontSize->24], "[", "n_", "]"}], " ", ":=", \(\(\(ym\ im\)\/2\) \(\[Integral]\_0\%L\ \(\((\[PartialD]\_\(x, \ x\)w[n])\)\^2\) \[DifferentialD]x\)\ + \ \(k\/2\) \(\[Integral]\_0\%L\ \(w[ n]\^2\) \[DifferentialD]x\)\ - \ q0\ \(\[Integral]\_0\%L w[n] 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