assn2_solution

assn2_solution - (************** Content-type:...

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Unformatted text preview: (************** Content-type: application/mathematica ************** CreatedBy='Mathematica 5.0' 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). NOTE: If you modify the data for this notebook not in a Mathematica- compatible application, you must delete the line below containing the word CacheID, otherwise Mathematica-compatible applications may try to use invalid cache data. For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: [email protected] phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. *******************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 15775, 577]*) (*NotebookOutlinePosition[ 56629, 1907]*) (* CellTagsIndexPosition[ 56585, 1903]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell["16.21 Techniques of structural analysis and design", "Title", TextAlignment->Center, FontSize->18], Cell["\<\ Home assignment 2 \ \>", "Subtitle", TextAlignment->Center, FontSize->18], Cell[TextData[{ "Question 1: The question in these problems is whether the differential \ equations of equilibrium are satisfied, i.e.:\n\n", Cell[BoxData[ \(TraditionalForm\`\[PartialD]\_\(x\_j\)\[Sigma]\_ji\ = \ \(\(0\)\(\ \ \)\(?\)\)\)]] }], "Subtitle", FontSize->18], Cell["\<\ a) (not for grade) \ \>", "Subtitle", FontSize->18], Cell[BoxData[{ \(\(\[Sigma]\_\(1, 1\)\ = \ \(-3\)\ x\_1\ + \ 6\ x\_2;\)\), "\[IndentingNewLine]", \(\(\[Sigma]\_\(1, 2\)\ = \ \(\[Sigma]\_\(\(2\)\(,\)\(1\)\(\ \ \)\) = 4\ x\_1\ + \ 3\ x\_2\);\)\), "\[IndentingNewLine]", \(\(\[Sigma]\_\(2, 2\)\ = \ 5\ x\_1\ + \ 4\ x\_2;\)\)}], "Input", FontSize->18], Cell[CellGroupData[{ Cell[BoxData[ \(\(\(Table[ Sum[\[PartialD]\_\(x\_j\)\[Sigma]\_\(j, i\), \ {j, 3}], {i, 3}]\)\(\ \)\)\)], "Input", FontSize->18], Cell[BoxData[ \({0, 8, 0}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["\<\ The stress field given is not equilibrium (b)\ \>", "Subtitle", FontSize->18], Cell[BoxData[{ \(\(\[Sigma]\_\(1, 1\)\ = \ c\_1\ x\_1\ + \ c\_2\ x\_\(\(2\)\(\ \)\)\^2 + \ c\_3\ x\_1\ x\_2\ + \ c\_4\ x\_1;\)\), "\[IndentingNewLine]", \(\(\[Sigma]\_\(1, 2\)\ = \ \(\[Sigma]\_\(\(2\)\(,\)\(1\)\(\ \ \)\) = \(\...
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This note was uploaded on 11/07/2011 for the course AERO 16.30 taught by Professor Ericferon during the Spring '04 term at MIT.

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assn2_solution - (************** Content-type:...

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