<?xml version="1.0" encoding="UTF-8"?>
<Worksheet>
<Version major="7" minor="1"/>
<Label-Scheme value="2" prefix=""/>
<View-Properties presentation="false"><Hide name="Group Range"/><Hide name="Section Range"/></View-Properties>
<MapleNet-Properties warnlevel="3" longdelim="true" plotoptions="" echo="1" errorcursor="false" elisiontermsthreshold="10000" elisiontermsbefore="100" errorbreak="1" prettyprint="3" prompt="&gt; " latexwidth="9.0" useclientjvm="true" ansi="false" screenheight="25" labelwidth="20" plotdevice="inline" typesetting="standard" displayprecision="-1" indentamount="4" elisiondigitsthreshold="10000" quiet="false" plotoutput="terminal" rtablesize="10" preplot="" showassumed="1" plotdriver="openviz" elisiontermsafter="100" labelling="true" postplot="" screenwidth="79" elisiondigitsbefore="100" elisiondigitsafter="100" verboseproc="1" imaginaryunit="I" ShowLabels="true"/>
<Styles><Font name="Heading 4" background="[255,255,255]" bold="false" executable="false" family="Serif" foreground="[0,0,0]" italic="true" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false"/>
<Font name="Ordered List 5" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false"/>
<Font name="Ordered List 1" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false"/>
<Font name="Text Output" background="[255,255,255]" bold="false" executable="false" family="Monospaced" foreground="[0,0,255]" italic="false" opaque="false" readonly="true" size="12" subscript="false" superscript="false" underline="false"/>
<Font name="Bullet Item" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false"/>
<Font name="Equation Label" background="[255,255,255]" bold="true" executable="false" family="Monospaced" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false"/>
<Font name="Author" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false"/>
<Font name="Text" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false"/>
<Font name="Diagnostic" background="[255,255,255]" bold="false" executable="false" family="Monospaced" foreground="[40,120,40]" italic="false" opaque="false" readonly="true" size="12" subscript="false" superscript="false" underline="false"/>
<Font name="Heading 2" background="[255,255,255]" bold="true" executable="false" family="Serif" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="16" subscript="false" superscript="false" underline="false"/>
<Font name="Page Number" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="10" subscript="false" superscript="false" underline="false"/>
<Font name="Ordered List 3" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false"/>
<Font name="Maple Plot" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false"/>
<Font name="Normal" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false"/>
<Font name="Maple Input" background="[255,255,255]" bold="true" executable="true" family="Monospaced" foreground="[255,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false"/>
<Font name="Annotation Title" background="[255,255,255]" bold="true" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="18" subscript="false" superscript="false" underline="false"/>
<Font name="2D Output" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,255]" italic="false" opaque="false" readonly="true" size="12" subscript="false" superscript="false" underline="false"/>
<Font name="2D Inert Output" background="[255,255,255]" bold="false" executable="true" family="Times New Roman" foreground="[144,144,144]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false"/>
<Font name="Dictionary Hyperlink" background="[255,255,255]" bold="false" executable="false" family="Serif" foreground="[147,0,15]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="true"/>
<Font name="Dash Item" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false"/>
<Font name="Heading 3" background="[255,255,255]" bold="true" executable="false" family="Serif" foreground="[0,0,0]" italic="true" opaque="false" readonly="false" size="14" subscript="false" superscript="false" underline="false"/>
<Font name="Ordered List 4" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false"/>
<Font name="Maple Output" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false"/>
<Font name="List Item" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false"/>
<Font name="2D Input" background="[255,255,255]" bold="false" executable="true" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false"/>
<Font name="Line Printed Output" background="[255,255,255]" bold="false" executable="false" family="Monospaced" foreground="[0,0,255]" italic="false" opaque="false" readonly="true" size="12" subscript="false" superscript="false" underline="false"/>
<Font name="Maple Input Placeholder" background="[255,255,255]" bold="true" executable="true" family="Monospaced" foreground="[200,0,200]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false"/>
<Font name="2D Math" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false"/>
<Font name="Error" background="[255,255,255]" bold="false" executable="false" family="Monospaced" foreground="[255,0,255]" italic="false" opaque="false" readonly="true" size="12" subscript="false" superscript="false" underline="false"/>
<Font name="Warning" background="[255,255,255]" bold="false" executable="false" family="Monospaced" foreground="[0,0,255]" italic="false" opaque="false" readonly="true" size="12" subscript="false" superscript="false" underline="false"/>
<Font name="Heading 1" background="[255,255,255]" bold="true" executable="false" family="Serif" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="18" subscript="false" superscript="false" underline="false"/>
<Font name="Annotation Text" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false"/>
<Font name="Title" background="[255,255,255]" bold="true" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="18" subscript="false" superscript="false" underline="false"/>
<Font name="Ordered List 2" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false"/>
<Font name="Hyperlink" background="[255,255,255]" bold="false" executable="false" family="Serif" foreground="[0,128,128]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="true"/>
<Layout name="Ordered List 5" alignment="left" bullet="ROMAN" firstindent="0" leftmargin="144" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="-1"/>
<Layout name="Heading 4" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0"/>
<Layout name="Text Output" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="newline" pagebreak-before="false" initial="0"/>
<Layout name="Ordered List 1" alignment="left" bullet="numeric" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="-1"/>
<Layout name="Annotation Title" alignment="centred" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="12" spacebelow="12" linebreak="space" pagebreak-before="false" initial="0"/>
<Layout name="Bullet Item" alignment="left" bullet="dot" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="0"/>
<Layout name="Author" alignment="centred" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="8" spacebelow="8" linebreak="space" pagebreak-before="false" initial="0"/>
<Layout name="Dash Item" alignment="left" bullet="dash" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="0"/>
<Layout name="Heading 3" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0"/>
<Layout name="Diagnostic" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="any" pagebreak-before="false" initial="0"/>
<Layout name="Ordered List 4" alignment="left" bullet="ALPHABETIC" firstindent="0" leftmargin="108" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="-1"/>
<Layout name="Maple Output" alignment="centred" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.3" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0"/>
<Layout name="Line Printed Output" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="any" pagebreak-before="false" initial="0"/>
<Layout name="List Item" alignment="left" bullet="indent" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="0"/>
<Layout name="Heading 2" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="7" spacebelow="2" linebreak="space" pagebreak-before="false" initial="0"/>
<Layout name="Ordered List 3" alignment="left" bullet="roman" firstindent="0" leftmargin="72" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="-1"/>
<Layout name="Error" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0"/>
<Layout name="Maple Plot" alignment="centred" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0"/>
<Layout name="Warning" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0"/>
<Layout name="Heading 1" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="7" spacebelow="4" linebreak="space" pagebreak-before="false" initial="0"/>
<Layout name="Title" alignment="centred" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="12" spacebelow="12" linebreak="space" pagebreak-before="false" initial="0"/>
<Layout name="Ordered List 2" alignment="left" bullet="alphabetic" firstindent="0" leftmargin="36" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="-1"/>
<Layout name="Normal" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0"/>
<Pencil-style name="Pencil 3" pen-color="[0,0,0]" pen-height="3.0" pen-width="3.0" pen-opacity="1.0"/>
<Pencil-style name="Pencil 1" pen-color="[0,0,0]" pen-height="1.0" pen-width="1.0" pen-opacity="1.0"/>
<Pencil-style name="Pencil 5" pen-color="[255,0,0]" pen-height="5.0" pen-width="5.0" pen-opacity="1.0"/>
<Pencil-style name="Pencil 2" pen-color="[0,0,255]" pen-height="1.0" pen-width="1.0" pen-opacity="1.0"/>
<Pencil-style name="Pencil 4" pen-color="[0,0,255]" pen-height="3.0" pen-width="3.0" pen-opacity="1.0"/>
<Highlighter-style name="Highlighter 2" pen-color="[255,204,0]" pen-height="14.0" pen-width="14.0" pen-opacity="0.8"/>
<Highlighter-style name="Highlighter 4" pen-color="[0,255,255]" pen-height="32.0" pen-width="32.0" pen-opacity="0.8"/>
<Highlighter-style name="Highlighter 3" pen-color="[51,255,0]" pen-height="24.0" pen-width="24.0" pen-opacity="0.8"/>
<Highlighter-style name="Highlighter 1" pen-color="[255,153,255]" pen-height="12.0" pen-width="8.0" pen-opacity="0.8"/>
<Highlighter-style name="Highlighter 5" pen-color="[255,255,0]" pen-height="48.0" pen-width="48.0" pen-opacity="0.8"/>
</Styles>
<Page-Numbers enabled="false" first-number="1" first-numbered-page="1" horizontal-location="right" style="Page Number" vertical-location="bottom"/>
<Task-table>
    <Task-category name="&lt;default&gt;">
    </Task-category>
</Task-table><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L53" drawlabel="true">
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<Text-field style="Title" layout="Title"><Font family="Arial" size="22">The Relaxation function problem of an orthotropic cylinder</Font></Text-field>
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<Text-field style="Author" layout="Author"><Font bold="true" size="16">Co. H. Tran.</Font>
<Font italic="true">Faculty of Mathematics, University of Natural Sciences - VNU-HCM </Font></Text-field>
<Text-field style="Author" layout="Author">   <Hyperlink linktarget="mailto:coth123@math.com" hyperlink="true"><Font style="Author" underline="true" foreground="[0,128,128]">coth123@math.com</Font></Hyperlink>  &amp;   <Hyperlink linktarget="mailto:cohtran@math.com" hyperlink="true"><Font style="Author" underline="true" foreground="[0,128,128]">cohtran@math.com </Font></Hyperlink>          </Text-field>
<Text-field style="Normal" layout="Normal" alignment="centred">Copyright  2007</Text-field>
<Text-field style="Normal" layout="Normal" alignment="centred">June   06   2007</Text-field>
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<Text-field style="Normal" size="14" layout="Normal"><Font size="14">The worksheet presents some thoughts about the plane strain problem of the viscous orthotropic composite materials cylinder under internal and external pressure with</Font></Text-field>
<Text-field style="Normal" size="14" layout="Normal"><Font size="14">respect to using the direct method . To compute the interior stress , from the elastic solution we use the correspondence principle  and the  inverse Laplace transform . </Font></Text-field>
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<Text-field style="Heading 1" layout="Heading 1"><Font family="Arial">1. Analysis of  the composite orthotropic cylinder : </Font></Text-field></Title><Presentation-Block>
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<Text-field style="Text" layout="Normal">We examine an orthotropic viscoelastic composite material cylinder which has the horizontal section within limit of 2 circles : r = a , r = b ( a &lt; b ) . </Text-field>
<Text-field style="Text" layout="Normal">Choosing the cylindrical coordinates r , , z ( the axial z is along with the cylinder ) . The components of stress and deformation  <Image height="25" width="88" zoomable="false">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</Image></Text-field>
<Text-field style="Text" layout="Normal">are functions of  <Font italic="true"> r , t </Font>   respectively . The two components of deformation-tensor :  <Image height="43" width="256" zoomable="false">TUZOV3RLVWI8b2I8Uj1NRExDZE5GOj5aZT5bPEo6XFxLQEBWcnI7b1JMQ1RKY0RYb1h1dXRNS2ZyZ0RAeVVmZ2lQc1ZJY0lvPUY7UVRsPWhKcXNYS1ljY0ZsO0hlP1N1PUdMaXdQR1VST2ZRQ2hFU2lKQ2hfTVVqbUNtPWRSPXVzW0NYa1JbV1hUWWN1PXc8P0dOR1JpY2ZGSVd1P0Y/PWVXW2hmaWdhT0hqd2JnaUZ3dXdzeUdrQ2NzbUZLYXJeaVlhc1JNd2ZpeXh1cXVxeXhfaUNdU3NsO2Y8ZUZiT0RcXD9ESkVmRWRMZFxcWDs8VFtQUlE8cmBZU3FAckZobkppVWhxcF9wb3FNeXhNT2hBVG1xVGNgVGx5TFBlc05geXV5T2ptVF9YalFFcWd4TmlpbHBBVU1ZcUBoeF5xdFN5Vj1YeGlUTlB5cVNodT11dXE9eWBBVnl1TjxlWFBJUFNFUW9ETnlFbUQ8b3dRbGpEbXFtbk9JSkdxTztpVVZVTnc8V189VUVdeU5Mdz1JdXFpS0xpS0hQeTt0TkNkVXNkUHhQZT5GZ2RoeV15YExfeW9BdEZWdnJ3b1BncD5GYD5BYVFBdnFnXFxxUHBTUGdneFxcYVhjOklfb3llPWZgeFZbO0BwRWFxd3d5QkZzX3F4O3F5Z0hybUFzSGlza1ZyV0lpZ15jPEhebkdzPnldPF9taHF5UXBhc3FnYFldWz9cXD9pdVNmdXZYeGlOXWZpalp4XFw/R3ZpSWlqYXdfWXNhd15Bd2JtSHA7X3ZQWW1FWXFhX2BKTl5JRmVXb25gXndpZnZhUXBacGBKWGVmQXlJUWJtZltoP214aXFIQGVjVmJRP15GcHVpeXA7X29ybmJWR3h0T3Y/X3Y7dm1eUXlLP2RJb3Z0SXA+T2pRaXA6P3NjUFpyR2VLb21tT2FmX2BATnVHWGtbb3JUaHZEPm1weWBNb2dNV1xcbElcXFZgZXBoX3BvZjtWXj5OXj9uX2l3eVpWY1pIZTtGcGJBeXdJdm93W0JIX1tPeVRXWl1BeFxcSHRQRnllWWRKZ2dDT2RFQUBFeF9FRztVY3lzZTpjd3hBZGR5aGNnaVxcVXhYO2ZAeUhFO2ZFQ2ROU0lkaUh5W2lgeWlzUWVXY1luQ3I9ZUJIS2hsS1liaUZ0ZVlKd0hrQ3ZqcVU9U0Q+ZWJmP0k9UVk7T2VKd2NueVl4TXRXWXR4XVQ6eUVfS1dzRVZMV0VfZURaQUZNP2Y9b01McVZSVHZLVXR1YFg7PHVfZXNnTVd2YVQ/TG10UHRrPVNObXZLbHBKeWxIPXZicUxsZVtiPnI7SWRbUHVhTmZVYGRuZltaaWs7b2JmRmRRQWJQXlpzP2pUVnFFPnJlZltOR15fTmpER0lrWVtteUVhZHNdVTtVYmhVRFo9SWpNc09dY29HRnI7VlRNRkBtWGB3ZmZfZGRfWWxHR29Nc1RVeGZZRFpJWVFBdkdrdHZDUkdnZT87SExVaDtfRlJJVFZFVzp5ZFNfVldxWExBQ0FLZztfR3FLdT5DZD1jVHNtZFxcY2hrWXVid1JAUVJCO3ZZRWljXURDcVZET0ZkW0NiQ0hMUWJGb0Zkb3VURUJnRUNUY0hhR0NBRVhWU1VuUVg/O3NNXWdzd1NHU1ZzSVk6O2lmRUZIZ0dlX1U9aUR0RWhlY2NocVJvWVNnZXRkZWNgQWRiTUY9UVl3PWVDQUNgVVZjU2VLcWVuZ3lQR1VNTVRwb0VQcXQ6ZVNCUXhJVWhYaWY9U3hHT0lxVUViP3RWZ2ZVW2VjR0llcWVwbFhPcW5vZXZkeXFTZVdpaVBKVW5nYUplTFljWHZwTW9wSG9jRXFFdUpGTE1vbXdwbmJwb3hFd214dnFxX2lteGdqWGhIZnNoUXdyUW9ySXRcXGZ1VFF5XVllc0d3R1dlUnZgdz9sQ1liVFZkeGBnbHB2XFxXdXVndk5hc2dCSHN4a3V4dUlyT3lnSUd2dVFyZVlmbXlZeD9ZYldId3dJWV91eXNZcUl0XWVyaU1WcVFTQVN1UXdGW3dzWWtpRGl2dElocXl1W3l4RztWO1dUPHVUeD1YQG9IZ21TQT1jVmFpckt5Y1d5W1dZVT1DWnlzbGt1cUtDYXVWcFdnTmtVbHdWO1FoXFxHZEVtdGFjU0J5ZEdtdG5JR1VVRWVVR19vRnY/RkltRF5TYnZBVm5FRUVbaHNrUnRjY3VfWGZHVXB5Q21HZFBhdWlfYkN1WT9jZHc/VU9jaWtRY1hBQ1xcdXJFSVhwUVVlQWNeW1lTeVZHdWRsY0lQcUhIT0hvUUJSc1ddP1ZsP3hvTWZgPWV3XWNUS0RUPWNMO0ZAS2dMR2dXW3JHT2lkQ1RCO0dFUURPVXg/a2hHX2NpU3lmR3lRT2hqT0lOWUVnbUZNZ1NuPUVRP1dvQXZnZ3ZDS0RmW3ViP0VyO1ViW1ZSa3I9P3Nob3lyZ0NcXG1pZlVoYEFJX213bG9mXm9GZl9TSz9EVGdnU2VWbFNFbTtYVVV0aGNFZV9iQktZc0tkdFFiOztlcldTcXN2WkdDd0lXanNTcEVVPHdHdV9nU1N3eW9ib0t4SjtzXVtnP2dUbUVXQXFSckF2V2dkOl1HRFNDRkdTXU1pQ2dYRF9GQ11jQVdFb0VZcG1nYF9nWWlmXUdGSkdTPlVWRnlEWD1EZ2VYVl1WT2dIPUtzbkVVVUF2SjtTSk9JXFxlRlhzVmRbQnNTQ2RRdF9Vc21nZU9BaUV1ZnFfVUBhSWJrUj1lY3RPQ0FBRmA9VUdNZD9xQkhVY287eUpTczxraVpBZ2J3RGhTaFdRUjtFVmtJc1JVRl9fc2FbZ0tbWDxHaFFVRHVjRUpzVG9NdFA/d2NLZXBLd3ZzdTplVWc/UndjQkxXVm13YlRbWVRjV1tJdm5XQkFLZ2dpaXZlREJ1dU5hdmVFY1hVZlZtQlxcTUlpT2g6VWJlYUZRX0JgQVdcXG9SV21JbT9zQktmYXNlP3N0bndXTGNQZVBUUWlXcEF5dlhYSGVKVGh2RFVZYEFNYGl5QERMZVVrY1R4OlRXSEhLO1lQO1lyYXhqSWx5RHV5UFF5c1lvc3BYQUhXUXBLUnhQZGFPcDxUV1xcdHhVS0FBb3JUeT1cXHNURG1FTXd5WXQ9eXFZZFVbSE1XXFxXWW1xd0lzSVBtY0FxUnF4WGFzSjxXTjxUcGB5ckFrZXBOPD1YcGxMa1VPZUByOzxsXFw8TFxcUFZlXFxKPEhPSl1PX3lzZmFUSnB2RGxMPE1raVhPZGBOVUBPZl1QUEVSU0hQREVVY3B4dUxsPnRKW2BLPWBKY2BTblFuSHFWXFx4bnJUTzppTj49Vlh1VWFQcHBhakdJUmRNcjt1VHhJeV1dVFpNUUQ9WXZxSk90UHZtcE1hdD5YSmZdU2pJUGRMcGRBTU88bT08cFpFbUdoWU5tdGdlcFZsbmA8cEFZblVcXE1dUGpZSHFdZFF4VWpEWE90eXdiZFBbQEpleXE7SVBkXFxyQXlXSkVYW0VKcmRTRz1seUlSQHB5a0xPPltMeHVwX2xUQG5oPlo9WWZOO255dVZjRz9mTUBmbl9rRE9sVWZhRU9qRFFnbGFmSXdsW3FyeE5faHhyeVZfWnBqW3h5YGZsRD9sP3B5TWBhZF5oOz5kW1BiUT5aT05fO15seUladlF5dFFsUj9iUHg7PlpDZ2JIX2JoUGJaT0oyOlwiXHtcfQ==</Image></Text-field>
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<Text-field style="Text" layout="Normal">and the differential equation of equilibrium :  <Image height="43" width="228" zoomable="false">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</Image>    </Text-field>
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<Text-field style="Text" layout="Normal">The boundary conditions :  <Image height="23" width="218" zoomable="false">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</Image></Text-field>
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<Text-field style="Heading 1" layout="Heading 1"><Font family="Arial">2. Direct method  :</Font></Text-field></Title><Presentation-Block>
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The direct method is an approximate inversion technic based on  the direct relation between the time  dependence and the transformed solution . If the plot of the viscoelastic solution has small curvature when plotted  with  variables logt  then  :  </Text-field>
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<Text-field style="Text" layout="Normal"> <Image height="40" width="388" zoomable="false">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</Image></Text-field>
<Text-field style="Text" layout="Normal">   (1)                 </Text-field>
<Text-field style="Text" layout="Normal">where  <Image height="43" width="88" zoomable="false">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</Image>     C is Euler's constant ..  </Text-field>
<Text-field style="Text" layout="Normal"> (1) is exact if    <Image height="25" width="56" zoomable="false">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</Image>    ,     <Image height="25" width="56" zoomable="false">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</Image>   is proportional to  logt  .  </Text-field>
<Text-field style="Text" layout="Normal"> (1) can be rewritten  :</Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
<Text-field style="Text" layout="Normal">                   <Image height="39" width="400" zoomable="false">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</Image>                     (2)</Text-field>
<Text-field style="Text" layout="Normal">Note that  (2) is used when <Image height="35" width="90" zoomable="false">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</Image>   ,     <Image height="28" width="83" zoomable="false">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</Image>   has small  curvature with respect to logt .  </Text-field>
<Text-field style="Text" layout="Normal">From the correspondence principle   we obtain  the viscoelastic solution . </Text-field>
</Input>
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<Input>
<Text-field style="Text" layout="Normal"></Text-field>
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<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L24" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"></Text-field>
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</Group></Presentation-Block><Presentation-Block>
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<Text-field style="Text" layout="Normal">  is  a constant   at     t  =  0  (8)  .   We  have  <Image height="50" width="127" zoomable="false">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</Image>  ,  <Image height="26" width="67" zoomable="false">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</Image>  ,   <Image height="49" width="97" zoomable="false">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</Image>     (9)</Text-field>
<Text-field style="Text" layout="Normal">By the similar way , we find  out :  <Image height="40" width="75" zoomable="false">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</Image>(10)</Text-field>
<Text-field style="Text" layout="Normal">Assume that the relaxation moduli  have power form :  <Image height="56" width="355" zoomable="false">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</Image>   (11)</Text-field>
<Text-field style="Text" layout="Normal">where  <Image height="25" width="57" zoomable="false">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</Image>   are  constants .</Text-field>
<Text-field style="Text" layout="Normal">By applying the Laplace transfom for  (11)  ,  we  obtain  the operator moduli :      <Image height="56" width="228" zoomable="false">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</Image>   (12)</Text-field>
<Text-field style="Text" layout="Normal">with the values of Gamma function :   <Image height="22" width="93" zoomable="false">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</Image> ;     <Image height="22" width="93" zoomable="false">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</Image>      (13)  </Text-field>
</Input>
</Group></Presentation-Block>
</Section><Presentation-Block>
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<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 1" layout="Heading 1"><Font family="Arial">3. Parameters - The Numerical and Graphical Solution :</Font></Text-field></Title><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L22" drawlabel="true">
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<Group view="code" labelreference="L2" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">restart;
cycrstrecom:=proc(T,Gamma1,c1,P1,Q1,M1,d1)
global P,Q,sigmaat1,sigmaat2,sigmabt2,sigmabt1,sigmaatisotropic,sigmabtisotropic ; 
local To,E,E1,M,d,j,Gamma,Gamma_form,gamma;
with(inttrans):with(plottools):with(plots):
print(&quot; PARAMETERS DEFINITION : &quot;);
print( T=To,gamma=Gamma1,c=c1);
print(&quot; REPRESENTATION OF STRESS : &quot;);
sigma[theta](at):=(gamma*P*(1+c^(2*gamma))-gamma*Q*2*c^(gamma-1))/(1-c^(2*gamma));
print(sigma[theta](a)=sigma[theta](at));
sigma[theta](bt):=(gamma*P*2*c^(gamma+1)-Q*(1+c^(2*gamma)))/(1-c^(2*gamma));
print(sigma[theta](b)=sigma[theta](bt));
P:=P1;Q:=Q1;
To:=T;E[rt]:=(100*(t/To)^(-0.5)+1)*E[e];E[thetat]:=(100*(t/To)^(-0.1)+1)*E[e];
print(E[r]=E[rt]);
print(E[theta]=E[thetat]);
print(&quot; LAPLACE TRANSFORM OF MODULI : &quot;);
E1[rp]:=p*evalf(laplace(E[rt],t,p),3);
print(E1[r]=E1[rp]);
E1[thetap]:=p*evalf(laplace(E[thetat],t,p),3);
print(E1[theta]=E1[thetap]);
Gamma_form:=sqrt(E1[theta]/E1[r]);
print(&quot; EXPRESSION OF  : &quot;,gamma=Gamma_form);
Gamma:=evalf(sqrt(E1[thetap]/E1[rp]),5):
Gamma:=simplify(Gamma);
print(gamma=Gamma);
sigma[theta](a):=(Gamma*P1*(1+c1^(2*Gamma))-Gamma*Q1*2*c1^(Gamma-1))/(1-c1^(2*Gamma));
sigma[theta](b):=(Gamma*P1*2*c1^(Gamma+1)-Q1*(1+c1^(2*Gamma)))/(1-c1^(2*Gamma));
print(sigma[Theta](a)=sigma[theta](a));;print(sigma[Theta](b)=sigma[theta](b));
sigma[theta](at):=(gamma*P*(1+c^(2*gamma))-gamma*Q*2*c^(gamma-1))/(1-c^(2*gamma));
print(&quot; SUBSTITUTE &quot;,c=c1 ,p =1/(2*t),gamma=Gamma);
sigmaat1:=evalf(subs(c=(1/2),p=(1/(2*t)),gamma=Gamma,P=P1,Q=Q1,sigma[theta](a)),3);
sigmaat1:=evalf(simplify(sigmaat1),2);
print(sigma[Theta](a)=sigmaat1);
sigmaat2:=subs(t=10^(s)*To,sigmaat1):
sigmaat2:=evalf(simplify(sigmaat2),2)/P1;
sigmabt1:=evalf(subs(c=(1/2),p=(1/(2*t)),gamma=Gamma,P=P1,Q=Q1,sigma[theta](b)),3);
sigmabt1:=evalf(simplify(sigmabt1),2);
print(sigma[Theta](b)=sigmabt1);
sigmabt2:=subs(t=10^(s)*To,sigmabt1):
sigmabt2:=evalf(simplify(sigmabt2),2);
print(&quot; CHANGE THE PRESENTATION OF TIME INTO  LOG(t/To) &quot;);
print(sigma[Theta](a)=sigmaat2);
print(sigma[Theta](b)=sigmabt2);
sigmaatisotropic:=subs(s=0,sigmaat2);
sigmaatisotropic:=evalf(simplify(sigmaatisotropic),2);
print(sigmaa_isotropic=sigmaatisotropic);
sigmabtisotropic:=subs(s=0,sigmabt2):
sigmabtisotropic:=evalf(simplify(sigmabtisotropic),2);
print(&quot;   OUTPUT   DATA  &quot;);
M:=M1;
d:=d1;
<Font encoding="UTF-8">printf(&quot;    s=log(t/To)         sigma[Theta](a)(s)/P       \134n\134n&quot;);
</Font>for j from 0 to M do 
<Font encoding="UTF-8">printf(&quot;%10.1f                %10.4f    \134n&quot;, -d*(10-j), subs(s=-d*(10-j),sigmaat2));
</Font>end do;
for j from 1 to M do 
<Font encoding="UTF-8">printf(&quot;%10.1f                %10.4f    \134n&quot;, d*j, subs(s=d*j,sigmaat2));
</Font>end do;
print(&quot; NUMERICAL AND GRAPHICAL SOLUTION &quot;);
<Font encoding="UTF-8">printf(&quot;\134n%s&quot;,&quot;   KET THUC BAI TOAN ONG TRU COMPOSITE DAN NHOT TRUC HUONG BANG PHUONG PHAP TRUC TIEP &quot;);
</Font>plot([sigmaat2,sigmaat2,sigmaatisotropic],s=-10..30,y=0.85..5.2,color=[grey,black,black],style=[line,point,point],thickness=1,symbol=[cross,diamond,cross],linestyle=1,axes=boxed,labels=[&quot;logt/To&quot;,&quot;sigma(a,t)/P&quot;],legend=[`sigma(a,t)/P`,`sigma(a,t)/P`,`Isotropic solution`],title=&quot;Numerical solution&quot;);
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<Output>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ly0mSSZzaWdtYUc2IjYjSSZUaGV0YUdGJjYjSSJiR0YmLCQqKComLCYqJEkicEdGJiMiIiIiIzUkIiQyIiIiISRGMkY2RjJGMiwmKiYqJEYwISIiI0YyIiIjRjBGMiQiJHgiRjZGN0YyRjtGPClGPCwmKiRGLUY8RjJGMkYyRjIsJkYyRjIpRjwsJEZCRj1GO0Y7Rj0=</Equation></Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">NiZRLX5TVUJTVElUVVRFfjYiL0kiY0dGJCMiIiIiIiMvSSJwR0YkLCQqJEkidEdGJCEiIkYnL0kmZ2FtbWFHRiQqJComLCYqJEYrI0YoIiM1JCIkMiIiIiEkRihGOkYoRigsJiomKiRGK0YvRidGK0YoJCIkeCJGOkY7RihGL0Yn</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ly0mSSZzaWdtYUc2IjYjSSZUaGV0YUdGJjYjSSJhR0YmLCQqKCwmJCIiIiIiIUYvLUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YmNiMsJCokKihJInRHRiYjRi8iIiMsJiokKiRGOiEiIiNGLyIjNSRGQkYvRi5GL0YvLCYkIiM3Ri9GLyokRjpGO0YvRkBGOyQhIzlGQEYvRi9GOUY7LCYkRkBGMEYvRjFGL0ZARks=</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ly0mSSZzaWdtYUc2IjYjSSZUaGV0YUdGJjYjSSJiR0YmLCQqKCooSSJ0R0YmIyIiIiIiIywmKiQqJEYuISIiI0YwIiM1JEY3RjAkRjAiIiFGMEYwLCYkIiM3RjBGMCokRi5GL0YwRjVGLy1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJjYjLCYqJEYtRi8kISNwISIjRkdGMEYwLCYkRjVGOkYwLUZANiMsJEZGJCEjOUY1RjBGNSRGSUY6</Equation></Text-field>
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<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">UVJ+Q0hBTkdFflRIRX5QUkVTRU5UQVRJT05+T0Z+VElNRX5JTlRPfn5MT0codC9Ubyl+NiI=</Equation></Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUYjNiUtSSVtc3ViR0YkNiUtSSNtaUdGJDYlUSZzaWdtYUYnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictRiM2Iy1GMTYlUSZUaGV0YUYnRjRGNy8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnLUkjbW9HRiQ2MFEwJkFwcGx5RnVuY3Rpb247RidGNy8lJmZlbmNlR0Y2LyUqc2VwYXJhdG9yR0Y2LyUpc3RyZXRjaHlHRjYvJSpzeW1tZXRyaWNHRjYvJShsYXJnZW9wR0Y2LyUubW92YWJsZWxpbWl0c0dGNi8lJ2FjY2VudEdGNi8lJWZvcm1HUSZpbmZpeEYnLyUnbHNwYWNlR1EkMGVtRicvJSdyc3BhY2VHRlkvJShtaW5zaXplR1EiMUYnLyUobWF4c2l6ZUdRKWluZmluaXR5RictSShtZmVuY2VkR0YkNiQtRiM2Iy1GMTYlUSJhRicvRjVRJXRydWVGJy9GOFEnaXRhbGljRidGNy1GQzYwUSI9RidGN0ZGRkhGSkZMRk5GUEZSRlQvRlhRL3RoaWNrbWF0aHNwYWNlRicvRmVuRlxwRmZuRmluLUYjNiQtRkM2MFEqJnVtaW51czA7RidGN0ZGRkhGSkZMRk5GUEZSRlQvRlhRMG1lZGl1bW1hdGhzcGFjZUYnL0ZlbkZkcEZmbkZpbi1JJm1mcmFjR0YkNigtRiM2Jy1JI21uR0YkNiRRIzEuRidGNy1GQzYwUTEmSW52aXNpYmxlVGltZXM7RidGN0ZGRkhGSkZMRk5GUEZSRlRGV0ZaRmZuRmluLUZdbzYkLUYjNiVGW3EtRkM2MFEiK0YnRjdGRkZIRkpGTEZORlBGUkZURmNwRmVwRmZuRmluLUklbXN1cEdGJDYlLUZDNjBRLyZFeHBvbmVudGlhbEU7RidGN0ZGRkhGSkZMRk5GUEZSL0ZVUSdwcmVmaXhGJ0ZXL0ZlblEydmVyeXRoaW5tYXRoc3BhY2VGJ0ZmbkZpbi1GIzYkRmBwLUYjNiUtRlxxNiRRJDEuNEYnRjdGX3EtSSZtc3FydEdGJDYjLUZncDYoLUYjNiUtRltzNiMtRmpxNiVGXHItRiM2JS1GXHE2JFEkMi4zRidGN0ZfcS1GMTYlUSJzRidGZG9GZm8vJTFzdXBlcnNjcmlwdHNoaWZ0R0ZBRl9xLUZdbzYkLUYjNiUtRiM2JS1GXHE2JFElMTAwLkYnRjdGX3EtRmpxNiUtRl1vNiQtRmpxNiVGXHItRiM2JEZgcEZlc0ZddEY3LUYjNiUtRlxxNiRGaG5GNy1GQzYwUSIvRidGN0ZGRkgvRktGZW9GTEZORlBGUkZUL0ZYUS50aGlubWF0aHNwYWNlRicvRmVuRml1RmZuRmluLUZccTYkUSMxMEYnRjdGXXRGZnFGW3FGNy1GIzYjLUYjNiUtRlxxNiRRJTEyMC5GJ0Y3RmZxLUYjNiNGYXMvJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRlx3LyUpYmV2ZWxsZWRHRjZGXXRGN0ZfcUZqci1GIzYjLUYjNiZGYHBGW3FGZnFGaXFGZ3ZGanZGXXdGX3c=">Ly0mSSZzaWdtYUc2IjYjSSZUaGV0YUdGJjYjSSJhR0YmLCQqKCwmJCIiIiIiIUYvLUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YmNiMsJCokKigtRjI2IywkSSJzR0YmJCIjQiEiIiNGLyIiIywmKiQtRjI2IywkRj0kISNCRkAjRi8iIzUkRktGL0YuRi9GLywmJCIjN0YvRi8qJEY6RkFGL0ZARkEkISM5RkBGL0YvRjlGQSwmJEZARjBGL0YxRi9GQEZU</Equation></Text-field>
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<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ly0mSSZzaWdtYUc2IjYjSSZUaGV0YUdGJjYjSSJiR0YmLCQqKCooLUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YmNiMsJEkic0dGJiQiI0IhIiIjIiIiIiIjLCYqJC1GLzYjLCRGNSQhI0JGOCNGOiIjNSRGREY6JEY6IiIhRjpGOiwmJCIjN0Y6RjoqJEYuRjlGOkY4RjktRi82IywmKiRGLUY5JCEjcCEiI0ZQRjpGOiwmJEY4RkdGOi1GLzYjLCRGTyQhIzlGOEY6RjgkRlJGRw==</Equation></Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">L0kxc2lnbWFhX2lzb3Ryb3BpY0c2IiQiIzshIiI=</Equation></Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">UTN+fn5PVVRQVVR+fn5EQVRBfn42Ig==</Equation></Text-field>
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<Output>
<Text-field style="Line Printed Output" layout="Line Printed Output">    s=log(t/To)         sigma[Theta](a)(s)/P       

     -10.0                    1.4286    
      -9.0                    1.4286    
      -8.0                    1.4287    
      -7.0                    1.4289    
      -6.0                    1.4294    
      -5.0                    1.4305    
      -4.0                    1.4335    
      -3.0                    1.4409    
      -2.0                    1.4595    
      -1.0                    1.5056    
       0.0                    1.6182    
       1.0                    1.8804    
       2.0                    2.4264    
       3.0                    3.3300    
       4.0                    4.3240    
       5.0                    4.8725    
       6.0                    4.8419    
       7.0                    4.5127    
       8.0                    4.1110    
       9.0                    3.7260    
      10.0                    3.3828    
      11.0                    3.0857    
      12.0                    2.8323    
      13.0                    2.6184    
      14.0                    2.4396    
      15.0                    2.2913    
      16.0                    2.1691    
      17.0                    2.0691    
      18.0                    1.9877    
      19.0                    1.9217    
      20.0                    1.8684    
       1.0                    1.8804    
       2.0                    2.4264    
       3.0                    3.3300    
       4.0                    4.3240    
       5.0                    4.8725    
       6.0                    4.8419    
       7.0                    4.5127    
       8.0                    4.1110    
       9.0                    3.7260    
      10.0                    3.3828    
      11.0                    3.0857    
      12.0                    2.8323    
      13.0                    2.6184    
      14.0                    2.4396    
      15.0                    2.2913    
      16.0                    2.1691    
      17.0                    2.0691    
      18.0                    1.9877    
      19.0                    1.9217    
      20.0                    1.8684    
      21.0                    1.8255    
      22.0                    1.7910    
      23.0                    1.7634    
      24.0                    1.7413    
      25.0                    1.7237    
      26.0                    1.7096    
      27.0                    1.6984    
      28.0                    1.6894    
      29.0                    1.6823    
      30.0                    1.6766    </Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">UUN+TlVNRVJJQ0FMfkFORH5HUkFQSElDQUx+U09MVVRJT05+NiI=</Equation></Text-field>
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<Output>
<Text-field style="Line Printed Output" layout="Line Printed Output">
   KET THUC BAI TOAN ONG TRU COMPOSITE DAN NHOT TRUC HUONG BANG PHUONG PHAP TRUC TIEP </Text-field>
</Output>
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<Text-field style="Text" layout="Normal">[1] <Font encoding="UTF-8" bold="true">Ngo Thanh Phong , Nguyen Thoi Trung , Nguyen D\303\254nh Hien </Font>, <Font italic="true">Ap dung</Font></Text-field>
<Text-field style="Text" italic="true" layout="Normal"><Font italic="true">phap gan dung bien doi Laplace nguoc de giai bai toan bien dang phang trong</Font></Text-field>
<Text-field style="Text" layout="Normal"><Font italic="true">lieu  composite dan nhot truc huong </Font><Font encoding="UTF-8">, Tap ch\303\255 phat trien KHCN , tap 7 , so 4 &amp;</Font></Text-field>
<Text-field style="Text" layout="Normal">in Vietnamese ) , 2002 .</Text-field>
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<Text-field style="Text" layout="Normal">[2] <Font bold="true">R.A. Schapery </Font>, <Font italic="true">Stress Analysis of Viscoelastic Composite Materials</Font> ,</Text-field>
<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">Edited by G.P.Sendeckyj ,Academic Press , Newyork \342\200\223London , 1971 .</Font></Text-field>
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<Text-field style="Text" layout="Normal"><Font italic="true">Legal Notice: The copyright for this application is owned by the author(s). Neither Maplesoft nor the author are responsible for any errors contained within and are not liable for any damages resulting from the use of this material. This application is intended for non-commercial, non-profit use only. Contact the author for permission if you wish to use this application in for-profit activities.
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