Mathcad Professional 14.0 <description/> <author>andray</author> <company>Parametric Technology Corporation</company> <keywords/> <revisedBy>andray</revisedBy> </userData> <identityInfo> <revision>3</revision> <documentID>4CDF8DF5-F62D-45D8-8958-88E55AB35D30</documentID> <versionID>DF9151E4-8818-421E-816C-4E0E436FAFD7</versionID> <parentVersionID>00000000-0000-0000-0000-000000000000</parentVersionID> <branchID>00000000-0000-0000-0000-000000000000</branchID> </identityInfo> </metadata> <settings> <presentation> <textRendering> <textStyles> <textStyle name="Normal"> <blockAttr margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit"/> <inlineAttr font-family="Arial" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> <textStyle name="Heading 1"> <blockAttr margin-left="0" margin-right="0" text-indent="inherit" text-align="left" 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text-align="left" list-style-type="inherit" tabs="inherit"/> <inlineAttr font-family="Arial" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> <textStyle name="List"> <blockAttr margin-left="14.25" margin-right="0" text-indent="-14.25" text-align="left" list-style-type="inherit" tabs="inherit"/> <inlineAttr font-family="Arial" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> <textStyle name="Indent"> <blockAttr margin-left="108" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit"/> <inlineAttr font-family="Arial" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> <textStyle name="Title"> <blockAttr margin-left="0" margin-right="0" text-indent="inherit" text-align="center" list-style-type="inherit" tabs="inherit"/> <inlineAttr font-family="Times New Roman" font-charset="0" font-size="24" font-weight="bold" font-style="normal" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> <textStyle name="Subtitle" base-style="Title"> <blockAttr margin-left="0" margin-right="0" text-indent="inherit" text-align="center" list-style-type="inherit" tabs="inherit"/> <inlineAttr font-family="Times New Roman" font-charset="0" font-size="18" font-weight="normal" font-style="normal" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> </textStyles> </textRendering> <mathRendering equation-color="#000"> <operators multiplication="narrow-dot" derivative="derivative" literal-subscript="large" definition="colon-equal" global-definition="triple-equal" local-definition="left-arrow" equality="bold-equal" symbolic-evaluation="right-arrow"/> <mathStyles> <mathStyle name="Variables" font-family="Times New Roman" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="Constants" font-family="Times New Roman" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="User 1" font-family="Arial" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="User 2" font-family="Courier New" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="User 3" font-family="Arial" font-charset="0" font-size="10" font-weight="bold" font-style="normal" underline="false"/> <mathStyle name="User 4" font-family="Times New Roman" font-charset="0" font-size="10" font-weight="normal" font-style="italic" underline="false"/> <mathStyle name="User 5" font-family="Times New Roman" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="User 6" font-family="Arial" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="User 7" font-family="Times New Roman" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="Math Text Font" font-family="Times New Roman" font-charset="0" font-size="14" font-weight="normal" font-style="normal" underline="false"/> </mathStyles> <dimensionNames mass="mass" length="length" time="time" current="current" thermodynamic-temperature="temperature" luminous-intensity="luminosity" amount-of-substance="substance" display="false"/> <symbolics derivation-steps-style="vertical-insert" show-comments="false" evaluate-in-place="false"/> <results numeric-only="true"> <general precision="3" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="3"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true" fractional-unit-exponent="false"/> </results> </mathRendering> <pageModel show-page-frame="false" show-header-frame="false" show-footer-frame="false" header-footer-start-page="1" paper-code="1" orientation="portrait" print-single-page-width="false" page-width="612" page-height="792"> <margins left="86.4" right="86.4" top="86.4" bottom="86.4"/> <header use-full-page-width="false"/> <footer use-full-page-width="false"/> </pageModel> <colorModel background-color="#fff" default-highlight-color="#ffff80"/> <language math="ru" UI="ru"/> </presentation> <calculation> <builtInVariables array-origin="0" convergence-tolerance="0.001" constraint-tolerance="0.001" random-seed="1" prn-precision="4" prn-col-width="8"/> <calculationBehavior automatic-recalculation="true" matrix-strict-singularity-check="false" optimize-expressions="false" exact-boolean="true" strings-use-origin="false" zero-over-zero="error"> <compatibility multiple-assignment="MC12" local-assignment="MC11"/> </calculationBehavior> <units> <currentUnitSystem name="si" customized="false"/> </units> </calculation> <editor view-annotations="false" view-regions="false"> <ruler is-visible="false" ruler-unit="in"/> <plotTemplate> <xy item-idref="1"/> </plotTemplate> <grid granularity-x="6" granularity-y="6"/> </editor> <fileFormat image-type="image/png" image-quality="75" save-numeric-results="true" exclude-large-results="true" save-text-images="false" screen-dpi="96"/> <miscellaneous> <handbook handbook-region-tag-ub="565" can-delete-original-handbook-regions="true" can-delete-user-regions="true" can-print="true" can-copy="true" can-save="true" file-permission-mask="4294967295"/> </miscellaneous> </settings> <regions> <region region-id="137" left="18" top="2.25" width="389.25" height="60" align-x="18" align-y="12" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Задача: Панель из углепластика находится в плоском напряженно-деформированном состоянии. Определить:</p> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">1. Напряжения в осях материала 1-2.</p> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">2. Деформации в осях материала 1-2.</p> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">3. Деформации в осях нагружения x-y.</p> </text> </region> <region region-id="110" left="18" top="69" width="51" height="12.75" align-x="33.75" align-y="78" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">σx</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:real>70</ml:real> <ml:id xml:space="preserve">MPa</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="2"/> </region> <region region-id="111" left="84" top="69" width="52.5" height="12.75" align-x="101.25" align-y="78" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">σy</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:real>14</ml:real> <ml:id xml:space="preserve">MPa</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="3"/> </region> <region region-id="112" left="150" top="69" width="51" height="12.75" align-x="170.25" align-y="78" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">τxy</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:real>7</ml:real> <ml:id xml:space="preserve">MPa</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="4"/> </region> <region region-id="113" left="216" top="69" width="34.5" height="12.75" align-x="227.25" align-y="78" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">θ</ml:id> <ml:apply> <ml:mult/> <ml:real font="0">45</ml:real> <ml:id xml:space="preserve">°</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="5"/> </region> <region region-id="114" left="258" top="63" width="65.25" height="18.75" align-x="273.75" align-y="78" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">E1</ml:id> <ml:apply> <ml:mult/> <ml:real>1.4</ml:real> <ml:apply> <ml:mult style="auto-select"/> <ml:apply> <ml:pow/> <ml:real>10</ml:real> <ml:real>11</ml:real> </ml:apply> <ml:id xml:space="preserve">Pa</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="6"/> </region> <region region-id="426" left="348" top="63" width="51" height="18.75" align-x="363.75" align-y="78" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">E2</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:apply> <ml:pow/> <ml:real>10</ml:real> <ml:real>10</ml:real> </ml:apply> <ml:id xml:space="preserve">Pa</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="7"/> </region> <region region-id="116" left="18" top="87" width="68.25" height="18.75" align-x="39" align-y="102" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">G12</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:apply> <ml:mult/> <ml:real>7</ml:real> <ml:apply> <ml:pow/> <ml:real>10</ml:real> <ml:real>3</ml:real> </ml:apply> </ml:apply> <ml:id xml:space="preserve">MPa</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="8"/> </region> <region region-id="117" left="102" top="93" width="43.5" height="12.75" align-x="122.25" align-y="102" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">ν12</ml:id> <ml:real>0.34</ml:real> </ml:define> </math> <rendering item-idref="9"/> </region> <region region-id="118" left="162" top="93" width="65.25" height="12.75" align-x="194.25" align-y="102" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:id xml:space="preserve">θ</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.70710678118654757</ml:real> </result> </ml:eval> </math> <rendering item-idref="10"/> </region> <region region-id="427" left="18" top="120" width="218.25" height="189.75" align-x="18" align-y="120" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <picture> <metafile mapping-mode="8" x-extent="216.5953" y-extent="188.0504" item-idref="11"/> </picture> <rendering item-idref="12"/> </region> <region region-id="428" left="18" top="326.25" width="291.75" height="12" align-x="18" align-y="336" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">1. Определим напряжения в осях 1-2 с помощью выражения </p> </text> </region> <region region-id="449" left="24" top="348" width="330" height="57.75" align-x="24" align-y="348" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#ffff80" tag=""> <ole clsid="{0002CE02-0000-0000-C000-000000000046}" type="embedded" item-idref="13"/> <rendering item-idref="14"/> </region> <region region-id="454" left="36" top="418.5" width="186.75" height="45.75" align-x="57" align-y="444" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">σ12</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:mult/> <ml:matrix rows="3" cols="3"> <ml:real>0.5</ml:real> <ml:real>0.5</ml:real> <ml:real>-0.5</ml:real> <ml:real>0.5</ml:real> <ml:real>0.5</ml:real> <ml:real>0.5</ml:real> <ml:real>1</ml:real> <ml:real>-1</ml:real> <ml:real>0</ml:real> </ml:matrix> <ml:matrix rows="3" cols="1"> <ml:id xml:space="preserve">σx</ml:id> <ml:id xml:space="preserve">σy</ml:id> <ml:id xml:space="preserve">τxy</ml:id> </ml:matrix> </ml:apply> <ml:unitOverride> <ml:id xml:space="preserve">MPa</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:matrix rows="3" cols="1"> <ml:real>49</ml:real> <ml:real>35</ml:real> <ml:real>-28</ml:real> </ml:matrix> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="megapascal"/> </unitMonomial> </unitedValue> </result> </ml:eval> </ml:define> </math> <rendering item-idref="15"/> </region> <region region-id="452" left="24" top="476.25" width="337.5" height="12" align-x="24" align-y="486" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">2. Определим деформации в осях 1-2 с помощью выражения (28) или (29)</p> </text> </region> <region region-id="461" left="24" top="492" width="162" height="99.75" align-x="24" align-y="492" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#ffff80" tag=""> <ole clsid="{0002CE02-0000-0000-C000-000000000046}" type="embedded" item-idref="16"/> <rendering item-idref="17"/> </region> <region region-id="495" left="210" top="498" width="140.25" height="56.25" align-x="210" align-y="498" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#ffff80" tag=""> <ole clsid="{0002CE02-0000-0000-C000-000000000046}" type="embedded" item-idref="18"/> <rendering item-idref="19"/> </region> <region region-id="517" left="444" top="630" width="453.75" height="651.75" align-x="444" align-y="630" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <ole clsid="{00020906-0000-0000-C000-000000000046}" type="embedded" item-idref="20"/> <rendering item-idref="21"/> </region> <region region-id="471" left="36" top="624" width="226.5" height="90.75" align-x="51.75" align-y="672" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">ε1</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:mult/> <ml:matrix rows="3" cols="3"> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:id xml:space="preserve">E1</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">ν12</ml:id> </ml:apply> <ml:id xml:space="preserve">E1</ml:id> </ml:apply> <ml:real>0</ml:real> <ml:apply> <ml:div/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">ν12</ml:id> </ml:apply> <ml:id xml:space="preserve">E1</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:id xml:space="preserve">E2</ml:id> </ml:apply> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:id xml:space="preserve">G12</ml:id> </ml:apply> </ml:matrix> <ml:id xml:space="preserve">σ12</ml:id> </ml:apply> <ml:unitOverride> <ml:apply> <ml:pow/> <ml:real>10</ml:real> <ml:real>-6</ml:real> </ml:apply> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="3" cols="1"> <ml:real>265</ml:real> <ml:real>3381</ml:real> <ml:real>-4000.0000000000005</ml:real> </ml:matrix> </result> </ml:eval> </ml:define> </math> <rendering item-idref="22"/> </region> <region region-id="473" left="24" top="716.25" width="421.5" height="36" align-x="24" align-y="726" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">3. Деформации в осях x-y можно получить путем преобразования деформаций из осей 1-2 (см. пред. пункт) используя обратное преобразование или заменив на угол -θ в матрице преобразования</p> </text> </region> <region region-id="493" left="42" top="763.5" width="203.25" height="63.75" align-x="57" align-y="798" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">εx</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:matrix rows="3" cols="3"> <ml:real>0.5</ml:real> <ml:real>0.5</ml:real> <ml:real>-1</ml:real> <ml:real>0.5</ml:real> <ml:real>0.5</ml:real> <ml:real>1</ml:real> <ml:real>0.5</ml:real> <ml:real>-0.5</ml:real> <ml:real>0</ml:real> </ml:matrix> <ml:real>-1</ml:real> </ml:apply> <ml:id xml:space="preserve">ε1</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="3" cols="1"> <ml:real>0.003823</ml:real> <ml:real>-0.00017700000000000007</ml:real> <ml:real>-0.003116</ml:real> </ml:matrix> </result> </ml:eval> </ml:define> </math> <rendering item-idref="23"/> </region> <region region-id="494" left="30" top="836.25" width="314.25" height="12" align-x="45.75" align-y="846" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Другим способом можно получить деформации из закона Гука и<sp count="2"/> </p> </text> </region> <region region-id="496" left="210" top="570" width="198" height="33.75" align-x="210" align-y="570" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#ffff80" tag=""> 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<ml:real>4</ml:real> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="38"/> </region> <region region-id="519" left="450" top="1290" width="453.75" height="229.5" align-x="450" align-y="1290" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <ole clsid="{00020906-0000-0000-C000-000000000046}" type="embedded" item-idref="39"/> <rendering item-idref="40"/> </region> <region region-id="525" left="54" top="1282.5" width="173.25" height="45.75" align-x="67.5" align-y="1308" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">SI</ml:id> <ml:unitOverride> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:id xml:space="preserve">MPa</ml:id> </ml:apply> <ml:apply> <ml:pow/> <ml:real>10</ml:real> <ml:real>-5</ml:real> </ml:apply> </ml:apply> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="3" cols="3"> <ml:real>6.1285714285714272</ml:real> <ml:real>-1.014285714285714</ml:real> <ml:real>-4.6428571428571432</ml:real> <ml:real>-1.014285714285714</ml:real> <ml:real>6.128571428571429</ml:real> <ml:real>-4.6428571428571415</ml:real> <ml:real>-4.6428571428571432</ml:real> <ml:real>-4.6428571428571415</ml:real> <ml:real>10.714285714285714</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="41"/> </region> <region region-id="526" left="48" top="1348.5" width="157.5" height="57.75" align-x="63" align-y="1380" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">εx</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">SI</ml:id> <ml:matrix rows="3" cols="1"> <ml:id xml:space="preserve">σx</ml:id> <ml:id xml:space="preserve">σy</ml:id> <ml:id xml:space="preserve">τxy</ml:id> </ml:matrix> </ml:apply> <ml:unitOverride> <ml:apply> <ml:pow/> <ml:real>10</ml:real> <ml:real>-6</ml:real> </ml:apply> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="3" cols="1"> <ml:real>3822.9999999999995</ml:real> <ml:real>-176.99999999999974</ml:real> <ml:real>-3150.0000000000009</ml:real> </ml:matrix> </result> </ml:eval> </ml:define> </math> <rendering item-idref="42"/> </region> <region region-id="520" left="48" top="1412.25" width="330.75" height="12" align-x="70.5" align-y="1422" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Результаты аналогичны получаемым через преобразование деформаций</p> </text> </region> <region region-id="521" left="48" top="1442.25" width="384" height="36" align-x="70.5" align-y="1452" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Для ортотропного слоя с углом ориентации θ рассчитать:</p> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Модуль Юнга Ех и Еу, модуль сдвига Gxy и коэффициент Пуассона vxy для углов θ 10, 20, 30, 40, 50, 60, 70, 80 и 90 градусов.</p> </text> </region> <region region-id="537" left="48" top="1494.75" width="60" height="161.25" align-x="59.25" align-y="1578" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">θ</ml:id> <ml:apply> <ml:mult/> <ml:matrix rows="10" cols="1"> <ml:real>0</ml:real> <ml:real>10</ml:real> <ml:real>20</ml:real> <ml:real>30</ml:real> <ml:real>40</ml:real> <ml:real>50</ml:real> <ml:real>60</ml:real> <ml:real>70</ml:real> <ml:real>80</ml:real> <ml:real>90</ml:real> </ml:matrix> <ml:id xml:space="preserve">deg</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="43"/> </region> <region region-id="538" left="42" top="1668" width="341.25" height="90.75" align-x="53.25" align-y="1716" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">S</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:matrix rows="3" cols="3"> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:id xml:space="preserve">E1</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">ν12</ml:id> </ml:apply> <ml:id xml:space="preserve">E1</ml:id> </ml:apply> <ml:real>0</ml:real> <ml:apply> <ml:div/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">ν12</ml:id> </ml:apply> <ml:id xml:space="preserve">E1</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:id xml:space="preserve">E2</ml:id> </ml:apply> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:id xml:space="preserve">G12</ml:id> </ml:apply> </ml:matrix> <ml:unitOverride> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:id 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