📄 node20.html
字号:
<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML 3.2 Final//FR"><!-- Converted with LaTeX2HTML 95.1 (Fri Jan 20 1995) --><!-- by Nikos Drakos (nikos@cbl.leeds.ac.uk), CBLU, University of Leeds --><!-- Modified Simulog 03/97 --><HTML><HEAD><TITLE>2.4 Test 3: Plate problem</TITLE><LINK REL=STYLESHEET TYPE="text/css" HREF="./Modulef.css" TITLE="Modulef CSS"><meta name="description" value="2.4 Test 3: Plate problem"><meta name="keywords" value="Guide1"><meta name="resource-type" value="document"><meta name="distribution" value="global"></HEAD><BODY BGCOLOR="#FFFFFF"><P> <IMG SRC="../icons/smallmod.gif" WIDTH=211 HEIGHT=50 ALIGN=BOTTOM ALT="Modulef"><A NAME=tex2html436 HREF="node19.html"><IMG BORDER=0 ALIGN=BOTTOM SRC="../icons/previous_motif.gif" ALT="previous"></A><A NAME=tex2html440 HREF="node16.html"><IMG BORDER=0 ALIGN=BOTTOM SRC="../icons/up_motif.gif" ALT="up"></A><A NAME=tex2html442 HREF="node21.html"><IMG BORDER=0 ALIGN=BOTTOM SRC="../icons/next_motif.gif" ALT="next"></A><A NAME=tex2html444 HREF="node2.html"><IMG BORDER=0 ALIGN=BOTTOM SRC="../icons/contents_motif.gif" ALT="contents"></A><A HREF="../Guide1-18/node20.html"><IMG BORDER=0 SRC="../icons/zoom18.gif" ALIGN=BOTTOM ALT="[BIG]"></A><A HREF="../Guide1-14/node20.html"><IMG BORDER=0 SRC="../icons/zoom14.gif" ALIGN=BOTTOM ALT="[Normal]"></A><A HREF="../Guide1-10/node20.html"><IMG BORDER=0 SRC="../icons/zoom10.gif" ALIGN=BOTTOM ALT="[small]"></A><BR><B> Next: </B> <A NAME=tex2html443 HREF="node21.html">3 Batch tests</A><B>Up: </B> <A NAME=tex2html441 HREF="node16.html">2 Conversational tests</A><B> Prev: </B> <A NAME=tex2html437 HREF="node19.html">2.3 Test 2: 2D Elasticity Problem </A><B><A HREF="node2.html" >Contents</A></B><HR SIZE=3 WIDTH="75%"><H1><A NAME=SECTION04240000000000000000>2.4 Test 3: Plate problem</A></H1><P><P><P>This test has been proposed by NAFEMS (National Agency for Finite Element Methods & Standards) [<A HREF="node65.html#nafems2">Robinson</A>].<P><P><P><H2><A NAME=SECTION04241000000000000000>2.4.1 Description</A></H2><P><P><P><P><A NAME=2465> </A><IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img200.gif"><BR><STRONG>Figure 2.12:</STRONG> <i> Study of the rigid movement of a rectangular plate under bending</i><A NAME=fig8> </A><BR><P><P>The displacement in <IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img201.gif"> and <IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img202.gif"> is known as well as the rotation <IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img203.gif"> with respect to <b>y</b> at point <b>A</b>. Then at each point the displacement <b>w</b> and the rotations with respect to <IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img204.gif"> and <IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img205.gif"> are given by:<P><DIV ALIGN=center><IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img206.gif"></DIV><P><P><P><H2><A NAME=SECTION04242000000000000000>2.4.2 The boundary value problem</A></H2><P><P><P><DIV ALIGN=center><IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img207.gif"></DIV><P>and <b>D</b> is defined by:<DIV ALIGN=center><IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img208.gif"></DIV><P>where<P><DL COMPACT><DT><b>E</b><DD> is Young's modulus, <DT><b>e</b><DD> is the thickness of the plate, and <DT><IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img194.gif"><DD> is the Poisson ratio.<P> </DL><P>The type of finite element utilized in order to solve this problem: <b> TRIA DKTP</b> of library <b> ELAS</b>.<P><P><P>The physical values are defined as follows: <TABLE COLS=3 RULES=GROUPS><COL ALIGN=LEFT><COL ALIGN=CENTER><COL ALIGN=RIGHT><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> <b>l</b> </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> = </TD><TD VALIGN=BASELINE ALIGN=RIGHT NOWRAP> <b>10.0</b> </TD></TR><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> <b>e</b> </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> = </TD><TD VALIGN=BASELINE ALIGN=RIGHT NOWRAP> <b>0.01</b> </TD></TR><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> <b>c</b> </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> = </TD><TD VALIGN=BASELINE ALIGN=RIGHT NOWRAP> 1 </TD></TR><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> <b>E</b> </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> = </TD><TD VALIGN=BASELINE ALIGN=RIGHT NOWRAP> <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img209.gif"> </TD></TR><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img194.gif"> </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> = </TD><TD VALIGN=BASELINE ALIGN=RIGHT NOWRAP> <b>0.3</b> </TD></TR></TABLE><P><P><A NAME=2474> </A><IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img210.gif"><BR><STRONG>Figure 2.13:</STRONG> <i> Suggested mesh</i><A NAME=fig9> </A><BR><P><P><P><P><H2><A NAME=SECTION04243000000000000000>2.4.3 Execution of the test</A></H2><P><P><P><b> Step 1:</b> Mesh<P><TABLE COLS=3 RULES=GROUPS><COL ALIGN=LEFT><COL ALIGN=LEFT><COL ALIGN=LEFT><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP>Call preprocessor: </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> <b> APNOXX</b> </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP></TD></TR><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP></TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP></TD></TR><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> Modules used: </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> <b> APNOPO</b> </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> ... 2D mesh generator [<A HREF="node65.html#mod_104"><A NAME=tex2html37 HREF="../Guide3/welcome.html">MODULEF User Guide - 3</A></A>] </TD></TR><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> <b> QUACOO</b> </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> ... mesh generation utilizing quadrangles </TD></TR><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP></TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP></TD></TR><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> Specify input data file: </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> <b> D3NOPO.D</b> </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP></TD></TR><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> Output data structure: </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> <b> T3NOPO</b> </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP></TD></TR></TABLE><P><P><P><b> Step 2:</b> Interpolation [<A HREF="node65.html#mod_13">13</A>]<P><TABLE COLS=2 RULES=GROUPS><COL ALIGN=LEFT><COL ALIGN=LEFT><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP>Call preprocessor: </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> <b> COMAXX</b> </TD></TR><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP></TD></TR><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> Module used: </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> <b> COMACO</b> </TD></TR><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> Finite element library: </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> <b> ELAS</b> </TD></TR><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> Element type: </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> <b> TRIA DKTP</b> </TD></TR><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP></TD></TR><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> Specify input data file: </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> <b> D3COMA.D</b> </TD></TR><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> Output data structures: </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> <b> T3MAIL</b> </TD></TR><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> <b> T3COOR</b> </TD></TR></TABLE><P><P><P><b> Step 3:</b> Description of data [<A HREF="node65.html#mod_14">14</A>]<P><TABLE COLS=2 RULES=GROUPS><COL ALIGN=LEFT><COL ALIGN=LEFT><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP>Call preprocessor: </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> <b> FOMIXX</b> </TD></TR><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP></TD></TR><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> Modules used: </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> <b> COFORC</b> </TD></TR><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> <b> COMILI</b></TD></TR><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP></TD></TR><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> Specify input data file: </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> <b> D3FOMI.D</b> </TD></TR><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> Output data structures: </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> <b> T3FORC</b> </TD></TR><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> <b> T3MILI</b> </TD></TR></TABLE><P><P><P><b> Step 4:</b> Calculation of the element arrays (general case) [<A HREF="node65.html#mod_14">14</A>]<P><TABLE COLS=2 RULES=GROUPS><COL ALIGN=LEFT><COL ALIGN=LEFT><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP>Call preprocessor: </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> <b> THELXX</b> </TD></TR><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP></TD></TR><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> Module used: </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> <b> THENEW</b> </TD></TR><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP></TD></TR><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> Specify input data file: </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> <b> D3TAE.D</b> </TD></TR><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> Output data structure: </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> <b> T3TAE</b> </TD></TR></TABLE><P><P><P><b> Step 5:</b> Description of boundary conditions [<A HREF="node65.html#mod_18">18</A>]<P><TABLE COLS=2 RULES=GROUPS><COL ALIGN=LEFT><COL ALIGN=LEFT><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP>Call preprocessor: </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> <b> COBDXX</b> </TD></TR><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP></TD></TR><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> Module used: </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> <b> COBDC1</b> </TD></TR><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP></TD></TR><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> Specify input data file: </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> <b> D3BDCL.D</b> </TD></TR><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> Output data structure: </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> <b> T3BDCL</b> </TD></TR></TABLE><P><P><P><b> Step 6:</b> Assembly and solution by a direct Cholesky method <BR>[4][<A HREF="node65.html#mod_5"><A NAME=tex2html39 HREF="../Guide5/welcome.html">MODULEF User Guide - 5</A></A>]<P><TABLE COLS=3 RULES=GROUPS><COL ALIGN=LEFT><COL ALIGN=LEFT><COL ALIGN=LEFT><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP>Call preprocessor: </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> <b> CHOLXX</b> </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP></TD></TR><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP></TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP></TD></TR><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> Modules used: </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> <b> PREPAC</b> </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> ... allocation of pointers </TD></TR><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> <b> ASSMUA</b> </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> ... assembly of matrix in m.m. </TD></TR><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> <b> ASEMBV</b> </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> ... assembly of RHS vector in main memory </TD></TR><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> <b> CLIMPC</b> </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> ... incorporate boundary conditions </TD></TR><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> <b> DRCHPC</b> </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> ... forward and backward substitution </TD></TR><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP></TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP></TD></TR><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> Specify input data file: </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> <b> D3B.D</b> </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP></TD></TR><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> Output data structure: </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> <b> T3B</b> </TD><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP></TD></TR></TABLE><P>The number of words necessary to assemble the matrix is 2330.<P>The number of words necessary to assemble the corresponding right-hand-side (RHS) vector is 195.<P><P><P><H2><A NAME=SECTION04244000000000000000>2.4.4 Memory usage and execution time</A></H2><P><P><P>The table below represents the approximate maxima of the values.<P><P><P><TABLE COLS=3 BORDER FRAME=BOX RULES=GROUPS><COLGROUP><COL ALIGN=LEFT><COLGROUP><COL ALIGN=CENTER><COLGROUP><COL ALIGN=CENTER><TBODY><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP>Step </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> Dimension of </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> Execution time </TD></TR><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> the super array </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> (DPS8 Multics) </TD></TR></TBODY><TBODY><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP>Mesh </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> 6 000 </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> 9.5 </TD></TR><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> Interpolation </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> 3 000 </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> 4.9 </TD></TR><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> Element matrices </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> 4 000 </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> 5.0 </TD></TR><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> Boundary conditions </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> 2 000 </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> 3.8 </TD></TR><TR><TD VALIGN=BASELINE ALIGN=LEFT NOWRAP> Solution </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> 3 000 </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> 6.4 </TD></TR></TBODY></TABLE>⌨️ 快捷键说明
复制代码
Ctrl + C
搜索代码
Ctrl + F
全屏模式
F11
切换主题
Ctrl + Shift + D
显示快捷键
?
增大字号
Ctrl + =
减小字号
Ctrl + -