1、复合材料力学上机编程作业学院:School of Civil Engineering专业:Engineering Mechanics小组成员信息:James Wilson(201203189001)、Tau Young(201203189001)复合材料力学学了五个星期,这是这门课的第一次编程作业。我和杨涛结成一个小组,我用的是Fortran编制的程序,Tau Young用的是matlab编制。其中的算例以我的Fortran计算结果为准。Matlab作为可视化界面有其独到之处,在附录2中将会有所展示。作业的内容是层合板的刚度的计算和验算,包括拉伸刚度A、弯曲刚度D以及耦合刚度B。首先要给定层合
2、板的各个参数,具体有:层合板的层数N;各单层的弹性常数E1、E2、G12;各单层对应的厚度;各单层对应的主方向夹角。然后就要计算每个单层板的二维刚度矩阵Q,具体公式如下:;得到Q矩阵后,根据课本上讲到的得到。然后根据z坐标的定义求出到,接下来,最重要的一步,根据下式计算A、B、D。一、书上P110的几个问题可以归纳为以下几个类型。(1)正交铺设5层对称层合板(T5-7)数据文档层数 5层序数 厚度m E1(Pa) E2(Pa) v12 v21 G12(Pa) 角度()1 1.00E-03 9.60E+10 2.40E+10 0.10 0.40 1.00E+10 0.002 1.00E-03 9
3、.60E+10 2.40E+10 0.10 0.40 1.00E+10 90.003 1.00E-03 9.60E+10 2.40E+10 0.10 0.40 1.00E+10 0.004 1.00E-03 9.60E+10 2.40E+10 0.10 0.40 1.00E+10 90.005 1.00E-03 9.60E+10 2.40E+10 0.10 0.40 1.00E+10 0.00(2)正交铺设6层反对称层合板(T5-8)数据文档层数 6层序数 厚度m E1(Pa) E2(Pa) v12 v21 G12(Pa) 角度()1 1.00E-03 9.60E+10 2.40E+10 0.
4、10 0.40 1.00E+10 0.002 1.00E-03 9.60E+10 2.40E+10 0.10 0.40 1.00E+10 90.003 1.00E-03 9.60E+10 2.40E+10 0.10 0.40 1.00E+10 0.004 1.00E-03 9.60E+10 2.40E+10 0.10 0.40 1.00E+10 90.005 1.00E-03 9.60E+10 2.40E+10 0.10 0.40 1.00E+10 0.006 1.00E-03 9.60E+10 2.40E+10 0.10 0.40 1.00E+10 90.00(3)5层对称角铺设层合板(T5
5、-9)数据文档层数 5层序数 厚度m E1(Pa) E2(Pa) v12 v21 G12(Pa) 角度()1 1.00E-03 9.60E+10 2.40E+10 0.10 0.40 1.00E+10 30.002 1.00E-03 9.60E+10 2.40E+10 0.10 0.40 1.00E+10 -30.003 1.00E-03 9.60E+10 2.40E+10 0.10 0.40 1.00E+10 30.004 1.00E-03 9.60E+10 2.40E+10 0.10 0.40 1.00E+10 -30.005 1.00E-03 9.60E+10 2.40E+10 0.10
6、 0.40 1.00E+10 30.00(4)6层反对称角铺设层合板(T5-10)数据文档层数 6层序数 厚度m E1(Pa) E2(Pa) v12 v21 G12(Pa) 角度()1 1.00E-03 9.60E+10 2.40E+10 0.10 0.40 1.00E+10 30.002 1.00E-03 9.60E+10 2.40E+10 0.10 0.40 1.00E+10 -30.003 1.00E-03 9.60E+10 2.40E+10 0.10 0.40 1.00E+10 30.004 1.00E-03 9.60E+10 2.40E+10 0.10 0.40 1.00E+10 -
7、30.005 1.00E-03 9.60E+10 2.40E+10 0.10 0.40 1.00E+10 30.006 1.00E-03 9.60E+10 2.40E+10 0.10 0.40 1.00E+10 -30.00(5)我还想验证一个书上的例题,在课本P114。三层层合板,外层厚度t1,内层10t1,正交铺设比m=0.2,。玻璃/环氧单层板性能:E1=5.4E10Pa,E2=1.8E10Pa,v21=0.25,G12=8.8E9Pa。数据文档层数 3层序数 厚度m E1(Pa) E2(Pa) v12 v21 G12(Pa) 角度()1 1.00E+00 5.40E+10 1.80E+
8、10 0.083 0.250 8.80E+09 0.002 1.00E+01 5.40E+10 1.80E+10 0.083 0.250 8.80E+09 90.003 1.00E+00 5.40E+10 1.80E+10 0.083 0.250 8.80E+09 0.00二、验证Verchery的论文里给出的数值算例。这里一直到Table5的数据都是从Verchery的论文中截获。Verchery论文中的18层序列,第(21)式【laminates without bending-extension coupling】的排列有两种材料,一种是Boron-Epoxy,一种是Glass-Epox
9、y。而且都给出了最终的计算结果Q,A*,D*。下面是我的Fortran计算数据文档和结果文档。(1)Boron-Epoxy材料。(Boron-Epoxy)数据文档层数 18层序数 厚度m E1(Pa) E2(Pa) v12 v21 G12(Pa) 角度()1 1.00E-03 2.04E+11 1.85E+10 0.021 0.230 5.59E+09 0.002 1.00E-03 2.04E+11 1.85E+10 0.021 0.230 5.59E+09 0.003 1.00E-03 2.04E+11 1.85E+10 0.021 0.230 5.59E+09 60.004 1.00E-0
10、3 2.04E+11 1.85E+10 0.021 0.230 5.59E+09 60.005 1.00E-03 2.04E+11 1.85E+10 0.021 0.230 5.59E+09 -60.006 1.00E-03 2.04E+11 1.85E+10 0.021 0.230 5.59E+09 -60.007 1.00E-03 2.04E+11 1.85E+10 0.021 0.230 5.59E+09 -60.008 1.00E-03 2.04E+11 1.85E+10 0.021 0.230 5.59E+09 60.009 1.00E-03 2.04E+11 1.85E+10 0.
11、021 0.230 5.59E+09 0.0010 1.00E-03 2.04E+11 1.85E+10 0.021 0.230 5.59E+09 -60.0011 1.00E-03 2.04E+11 1.85E+10 0.021 0.230 5.59E+09 -60.0012 1.00E-03 2.04E+11 1.85E+10 0.021 0.230 5.59E+09 60.0013 1.00E-03 2.04E+11 1.85E+10 0.021 0.230 5.59E+09 60.0014 1.00E-03 2.04E+11 1.85E+10 0.021 0.230 5.59E+09
12、0.0015 1.00E-03 2.04E+11 1.85E+10 0.021 0.230 5.59E+09 0.0016 1.00E-03 2.04E+11 1.85E+10 0.021 0.230 5.59E+09 0.0017 1.00E-03 2.04E+11 1.85E+10 0.021 0.230 5.59E+09 60.0018 1.00E-03 2.04E+11 1.85E+10 0.021 0.230 5.59E+09 -60.00(2)Glass-Epoxy材料。(Glass-Epoxy)数据文档层数18层序数厚度m E1(Pa)E2(Pa)v12v21G12(Pa)角度(
13、)11.00E-033.86E+108.27E+090.0560.2604.14E+090.0021.00E-033.86E+108.27E+090.0560.2604.14E+090.0031.00E-033.86E+108.27E+090.0560.2604.14E+0960.0041.00E-033.86E+108.27E+090.0560.2604.14E+0960.0051.00E-033.86E+108.27E+090.0560.2604.14E+09-60.0061.00E-033.86E+108.27E+090.0560.2604.14E+09-60.0071.00E-033.
14、86E+108.27E+090.0560.2604.14E+09-60.0081.00E-033.86E+108.27E+090.0560.2604.14E+0960.0091.00E-033.86E+108.27E+090.0560.2604.14E+090.00101.00E-033.86E+108.27E+090.0560.2604.14E+09-60.00111.00E-033.86E+108.27E+090.0560.2604.14E+09-60.00121.00E-033.86E+108.27E+090.0560.2604.14E+0960.00131.00E-033.86E+10
15、8.27E+090.0560.2604.14E+0960.00141.00E-033.86E+108.27E+090.0560.2604.14E+090.00151.00E-033.86E+108.27E+090.0560.2604.14E+090.00161.00E-033.86E+108.27E+090.0560.2604.14E+090.00171.00E-033.86E+108.27E+090.0560.2604.14E+0960.00181.00E-033.86E+108.27E+090.0560.2604.14E+09-60.00(3)当然我也验证了第(22)【laminates
16、with equal elastic properties in bending and extension】、(23)【quasi-homogeneous laminates】的排序,材料是Boron-Epoxy,下面给出计算的结果。从下面的两个结果表中可以知道,(22)排序的确是C=0,(23)的排序的确是B=0且C=0。验证成功。(A)第(22)排序。(B)第(23)排序。附件1:计算所用的程序代码。PROGRAM COMPOSITE!Coded by James WilsonIMPLICIT NONEREAL(8):A(3,3),B(3,3),D(3,3),MC(5),TEMP,ROT
17、(3,3)!A拉伸刚度;B耦合刚度;D弯曲刚度;!MC读入材料常数;ROT旋转矩阵REAL(8):TOTAL_TH,HALF_TH !总厚度;半厚度REAL(8),ALLOCATABLE:Q(:,:,:),AL(:),T(:),Z(:),Z1(:),Z2(:),Z3(:)!Q每层板相应刚度;AL转角;T每层板的厚度;Z坐标量INTEGER(4):N,I,J,K,SEQ,L!_IJK循环变量;N板的层数;SEQ序数CHARACTER(50):CHR(8),TEMPC,filename1,filename2!CHR、TEMPC:character variablesWRITE(*,*)Please
18、 insert the INP file name(a.txt for example):READ(*,*)filename1OPEN(8,file=filename1)!Open data file!Read in dataREAD(8,*)TEMPC,NALLOCATE(Q(3,3,N),AL(N),T(N),Z(N+1),Z1(N),Z2(N),Z3(N)READ(8,*)CHR(1:8)DO I=1,NREAD(8,*)SEQ,T(I),MC(1:5),AL(I)Q(:,:,I)=0!Calculate stiffness of each layer for the principal
19、 axisTEMP=1./(1-MC(3)*MC(4)Q(1,1,I)=MC(1)*TEMPQ(2,2,I)=MC(2)*TEMPQ(3,3,I)=MC(5)Q(1,2,I)=MC(4)*MC(2)*TEMPQ(2,1,I)=Q(1,2,I)AL(I)=AL(I)*3.1415926535898/180ROT(1,1)=(cos(AL(I)*2!Work out Rot MatrixROT(2,2)=ROT(1,1)ROT(3,3)=cos(2*AL(I)ROT(2,1)=1-ROT(1,1)ROT(1,2)=ROT(2,1)ROT(3,1)=0.5*sin(2*AL(I)ROT(3,2)=-
20、ROT(3,1)ROT(1,3)=-2*ROT(3,1)ROT(2,3)=-2*ROT(3,2)Q(:,:,I)=MATMUL(MATMUL(ROT,Q(:,:,I),TRANSPOSE(ROT)ENDDOTOTAL_TH=sum(T)HALF_TH=TOTAL_TH/2Z(1)=-HALF_TH!Work out ZDO I=1,NZ(I+1)=Z(I)+T(I)ENDDO!calculate tensor A、B and DDO K=1,NZ1(K)=(Z(K+1)-Z(K)Z2(K)=(Z(K+1)-Z(K)*(Z(K+1)+Z(K)/2Z3(K)=(Z(K+1)*3-Z(K)*3)/3
21、ENDDOA=0;B=0;D=0WRITE(*,*)Please insert the OUP file name(b.txt for example):READ(*,*)filename2OPEN(9,file=filename2)!Write in stiffness tensor for each single plyDO K=1,NWRITE(9,100)K100 FORMAT(The stiffness of number,1X,I2,2X,ply is:)DO I=1,3WRITE(9,200)Q(I,:,K)200 FORMAT(ES12.4,6X,ES12.4,6X,ES12.
22、4)ENDDOWRITE(9,(/)A=A+Q(:,:,K)*Z1(K)B=B+Q(:,:,K)*Z2(K)D=D+Q(:,:,K)*Z3(K)ENDDO!Output the actual stiffness of the laminateWRITE(9,(/);WRITE(9,(/)WRITE(9,*)The ACTUAL stiffness tensor of the laminate:WRITE(9,(/)WRITE(9,*)The extension stiffness A equals:DO I=1,3WRITE(9,200)A(I,1:3)ENDDOWRITE(9,(/)WRIT
23、E(9,*)The coupling stiffness B equals:DO I=1,3WRITE(9,200)B(I,1:3)ENDDOWRITE(9,(/)WRITE(9,*)The bending stiffness D equals:DO I=1,3WRITE(9,200)D(I,1:3)ENDDO!Normalised tensor outputWRITE(9,(/);WRITE(9,(/)WRITE(9,*)The NORMALISED stiffness tensor of the laminate:WRITE(9,(/)WRITE(9,*)The NORMALISED ex
24、tension stiffness A* equals:DO I=1,3WRITE(9,200)A(I,1:3)/TOTAL_THENDDOWRITE(9,(/)WRITE(9,*)The NORMALISED coupling tensor C equals:DO I=1,3WRITE(9,200)A(I,1:3)/TOTAL_TH-12*D(I,1:3)/TOTAL_TH*3ENDDOWRITE(9,(/)WRITE(9,*)The NORMALISED bending stiffness D* equals:DO I=1,3WRITE(9,200)12*D(I,1:3)/TOTAL_TH
25、*3ENDDOWRITE(*,*)OUTPUT successfully,please press any key to end program!READ(*,*)END PROGRAM COMPOSITE附2杨涛同学的MATLAB(GUI)计算程序。主要程序:(编了个小界面,程序略长,删掉一些程序自带解释语句,添加了一些对关键语句的解释。)界面是:作的一个算例如下:该算例结果与组内同伴James Wilson同学基本一致,其余算例结果也基本一致,仅仅在趋近于零时有略微差异,在此不赘于。后边附上源代码:functionvarargout = composit_plate(varargin)gu
26、i_Singleton = 1;gui_State = struct(gui_Name, mfilename,.gui_Singleton, gui_Singleton,.gui_OpeningFcn, composit_plate_OpeningFcn,.gui_OutputFcn, composit_plate_OutputFcn,.gui_LayoutFcn, ,.gui_Callback, );ifnargin & ischar(varargin1)gui_State.gui_Callback = str2func(varargin1);endifnargoutvarargout1:n
27、argout = gui_mainfcn(gui_State, varargin:);elsegui_mainfcn(gui_State, varargin:);endfunctioncomposit_plate_OpeningFcn(hObject, eventdata, handles, varargin)handles.output = hObject;guidata(hObject, handles);ha=axes(units,normalized,position,0 0 1 1);%嵌入坐标,为嵌入背景图片准备uistack(ha,down)%作为背景II=imread(武汉大学.jpg);%读入图片信息image(II)colormaphsvset(ha,handlevisib
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