复合材料力学上机编程作业(计算层合板刚度)要点

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（2012031890015）、Tau Young（2012031890011）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、υ21、G12；各单层对应的厚度；各单层对应的主方向夹角θ。

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：υ12=υ21E2E1；Q11=E11-υ12υ21；Q22=E21-υ12υ21；Q12=υ12E1； 1-υ12υ21Q66=G12得到Q矩阵后，根据课本上讲到的Q=(T-1)TQ(T-1)得到Q。

然后根据z坐标的定义求出z0到zn，接下来，最重要的一步，根据下式计算A、B、D。

n⎧⎪Aij=∑(Qij)k(zk-zk-1)k=1⎪⎪1n22⎨Bij=∑(Qij)k(zk-zk-1) 2k=1⎪⎪1n33⎪Dij=∑(Qij)k(zk-zk-1)3k=1⎩一、书上P110的几个问题可以归纳为以下几个类型。

第 1 页共 1 页（4）6层反对称角铺设层合板（T5-10）第 2 页共 2 页（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,。

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-Epoxy。

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。

第 3 页共 3 页（2）Glass-Epoxy材料。

第 4 页共 4 页（3）当然我也验证了第（22）【laminates 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。

第 5 页共 5 页附件1：计算所用的程序代码。

PROGRAM COMPOSITE !Coded by James Wilson IMPLICIT NONEREAL(8)::A(3,3),B(3,3),D(3,3),MC(5),TEMP,ROT(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 insert the INP file name(a.txt for example):" READ(*,*)filename1 OPEN(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 axis TEMP=1./(1-MC(3)*MC(4)) Q(1,1,I)=MC(1)*TEMP Q(2,2,I)=MC(2)*TEMP Q(3,3,I)=MC(5)Q(1,2,I)=MC(4)*MC(2)*TEMP Q(2,1,I)=Q(1,2,I)AL(I)=AL(I)*3.1415926535898/180ROT(1,1)=(cos(AL(I)))**2!Work out Rot Matrix ROT(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)=-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/2 Z(1)=-HALF_TH !Work out Z DOI=1,NZ(I+1)=Z(I)+T(I) ENDDO!calculate tensor A、B and D DO K=1,NZ1(K)=(Z(K+1)-Z(K))Z2(K)=(Z(K+1)-Z(K))*(Z(K+1)+Z(K))/2 Z3(K)=(Z(K+1)**3-Z(K)**3)/3 ENDDOA=0;B=0;D=0WRITE(*,*)"Please insert the OUP file name(b.txt for example):"READ(*,*)filename2 OPEN(9,file=filename2)!Write in stiffness tensor for each single ply DO 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,ES12.4) 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 laminate WRITE(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,"(/)")WRITE(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 output WRITE(9,"(/)");WRITE(9,"(/)")WRITE(9,*)"The NORMALISED stiffness tensor of the laminate:" WRITE(9,"(/)") WRITE(9,*)"The NORMALISED extension stiffness A* equals:" DO I=1,3WRITE(9,200)A(I,1:3)/TOTAL_TH ENDDOWRITE(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**3 ENDDOWRITE(9,"(/)")WRITE(9,*)"The NORMALISED bending stiffness D* equals:" DO I=1,3WRITE(9,200)12*D(I,1:3)/TOTAL_TH**3 ENDDOWRITE(*,*)"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：第 6 页共 6 页作的一个算例如下：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：function varargout = composit_plate(varargin)gui_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', []);if nargin && ischar(varargin{1})gui_State.gui_Callback = str2func(varargin{1});endif nargout[varargout{1:nargout}] = gui_mainfcn(gui_State, varargin{:});elsegui_mainfcn(gui_State, varargin{:});endfunction composit_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)第 7 页共 7 页colormap hsvset(ha,'handlevisibility','off','visible','off')function varargout = composit_plate_OutputFcn(hObject, eventdata, handles) varargout{1} = handles.output;function edit1_Callback(hObject, eventdata, handles)function edit1_CreateFcn(hObject, eventdata, handles)if ispc && isequal(get(hObject,'BackgroundColor'),get(0,'defaultUicontrolBackgroundColor'))set(hObject,'BackgroundColor','white');endfunction edit2_Callback(hObject, eventdata, handles)function edit2_CreateFcn(hObject, eventdata, handles)if ispc && isequal(get(hObject,'BackgroundColor'),get(0,'defaultUicontrolBackgroundColor'))set(hObject,'BackgroundColor','white');endfunction edit3_Callback(hObject, eventdata, handles)function edit3_CreateFcn(hObject, eventdata, handles)if ispc && isequal(get(hObject,'BackgroundColor'),get(0,'defaultUicontrolBackgroundColor'))set(hObject,'BackgroundColor','white');endfunction edit4_Callback(hObject, eventdata, ~)function edit4_CreateFcn(hObject, eventdata, handles)if ispc && isequal(get(hObject,'BackgroundColor'),get(0,'defaultUicontrolBackgroundColor'))set(hObject,'BackgroundColor','white');endfunction pushbutton1_Callback(hObject, eventdata, handles) syms e1e2v21g12ang%本程序采用符号运算v12=v21*e2/e1;q=[e1/(1-v12*v21),v21*e2/(1- v12*v21),0v21*e2/(1-v12*v21),e2/(1-v12*v21),00,0,g12];tran=[ cos(ang)^2, sin(ang)^2, -sin(2*ang)sin(ang)^2, cos(ang)^2, sin(2*ang)sin(2*ang)/2, -sin(2*ang)/2, cos(2*ang)];q1=tran*q*tran';%得到Qn=str2num(get(handles.edit2,'string'));%读入层数n=floor(n);nn=0;A=0;B=0;D=0;t=str2num(get(handles.edit3,'string'));%读入每层厚度t1=zeros(1,n+1);t1(1)=0;for nn=1:nt1(nn+1)=t1(nn)+t(nn);endang1=str2num(get(handles.edit4,'string'));%读入每层角度const=str2num(get(handles.edit1,'string'));%读入材料系数t0=sum(t)/2;t1=t1-t0;e1=const(1);e2=const(2);v21=const(3);g12=const(4);q11=subs(q1);for nn=1:nang=ang1(nn);nn=nn+1;A=A+subs(q11*(t1(nn)-t1(nn-1)));B=B+subs(0.5*q11*(t1(nn)^2-t1(nn-1)^2));D=D+subs(1/3*q11*(t1(nn)^3-t1(nn-1)^3));end%累加计算set(handles.edit5,'string',num2str(A(1,:)));%以下为输出结果set(handles.edit6,'string',num2str(A(2,:)));set(handles.edit7,'string',num2str(A(3,:)));set(handles.edit8,'string',num2str(B(1,:)));set(handles.edit9,'string',num2str(B(2,:)));set(handles.edit10,'string',num2str(B(3,:)));set(handles.edit11,'string',num2str(D(1,:)));set(handles.edit12,'string',num2str(D(2,:)));第 8 页共 8 页set(handles.edit13,'string',num2str(D(3,:)));function edit5_Callback(hObject, eventdata, handles) function edit5_CreateFcn(hObject, eventdata, handles) if ispc && isequal(get(hObject,'BackgroundColor'),get(0,'defaultUicontrolBackgroundColor'))set(hObject,'BackgroundColor','white');endfunction edit6_Callback(hObject, eventdata, handles) function edit6_CreateFcn(hObject, eventdata, handles) if ispc && isequal(get(hObject,'BackgroundColor'),get(0,'defaultUicontrolBackgroundColor'))set(hObject,'BackgroundColor','white');endfunction edit7_Callback(hObject, eventdata, handles) function edit7_CreateFcn(hObject, eventdata, handles) if ispc && isequal(get(hObject,'BackgroundColor'),get(0,'defaultUicontrolBackgroundColor'))set(hObject,'BackgroundColor','white');endfunction edit8_Callback(hObject, eventdata, handles) function edit8_CreateFcn(hObject, eventdata, handles) if ispc && isequal(get(hObject,'BackgroundColor'),get(0,'defaultUicontrolBackgroundColor'))set(hObject,'BackgroundColor','white');endfunction edit9_Callback(hObject, eventdata, handles) function edit9_CreateFcn(hObject, eventdata, handles) if ispc && isequal(get(hObject,'BackgroundColor'),get(0,'defaultUicontrolBackgroundColor'))set(hObject,'BackgroundColor','white');endfunction edit10_Callback(hObject, eventdata, handles) functionedit10_CreateFcn(hObject, eventdata, handles) if ispc &&isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor')) set(hObject,'BackgroundColor','white');endfunction edit11_Callback(hObject, eventdata, handles) functionedit11_CreateFcn(hObject, eventdata, handles) if ispc &&isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor')) set(hObject,'BackgroundColor','white');endfunction edit12_Callback(hObject, eventdata, handles) functionedit12_CreateFcn(hObject, eventdata, handles) if ispc &&isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor')) set(hObject,'BackgroundColor','white');endfunction edit13_Callback(hObject, eventdata, handles) functionedit13_CreateFcn(hObject, eventdata, handles) if ispc &&isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor')) set(hObject,'BackgroundColor','white');end第 9 页共 9 页。