[热点讨论]请大家帮我看下我的MATLAB卷积分问题出在哪里？谢谢！ [复制链接]

用MATLAB自带卷积分函数计算弹性半空间在一三角脉冲荷载下自由表面的竖向位移，与文献正确结果相差10的5次方倍，但自己编写卷积分代码，反而得到文献结果。请大家帮我看下问题出在哪？谢谢！ 8X I?  
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另外，为何MATLAB自带卷积分函数结果矩阵的维数会是被卷积两矩阵维数之和减1？ 9JWa$iBH@  
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1. 问题描述，如下图1所示： <ERB.d!  
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2. 格林函数，如下图2所示： ]r-C1bKD`  
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3. 参考文献正确解，如下图3所示： 0jzbG]pc:E  
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4. 本人直接用自编卷积分MATLAB代码算的出解（如下图4）及相应代码： NBF MN%  
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clear; [j"9rO" +  
clc; &|aqP \Q5  
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%loading history 0Hs|*:Y1D  
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dt=0.01; *c)uGz'cD  
ti=0.0008; }'OHE(s
  
te=12; ~Aq5XI%i  
t=ti:dt:te; oxj3[</'k  
pt=(10*t./1.5).*(t>=0 & t<=1.5)+(20-10*t./1.5).*(t>1.5 & t<=3)+0.*(t>3); Q.Aw2  
m=length(pt); )?2e  
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%load distribution in space 5VO;s1  
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rp=0.1; 2Sq_Tw3^  
ri=0; HAYMX:%  
rc=0.1; QW_agm  
dr=0.001; {ls+dx/  
r=ri:dr:rc; SSBg?H'T  
pr=1*(r<=rp)+0*(r>rp); yIb,,!y9{  
n=length(pr);
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%load function with respect to t and r 1shBY@mlq  
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p=pr.'*pt; < pTTo  
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%green's function +Ug/rtK4  
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G=1; &ff&Y.q~  
cs=1; \#'TNmS  
for i=1:1:m ^Cv^yTj;&  
  for j=1:1:n Gq#~vr  
    u(j,i)=heaviside(cs*t(i)-r(j))/(pi*G*sqrt(t(i)^2-(r(j)/cs)^2)); jxgj,h"}9`  
  end "&Qctk`<P  
end i{^Z1;Yl  
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%convolution and response of displacement ( #Z`  
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for i=1:1:m N:VX!w  
  for j=1:1:n sP'0Sl~NU  
    v(j,i)=0; !}M,  
    for k=1:1:i *FR$vL
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      for g=1:1:j Q6C-4ja  
        v(j,i)=v(j,i)+p(g,k)*u(j-g+1,i-k+1)*dr*dt; .7ayQp  
      end; V2|3i}V"  
    end; 2h {q h  
  end; K:y^OAZfV  
end; ~9Cz6yF  
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%plot the response history MVCl.o  
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plot(t,v(n,); Z<b"`ty.  
xlabel('t/s'); ']ood!  
ylabel('v/m'); IO.<q,pP!_  
grid on; -m 5}#P89  
title('response of point A or C'); @LD6:gy  
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5. 直接用MATLAB自带卷积分算的出解（如下图5）及相应代码： h7_)%U<J2  
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clear; ~H@+D}J?  
clc; _q>SE1j+W=  
@=]8^?$t 0  
%loading history T9y;OG  
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dt=0.01; \Mx JH[  
ti=0.0008; j;P+_Hfe/E  
te=12; t]_S  
t=ti:dt:te; iT)WR90  
pt=(10*t./1.5).*(t>=0 & t<=1.5)+(20-10*t./1.5).*(t>1.5 & t<=3)+0.*(t>3); }3/~x  
m=length(pt); *8g<R  
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%load distribution in space EH9Hpo  
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rp=0.1; &y_? rH  
ri=0; zDBD.5R;  
rc=0.1; h#f&|*Q5m  
dr=0.001; m24v@?*  
r=ri:dr:rc; \MYU<6{u  
pr=1*(r<=rp)+0*(r>rp); ij)Cm]4(2  
n=length(pr); M StX*Zw  
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%load function with respect to t and r 99ASIC!  
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p=pr.'*pt; 'wQy]zm$  
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%green function ;lfWuU%R  
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G=1; $Lq:=7&LRn  
cs=1; LdTIR]  
for i=1:1:m a?<?5  
  for j=1:1:n U}P,EP%p  
    u(j,i)=heaviside(cs*t(i)-r(j))/(pi*G*sqrt(t(i)^2-(r(j)/cs)^2)); 7!d$M{0"  
  end U~QMR-bz  
end yz)ESQ~va  
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%convolution and response of displacement VO9f~>`(  
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v=conv2(u,p); kEAhTh&g*  
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%plot the response history {[3YJkrM  
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rr=r(n); 8tZ};="F  
[tpu,rpu]=meshgrid(ti:dt:2*te-dt,ri:dr:2*rc); |3@=CE7G  
[X,Y,Z]=meshgrid(linspace(min(tpu(),max(tpu()),linspace(min(rpu(),max(rpu()),linspace(min(v(),max(v())); IA4+ad'\E  
V=Y; ZlM_m >,o  
h=contourslice(X,Y,Z,V,tpu,rpu,v,[0 0]+rr); 8eww7k^R  
set(h,'edgecolor','k'); 8kbBz  
contourslice(X,Y,Z,V,tpu,rpu,v,[0 0]+rr); hZF(/4Z2  
xlabel('t/s'); Q&wYc{TUbm  
ylabel('r/m'); +u#Sl)F  
zlabel('v/m'); zlMlMyG4  
axis([0 12 0 0.1 0 12e4]); 4<yK7x  
view(0,0); (HSw%e  
grid on; "`]'ZIx[R/  
title('displacement response history of point A or C');