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- clc
- syms r w(r) G(r) v h r dG(r) d P E1(r) dE1(r) R
- %R=1.2;% (мм) радиус пластинки
- % P=35;% (мм рт ст) = p[-]-p[+]
- % d=1;%(мм)радиус дырки
- % v=0.45;%коэф Пуассона, сокращение в плоскости изотропии при растяжении в той же плоскости
- % h=0.25;%(мм) ширина примерно пластиныы
- E1(r) =5*r^2;
- dE1(r)=diff(E1,r,1);
- G(r)=E1(r)/(2*(1+v));
- dG(r) = diff(G,r,1);
- eqn = E1(r) * ( diff(w(r), r, 3) + 1/r * diff(w(r), r, 2) -...
- 1/r^2 * diff(w(r), r) ) + diff(E1(r), r) *...
- (diff(w(r), r, 2) + v/r * diff(w(r), r)) == (6*P/h^3 ) *...
- (r - d/r) * (1-v^2) - diff(E1(r), r) *3*P/(5*h* dG(r) )*...
- (1 + v + d/r^2 * (1 - v ))
- y2= diff(w,r,2);
- y1= diff(w,r);
- cond1 = [y2(d) == 6*P/(5*dG(r)*h), y1(R)==3*35/G(R)*(d/R - R),w(R)==0]
- cond2 = [y2(d) == 6*P/(5*dG(r)*h), w(R)==0,-y2(R)-v*y1(R)/r+h^2/...
- (10*dG(R))*(-12*P/h^3)+6*(1+v)*v*P/(5*E1(R)*h)==0]
- solw1(r) = dsolve(eqn, cond1);
- solw2(r)=dsolve(eqn, cond2);
- s11(r) = subs(solw(r),P,35);
- s22(r)=subs(s11(r),d,1);
- s33(r)=subs(s22(r),v,0.45);
- s44(r)=subs(s33(r),h,0.25);
- r=d:0.001:R;
- func=s4(r);
- func2=s44(r);
- plot (r,func)
- plot (r,func2)
- %
- % z(x,y) = (s4(sqrt(x.^2 + y.^2)))
- % for fi=0 :(pi/3):2*pi
- % for r= 0.1:0.1: 1.2
- %
- % x = [x r.*cos(fi)];
- % y=[y r.*sin(fi)];
- % end
- % end
- %
- % [X, Y] = meshgrid(x, y);
- % z =double(s4(sqrt(X.^2 + Y.^2)));
- % surf(x, y, z);
- % colormap(cool);
- % shading flat;
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