clc
clear all
echo on
close all
syms a11 a12 a13 a14 l x;
v=a11*sin(pi*x/l)+a12*sin(2*pi*x/l)+a13*sin(3*pi*x/l)+a14*sin(4*pi*x/l);
p11_v=diff(v);
p12_v=diff(p11_v);

Sx_a11=diff((p12_v)^2,a11);
Sx_a11=diff(Sx_a11,a11);
C_a11=int(Sx_a11,x);
C11=a11*(subs(C_a11,x,l)-subs(C_a11,x,0));

Sx_a12=diff((p12_v)^2,a12);
Sx_a12=diff(Sx_a12,a12);
C_a12=int(Sx_a12,x);
C12=a12*(subs(C_a12,x,l)-subs(C_a12,x,0));

Sx_a13=diff((p12_v)^2,a13);
Sx_a13=diff(Sx_a13,a13);
C_a13=int(Sx_a13,x);
C13=a13*(subs(C_a13,x,l)-subs(C_a13,x,0));

Sx_a14=diff((p12_v)^2,a14);
Sx_a14=diff(Sx_a14,a14) ;
C_a14=int(Sx_a14,x);
C14=a14*(subs(C_a14,x,l)-subs(C_a14,x,0));
syms Wo;

Sx=Wo+(1-(x/l))^4;
a11_Sx=diff(Sx,a11);
C_a11_Sx=int(a11_Sx,x);
Cp11=subs(C_a11_Sx,x,l)-subs(C_a11_Sx,x,0);
Cp11=simplify(Cp11);

a12_Sx=diff(Sx,a12);
C_a12_Sx=int(a12_Sx,x);
Cp12=subs(C_a12_Sx,x,l)-subs(C_a12_Sx,x,0);
Cp12=simplify(Cp12);

a13_Sx=diff(Sx,a13);
C_a13_Sx=int(a13_Sx,x);
Cp13=subs(C_a13_Sx,x,l)-subs(C_a13_Sx,x,0);
Cp13=simplify(Cp13);

a14_Sx=diff(Sx,a14);
C_a14_Sx=int(a14_Sx,x);
Cp14=subs(C_a14_Sx,x,l)-subs(C_a14_Sx,x,0);
Cp14=simplify(Cp14);

pause

syms E J;
C1=sym(zeros(4,4)); b1=sym(zeros(4,1));
C1(1,1)=C11/a11; b1(1,1)=Cp11;
C1(2,2)=C12/a12; b1(2,1)=Cp12;
C1(3,3)=C13/a13; b1(3,1)=Cp13;
C1(4,4)=C14/a14; b1(4,1)=Cp14;
C1=(E*J/2)*C1;
a1=C1\b1;
F_a11=@(E,l,J,Wo)eval(a1(1,1));
F_a12=@(E,l,J,Wo)eval(a1(2,1));
F_a13=@(E,l,J,Wo)eval(a1(3,1));
F_a14=@(E,l,J,Wo)eval(a1(4,1));

pause

E=1;
l=3;
J=1;
Wo=2;
a11=F_a11(E,l,J,Wo);
a12=F_a12(E,l,J,Wo);
a13=F_a13(E,l,J,Wo);
a14=F_a14(E,l,J,Wo);

echo off
v1=[];
x=0:0.001:3;
for i1=1:length(x)
v1(i1)=a11*sin(pi*x(i1)/l)+a12*sin(2*pi*x(i1)/l)+a13*sin(3*pi*x(i1)/l)+a14*sin(4*pi*x(i1)/l);
end
figure(1)
plot(x,v1,'b--')
hold on
legend('Rozw. przybliżone');
title('Ugięcia belki'); xlabel('x'); ylabel('v(x)'); grid;