matlab compliances matrix
function y = OrthotropicCompliance(E1,E2,E3,NU12,NU23,NU13,G12,G23,G13)
%OrthotropicCompliance This function returns the compliance matrix
% for orthotropic materials. There are nine
% arguments representing the nine independent
% material constants. The size of the compliance
% matrix is 6 x 6.
y = [1/E1 -NU12/E1 -NU13/E1 0 0 0 ; -NU12/E1 1/E2 -NU23/E2 0 0 0 ;
-NU13/E1 -NU23/E2 1/E3 0 0 0 ; 0 0 0 1/G23 0 0 ; 0 0 0 0 1/G13 0 ;
0 0 0 0 0 1/G12];
end
function y = OrthotropicStiffness(E1,E2,E3,NU12,NU23,NU13,G12,G23,G13)
%OrthotropicStiffness This function returns the stiffness matrix
% for orthotropic materials. There are nine
% arguments representing the nine independent
% material constants. The size of the stiffness
% matrix is 6 x 6.
x = [1/E1 -NU12/E1 -NU13/E1 0 0 0 ; -NU12/E1 1/E2 -NU23/E2 0 0 0 ;
-NU13/E1 -NU23/E2 1/E3 0 0 0 ; 0 0 0 1/G23 0 0 ; 0 0 0 0 1/G13 0 ;
0 0 0 0 0 1/G12];
y = inv(x);
end
function y = TransverselyIsotropicCompliance(E1,E2,NU12,NU23,G12)
%TransverselyIsotropicCompliance This function returns the
% compliance matrix for
% transversely isotropic
% materials. There are five
% arguments representing the
% five independent material
% constants. The size of the
% compliance matrix is 6 x 6.
y = [1/E1 -NU12/E1 -NU12/E1 0 0 0 ; -NU12/E1 1/E2 -NU23/E2 0 0 0 ;
-NU12/E1 -NU23/E2 1/E2 0 0 0 ; 0 0 0 2*(1+NU23)/E2 0 0 ;
0 0 0 0 1/G12 0 ; 0 0 0 0 0 1/G12];
end
function y = TransverselyIsotropicStiffness(E1,E2,NU12,NU23,G12)
%TransverselyIsotropicStiffness This function returns the
% stiffness matrix for
% transversely isotropic
% materials. There are five
% arguments representing the
% five independent material
% constants. The size of the
% stiffness matrix is 6 x 6.
x = [1/E1 -NU12/E1 -NU12/E1 0 0 0 ; -NU12/E1 1/E2 -NU23/E2 0 0 0 ;
-NU12/E1 -NU23/E2 1/E2 0 0 0 ; 0 0 0 2*(1+NU23)/E2 0 0 ;
0 0 0 0 1/G12 0 ; 0 0 0 0 0 1/G12];
y = inv(x);
end
function y = IsotropicCompliance(E,NU)
%IsotropicCompliance This function returns the
% compliance matrix for isotropic
% materials. There are two
% arguments representing the
% two independent material
% constants. The size of the
% compliance matrix is 6 x 6.
y = [1/E -NU/E -NU/E 0 0 0 ; -NU/E 1/E -NU/E 0 0 0 ;
-NU/E -NU/E 1/E 0 0 0 ; 0 0 0 2*(1+NU)/E 0 0 ;
0 0 0 0 2*(1+NU)/E 0 ; 0 0 0 0 0 2*(1+NU)/E];
end
function y = IsotropicStiffness(E,NU)
%IsotropicStiffness This function returns the
% stiffness matrix for isotropic
% materials. There are two
% arguments representing the
% two independent material
% constants. The size of the
% stiffness matrix is 6 x 6.
x = [1/E -NU/E -NU/E 0 0 0 ; -NU/E 1/E -NU/E 0 0 0 ;
-NU/E -NU/E 1/E 0 0 0 ; 0 0 0 2*(1+NU)/E 0 0 ;
0 0 0 0 2*(1+NU)/E 0 ; 0 0 0 0 0 2*(1+NU)/E];
y = inv(x);
end