Abbd Matrix Matlab Code
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%%%%%%%%ABBD MATRIX MATLAB CODE %%%%%%DONE BY JAGATH %%% WITH REFERENCE OF Aerospace Structural Composites www2.mae.ufl.edu/haftka/ %University of Florida close all;clc;clear all; % Sir i have taken the problem of "ORTHOTROPIC (PLANE STRESS)"condition % If i take only orthotropic i need to initalize % E1,E2,E3,G12,G31,G23,?21,?31,?32(9=indipendent constants) all these values this will become a % complex problem so for the simplification purpose i have taken % "ORTHOTROPIC (PLANE STRESS )" case(4=indipendent constants) % Initial Constants for the given materials E1 = 38.6e9; % Youngs Modulus for material 1 E2 = 8.27e9; % Youngs Modulus for material 2 G12 = 4.14e9; % Shear Modulus for the given materials nu12 = 0.26; % Poisson's Ratio for the given materials ,assume that 'nu'is'?' Poisson's Ratio symbol t = 0.001; % individual ply thickness (m) theta = 30;% assume theta= mathamatical angle representation '?' ang = [theta; theta+90; theta+90; theta; theta; theta+90; theta+90; theta;%ang is nothing but angle 45; -45; -45; 45; 45; -45; -45; 45];% I have taken 16 layers of composite laminate ply_ang = ang.*pi./180; % converting to rad n = length(ang); % Number of plies can be calculated by using this formula th = ply_ang; h = n*t; % Checking whether the number of plies match the number ply angles % But in general the below if not required because i have given already ''ply_ang = ang.*pi./180;'' if(n~=length(ply_ang)) display('Insufficient number of ply angles provided') exit; end nu21 = E2*nu12/E1; % This relation taken from jhonson book
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Abbd Matrix Matlab Code
Transcript of Abbd Matrix Matlab Code
%%%%%%%%ABBD MATRIX MATLAB CODE%%%%%%DONE BY JAGATH%%% WITH REFERENCE OF Aerospace Structural Composites www2.mae.ufl.edu/haftka/%University of Floridaclose all;clc;clear all;% Sir i have taken the problem of "ORTHOTROPIC (PLANE STRESS)"condition% If i take only orthotropic i need to initalize% E1,E2,E3,G12,G31,G23,?21,?31,?32(9=indipendent constants) all these values this will become a% complex problem so for the simplification purpose i have taken% "ORTHOTROPIC (PLANE STRESS )" case(4=indipendent constants)% Initial Constants for the given materials E1 = 38.6e9; % Youngs Modulus for material 1E2 = 8.27e9; % Youngs Modulus for material 2G12 = 4.14e9; % Shear Modulus for the given materialsnu12 = 0.26; % Poisson's Ratio for the given materials ,assume that 'nu'is'?' Poisson's Ratio symbolt = 0.001; % individual ply thickness (m)theta = 30;% assume theta= mathamatical angle representation '?'ang = [theta; theta+90; theta+90; theta; theta; theta+90; theta+90; theta;%ang is nothing but angle45; -45; -45; 45; 45; -45; -45; 45];% I have taken 16 layers of composite laminateply_ang = ang.*pi./180; % converting to radn = length(ang); % Number of plies can be calculated by using this formulath = ply_ang;h = n*t;% Checking whether the number of plies match the number ply angles% But in general the below if not required because i have given already ''ply_ang = ang.*pi./180;''if(n~=length(ply_ang))display('Insufficient number of ply angles provided')exit;endnu21 = E2*nu12/E1; % This relation taken from jhonson book% Q-matrixQ11 = E1/(1-nu12*nu21);Q22 = E2/(1-nu12*nu21);Q12 = (nu12*E2)/(1-nu12*nu21);Q66 = G12;% Material invariants (Us)U1 = (1/8)*(3*Q11 + 3*Q22 + 2*Q12 + 4*Q66);U2 = (1/2)*(Q11 - Q22);
U3 = (1/8)*(Q11 + Q22 - 2*Q12 - 4*Q66);U4 = (1/8)*(Q11 + Q22 + 6*Q12 - 4*Q66);U5 = (1/8)*(Q11 + Q22 - 2*Q12 + 4*Q66);% Finding the z's for each plylayers = n/2;for i=1:2*layers+1z(i) = t*(layers-(i-1));endz = -z;% Vs where the invariants are defined % t is thickness of each individual layer and 'th' is ply angleV0A = n*t;% n is number of layers %[V0A to V4A invariants for A matrix V0B to V4B invariants for B matrix; V0B to V4B invariants for B matrix again V0D to V4D invariants for D matrix;V1A = sum(t.*cos(2.*th));V2A = sum(t.*sin(2.*th));V3A = sum(t.*cos(4.*th));V4A = sum(t.*sin(4.*th));V0B = 0;V1B = 0;V2B = 0;V3B = 0;V4B = 0;for i = 1:nV1B = V1B + t*((z(i)+z(i+1))/2)*cos(2*th(i));V2B = V2B + t*((z(i)+z(i+1))/2)*sin(2*th(i));V3B = V3B + t*((z(i)+z(i+1))/2)*cos(4*th(i));V4B = V4B + t*((z(i)+z(i+1))/2)*sin(4*th(i));endV0D = (h^3)/12;V1D = 0;V2D = 0;V3D = 0;V4D = 0;for i = 1:nV1D = V1D + t*(z(i)^2 + z(i)*z(i+1) + z(i+1)^2)/3*cos(2*th(i));V2D = V2D + t*(z(i)^2 + z(i)*z(i+1) + z(i+1)^2)/3*sin(2*th(i));V3D = V3D + t*(z(i)^2 + z(i)*z(i+1) + z(i+1)^2)/3*cos(4*th(i));V4D = V4D + t*(z(i)^2 + z(i)*z(i+1) + z(i+1)^2)/3*sin(4*th(i));end% A-matrixA11 = U1*V0A + U2*V1A + U3*V3A;A22 = U1*V0A - U2*V1A + U3*V3A;A12 = U4*V0A - U3*V3A;A66 = U5*V0A - U3*V3A;A16 = 0.5*U2*V2A + U3*V4A;
A26 = 0.5*U2*V2A - U3*V4A;A = [A11 A12 A16; A12 A22 A26; A16 A26 A66];% B-matrixB11 = U1*V0B + U2*V1B + U3*V3B;B22 = U1*V0B - U2*V1B + U3*V3B;B12 = U4*V0B - U3*V3B;B66 = U5*V0B - U3*V3B;B16 = 0.5*U2*V2B + U3*V4B;B26 = 0.5*U2*V2B - U3*V4B;B = [B11 B12 B16; B12 B22 B26; B16 B26 B66];% D-matrixD11 = U1*V0D + U2*V1D + U3*V3D;D22 = U1*V0D - U2*V1D + U3*V3D;D12 = U4*V0D - U3*V3D;D66 = U5*V0D - U3*V3D;D16 = 0.5*U2*V2D + U3*V4D;D26 = 0.5*U2*V2D - U3*V4D;D = [D11 D12 D16; D12 D22 D26; D16 D26 D66];% Sir is there any possibility to add non-linear terms for ABBD matrix which you already% explained in the class ,i have written and understood up to this but i am unable to underestand% how to add the extra terms for the non-linearity caseABBD=[A B;B D] % i have written all the A B B D values in a single matrix that is ABBDABBD%Results of ABD MATRIX% A = % 1.0e+08 * % 2.8725 1.2813 0.2307 % 1.2813 2.8725 -0.2307 % 0.2307 -0.2307 1.5946% B = % 1.0e+04 * % -5.3270 5.3270 -9.2267 % 5.3270 -5.3270 9.2267 % -9.2267 9.2267 5.3270% D = %1.0e+03 * %6.1895 2.7335 0.6069 %2.7335 6.0664 -0.3772 %0.6069 -0.3772 3.4019
