Things will be more clear if you read this first.
MATLAB Part :-
Function to get transformed stiffness matrix Q_xy from Q_12 :-
Create separate file with filename same as function name(transform_stiffness.m) Don't run this file.
Text :-
% Function to obtain transformed stiffness matrix Q_xy in loading % axes(x,y) from stiffness matrix in principle material axes Q_12 function Q_xy = transform_stiffness(Q_12,theta) m = cosd(theta); n = sind(theta); % Transformation matrix, T T = [m^2 n^2 2*m*n; n^2 m^2 -2*m*n; -m*n m*n m^2-n^2]; % Transformed stiffness matrix [Qxx Qxy 2*Qxs % Qyx Qyy 2*Qys % Qsx Qsy 2*Qss] Q_xy = inv(T)*Q_12*T; % We want [Qxx Qxy Qxs % Qyx Qyy Qys % Qsx Qsy Qss] Q_xy = [Q_xy(1:3,1:2), 0.5*Q_xy(1:3,3)]; end
Script file :-
Create separate file with any name of your choice, and run this
text :-
clc; clear; %###################################################### % Layer Properties % %###################################################### E1 = 128; % GPa E2 = 11; % GPa G12 = 4.5; % GPa v12 = 0.25; % calculation for v21 v21 = (E2/E1)*v12; % Layer Thickness tk = 2.5; % mm %################################################################## % Stifnness Matrix Q12 (Principal axes) % %################################################################## Q_12 = [ E1/(1-v12*v21) v21*E1/(1-v12*v21) 0; v21*E1/(1-v12*v21) E2/(1-v12*v21) 0; 0 0 2*G12]; %################################################################## % Calculation for [0]4 , 4 layers % %################################################################## thetas = [0 0 0 0]; % angles for all layers D1 = zeros(3,3); % Initializing bending stiffness matrix h = -2*tk:tk:2*tk; % hk of layers [h0,h1,...hk] -2tk to 2tk in steps of tk for k = 1:4 % For all layers theta = thetas(k); Q_xy = transform_stiffness(Q_12,theta); % Transformed stiffness matrix from developed function D1 = D1 + (1/3)*Q_xy*(h(k+1)^3 - h(k)^3); % Summation end fprintf('For [0]4 laminate, bending stiffness matrix in GPa-mm^3:\n') disp(num2str(round(D1,2))) % Display matrix with elements rounded to 2 decimal places %################################################################## % Calculation for [0/30]s , 4layers % %################################################################## thetas = [0 30 30 0]; D2 = zeros(3,3); % Initializing bending stiffness matrix h = -2*tk:tk:2*tk; % hk of layers for k = 1:4 theta = thetas(k); Q_xy = transform_stiffness(Q_12,theta); D2 = D2 + (1/3)*Q_xy*(h(k+1)^3 - h(k)^3); end fprintf('For [0/30]s laminate, bending stiffness matrix in GPa-mm^3:\n') disp(num2str(round(D2,2))) %################################################################## % Calculation for [0,+-45]s , 6layers % %################################################################## thetas = [0 45 -45 -45 45 0]; D3 = zeros(3,3); % Initializing bending stiffness matrix h = -3*tk:tk:3*tk; % hk of layers, -3tk to 3tk in steps of tk for k = 1:6 theta = thetas(k); Q_xy = transform_stiffness(Q_12,theta); D3 = D3 + (1/3)*Q_xy*(h(k+1)^3 - h(k)^3); end fprintf('For [0/+-45]s laminate, bending stiffness matrix in GPa-mm^3:\n') disp(num2str(round(D3,2)))
Results :-
Solve with matlab Determine the bending stiffness for the following laminates using the properties shown below....
please solve 2 and 3 1- The reduced stiffness matrix [Q] is given for a unidirectional lamina as follows: 5.681 0.3164 0 ] [Q]=0.3164 1.217 0 Msi I 0 0 0.6006 Calculate the four engineering constants E1, E2, V12, G12 of the lamina. 2- Calculate the transformed reduced stiffness [Q] for the above problem for 0 = 30°. Glass 3- A glass/epoxy lamina consists of 70% fiber volume fraction. Use properties of glass and epoxy from the tables below to...
Use the stiffness method to analyse the elastic frame ABC shown below. Use a model made up of 2 the elements (AB and CB) and the axis indicated in the figure. All members have the following properties: E = 2 -10% kPa, A = 0.005 m², 1 = 1.5e - 4 m. Also the lengths of the elements are the same: AB = BC = L = 3.1 m and 6 = 45 kN/m. ות 0 B 3 2 x...
Use the stiffness method to analyse the elastic frame ABC shown below. Use a model made up of 2 the elements (AB and CB) and the axis indicated in the figure. All members have the following properties: E = 2 -10% kPa, A = 0.005 m², 1 = 1.5e - 4 m. Also the lengths of the elements are the same: AB = BC = L = 3.1 m and 6 = 45 kN/m. ות 0 B 3 2 x...
Use the stiffness method to analyse the elastic frame ABC shown below. Use a model made up of 2 the elements (AB and CB) and the axis indicated in the figure. All members have the following properties: E = 2 -10% kPa, A = 0.005 m², 1 = 1.5e - 4 m. Also the lengths of the elements are the same: AB = BC = L = 3.1 m and 6 = 45 kN/m. ות 0 B 3 2 x...
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