*Use MatLab Please* In the analysis of plane trusses, it is necessary to assembl
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*Use MatLab Please* In the analysis of plane trusses, it is necessary to assemble a global stillness matrix based on the orientation, connectivity and stiffness properties of the individual truss elements. The stiffness matrix for each element ki, is given by ki = LiTk'Li where, the transformation matrix Li is given by Li= and, the local stiffness element matrix k' is given by k' = EA/ le [1 -1 -1 1] The (x, y) Coordinates of the end points can be used to calculate. I, m and le, as shown in the figures below. Determine the coordinates of the end points of each of the 4 elements of the plane truss shown above, and hence, use the equations to calculate the global stiffness matrix, k, in each case. Use point 1 as the origin with coordinates (x1, y1) = (0,0).Explanation / Answer
function [ G , M , K ] = matrices() % Calculation of Matrices (Green Matrix G, Mass Matrix M, Stiffness Matrix % K) % Reference: Petyt - Introduction to FE Vibration Analysis (S.196) global no_panels; global node_no; O_d = zeros(12,3*node_no,no_panels); % Definition of Transformation Matrix Q = node_definition(); % Geometry of Ice Floe for d = 1 : no_panels O_d(:,:,d) = transformation(d,Q); % Initializing of Transformation Matrix for Panel d end % Calculation of Green Matrix G G = zeros(3*node_no,3*node_no); for d = 1 : no_panels A = zeros(12,3*node_no); for e = 1 : no_panels % [m,n] = size(green_matrix(d,e)*O_d(:,:,e)) A = A + green_matrix(d,e)*O_d(:,:,e); end G = G + transpose(O_d(:,:,d))*A; end [mass_mtrx , steif_mtrx] = FEM_matrices(); % -> Matrices [m]_d & [k]_d M = zeros(3*node_no,3*node_no); K = zeros(3*node_no,3*node_no); % Calculation of M and K for d = 1 : no_panels M = M + transpose(O_d(:,:,d)) * mass_mtrx * O_d(:,:,d); K = K + transpose(O_d(:,:,d)) * steif_mtrx * O_d(:,:,d); end end
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