Find the global displacement for each node in the spring sys

Find the global displacement for each node in the spring system shown below using MATLAB Assign a mode at each plate and assume the rigid plates can move only in x-direction Calculate the displacement of each node using MATLAB. Output the displacement results to the command window using f print f. Calculate the reaction force at the fixed wall using MATLAB

Solution

In practise, element connectivity matrices are never formed. Instead the global stiffness matrix is set up using a process called assembly. Using Matlablike pseudo code, the assembly of the global stiffness matrix can be described as follows: K = initializeK; for e=1:nel edof = get global degree of freedom numbers(e); Ke = elementStiffnessMatrix(e); K(edof,edof) = K(edof,edof)+Ke; % With connectivity matrices: K = K + Ce’*Ke*Ce end Give for each element in the spring system shown below the values in the vector edof. Global node numbers are shown in larger font above the nodes; local in smaller font below1 .

e=1: edof = [3 4] e=2: edof = [1 4] e=3: edof = [2 1] For the system shown in the figure, with data k1 = 1, k2 = 2 and k3 = 3 say, the stiffness matrix can be assembled using the following specialized version of the above algorithm: ke = [1 2 3]; dof = [3 4; 1 4; 2 1]; K = zeros(4,4); for e=1:3 edof = dof(e,:); Ke = ke(e)*[1 -1; -1 1]; K(edof,edof) = K(edof,edof)+Ke; end You are recommended to copy the code, paste it into Matlab and run it.