For the following system find the displacements at each node

For the following system, find the displacements at each node and the forces in each spring. You will need to write Octave/MATLAB code to solve this problem. Submit your code in the drop box. Hard copies of the assignment should describe how you setup the problem along with results, i.e.. all elemental stiffness matrices, global stiffness matrix, reduced system stiffness matrix, and elemental forces.

Solution

Hi,

You can calculate the the matrix using the relation with mathematical calculations as: say with the example:

v denotes a vector quantity of dimension equal to the spacial dimension of the problem i.e.the displacement or velocity at a point, the bold non-italicized font d denotes a vector or matrix which is of dimension of the number of unknowns in the discrete system i.e. a system matrix like the stiffness matrix, an uppercase subscript denotes a node number whereas a lowercase subscript in general denotes a vector component along a Cartesian unit vector. So, if d is the system vector of nodal unknowns, uI is a displacement vector of node I and uIi is the component of the displacement at node I in the i direction, or uI · ei . Often Matlab syntax will be intermixed with mathematical notation which hopefully adds clarity to the explanation.

I hope it will solve your problem.