Truss Displacements

The structure stiffness matrix has many zero terms. For large structures it can be a very sparse matrix. This sparseness can be advantageously taken into account by the equation solving program. For our purposes we simply use a precompiled module "mumarray", written mainly in C.

The structure stiffness matrix is positive definite. In plane language, all the leading diagonal terms of the matrix are positive numbers. The matrix is also symmetrical, so that stiffness matrix elements are symmetrically placed along the leading diagonal, thus $K_{ij} = K_{ji}$

All these features, particularly sparsness of the stiffness matrix and symmetry, can be taken advantage of in the solution. The solution of sparsely populated matrices is a separate and large topic, which deserves separate treatise or treatises.

The solution of truss stiffness equations (3.13) yields displacements of all pins in global axes $\mathbf{u_s}$.

For our purposes we simply use a precompiled module "mumarray", written mainly in C.