Static Finite Element analysis of a truss assembly using MATLAB

The theme of this article is to present an approach for the development of matrix based stress analysis equations for trusses and demonstrating use of MATLAB software to expedite the solution of the matrix based equations. The approach involves developing displacement matrices for connected springs based on their spring constants, and then extending the technique to two dimensional rods by determining their equivalent stiffness through their axial displacement formula. The rod matrices are then adjusted for rod orientation angle and global matrices for trusses are assembled using the stiffness method. Techniques for inclusion of the boundary conditions in the global matrix equations are shown. MATLAB software has extensive matrix manipulation capabilities and features. MATLAB instructions are used to find the displacements for an example truss. The MATLAB produced results are compared against results obtained by classical techniques. The stresses in truss components can then be determined by using the displacements. A discussion regarding the application of the techniques to more complex scenarios where solutions cannot be easily obtained through classical techniques are discussed. The technique has uses as a supplement to traditional material in an intermediate level structural analysis course.