Finite element analysis on the collapse mechanism of a truss using object-oriented programming on MATLAB.
The TRUSS.m file represents the truss class that can be used to generate an instance of a truss object.
The TRUSS_script.m file represents an example script that can be used to conduct the analysis on a defined truss object.
Some syntax:
𝜆tot = load proportionality factor
𝐹tot = vector of total forces for each member
𝑈tot = vector of total displacement for each member
| Methods | Description |
|---|---|
| Class constructor | To initialise the truss object based on its given parameters |
| Assembly | To assemble the global stiffness matrix for the global truss structure |
| Solver | To partition and solve the matrix, obtaining displacements at each dofs as well as the reaction forces at the restrained dofs |
| Post processor | To obtain the 𝜆tot , 𝐹tot , 𝑈tot as well as the critical member at which failure will occur locally |
| Plotting | To plot the deformation state after each event of a member failure, as well as the axial forces within each member |
| Updater | To replace each failed member by its critical squash/buckling load resolved in the direction of its nodal dofs, stored in the global nodal force vector |
| Matrix singularity check | To check for the stability of the KFF sub-matrix before attempting to solve the global stiffness matrix |
Part 1: Formulation of truss geometry by specifying nodal coordinates, dofs and elemental connection.
Part 2: Materially Non-Linear Analysis (failure by plastic collapse only).
Part 3: Geometrically Non-Linear Analysis (failure by plastic collapse or elastic buckling).
Part 4: Varying the radii of each members to conduct analysis on truss geometries with members of varying radii.