## Finite Element Methods – Matlab

Finite Element Methods – Matlab

Paper details:
Analysis of simple self-supporting structures. Part A: Simple 2D structure using hand calculations and FE code. Part B: Simple 2D analysis of structures using your FE code only

MATH4701

Assignment I: Analysis of simple self-supporting structures

The aim of this assignment is to analyse simple self-supporting structures based on the theory of finite element developed so far. The objective of the assignment is to develop a matlab code capable of calculating the forces and displacements for simple, two dimensional structures.  In part A, you will solve a simple model by hand to calculate the displacement of the structure and the reaction forces.  You will then develop your FE code and solve the same problem and show that the results are the same.  In part B, you will apply your FE code to a more complex problem and again predict the overall displacements and the reaction forces for the structure.

Part A: Simple 2D structure using hand calculations and FE code

Figure 1 – Schematic diagram of a simple scissor truss frame

The structure shown in figure 1 is rigidly fixed at points A and B and has loads applied to points D and F.
i)    Calculate by hand the reaction forces acting at point A and B and the x and y deflections at points C, D, E and F using the finite element formulation.  Hint: I would like to see the how you develop the individual stiffness matrices, the overall global stiffness matrix and the force and displacement vectors.  The solution is tedious by hand, so you can feed the matrices into Matlab to solve for the unknowns.
ii)    Using Matlab, develop the FE code so that it is capable of solving this problem.  Hint: Try to make the code flexible, so that it can be extended to any geometry and loading/boundary conditions ready for use in the next section.
iii)    Repeat the calculations for the above structure using your Matlab code and verify that the code is working correctly.

This section of the report should include:

–    Overview of the hand calculations of the reaction forces and the deflection at points C, D,E and F
–    Matlab code, which is annotated to describe what the various sections of the code are doing.
–    Comparison of hand and Matlab code predicted reaction forces and displacements

Part B: Simple 2D analysis of structures using your FE code only

For each of the above structures, use your Matlab code to find:

i)    The location and magnitude of maximum x and y deflections
ii)    The location an magnitude of the maximally loaded beam in each structure
iii)    Identify beams, if any, that are redundant