Implementation of discrete Kirchhoff theory element in MATLAB

The main focus of this thesis is the implementation of a plate-bending element in MATLAB, which provides an interactive programming environment. The plate-bending element implemented is discrete Kirchhoff theory (DKT) element. DKT element is commonly used for analysis of thin plate structures. The algorithm (developed by Jeyachandrabose [6]) used in this thesis to formulate DKT element stiffness matrix is faster than the algorithm developed by Batoz [5]. This is because the formulation avoids the use of matrix triple product, which was required in the formulation used by Batoz to transform elasticity and stiffness matrix for every DKT element from local to global co-ordinate system. A finite element program is developed to implement DKT element in MATLAB. Several thin plate problems are analyzed using an interactive programming technique and results are compared with classical thin plate solution (Roark's solution) and finite element computer program ANSYS. Comparison of DKT element with twelve degree of freedom rectangular elements is also discussed in this thesis. The results indicate that displacements obtained using DKT elements are extremely accurate when compared with classical thin plate Roark's solution. Convergence towards classical thin plate solution is observed in both rectangular and circular plate problems. It is also observed that rate of convergence of DKT element is similar compared to SHELL 63 elements in ANSYS.