1. General consideration. Methods of structural analysis. Properties of linear and nonlinear structural analysis. Basic concepts of Finite Element Method. Brief history.
2. Energy method in structural analysis. The Principle of Virtual Work applied to FEM. FEM formulations in displacements and stresses.
3. MEF algorithm in displacements for the linear structural analysis.
4. Discretization types. Shape functions for bar FE-s. The FE stiffness matrix in local coordinates.
5. Stiffness matrix and load vector for truss structures and plane frames. Transformation (rotation) matrix, localization matrix, equivalent external forces in nodes.
6. Nonlinear geometric analysis for a simple bar.
7. Basic concepts of plane stress and plane strain (two-dimensional finite elements).
8. Derivation of the Constant Strain Triangle Element (CST Element) stiffness matrix.
9. Derivation of the Linear Strain Triangle Element (LST Element) stiffness matrix. Shape functions determination for CST / LST Elements.
10. Derivation of the stiffness matrix for connected elements: truss element connected to a plane element (CST Element).Global stiffness matrix assembly: basic concepts.
11. Four-node rectangular element. Derivation of shape functions using Lagrange interpolation method. Derivation of the stiffness matrix.
12. Four-node iso-parametric quadrilateral element (Q4). Iso-parametric mapping. Jacobian of mapping.
13. Four-node iso-parametric quadrilateral element (Q4). Derivation of the stiffness matrix. Potential energy of applied loads.
14. Numerical integration using gaussian quadrature.
