1.0 Comparison of static and dynamic problems solved by FEM
2.0 Finite element mass matrix
2.1 Bar element
2.2 Beam element
2.2.1 Bernoulli‘s beam, diagonal mass matrix
2.2.2 Thimoshenko‘s beam, the second spectrum of natural frequencies
2.3 Plane and space frame finite element
2.4 Selected types of finite elements
3.0 Natural frequencies and mode shapes of un-damped vibration
3.1 Matrix equation for solving natural frequencies and mode shapes (eigenvectors)
3.2 Normalization of the eigenvectors
3.3 Solution methods
3.3.1 Solutions using determinant, disadvantages
3.3.2 Power method (method of inverse iterations)
3.3.3 Subspace method (method of simultaneous iterations)
3.3.4 Lanczos method
4.0 Reduction method in dynamics
5.0 Damping matrix
6.0 Solving response of the linear mechanical system by using mode shapes (Modal analysis method)
6.1 Self-induced oscillations by changing the initial conditions
6.2 Harmonic excitation
6.3 General continuous excitation
7.0 The response solution of nonlinear dynamical systems
7.1 Implicit method
7.2 Explicit method
8.0 Buckling (collapse of structures shape)
8.1 Introduction
8.2 Geometric stiffness matrix of bar FE
8.3 Geometric stiffness matrix of plane frame FE (compression-tension + bending)
8.4 Practical examples
9.0 Solution of nonlinear static tasks
9.1 Introduction
9.2 Newton-Raphson method
10. Contacts in FEM
10.1. Introduction
10.2. Penalty method
10.3. Langrange multiplier method
10.4. Augmented Lagrange method
10.5. Partitioning (Semi-analytical) method
10.6. Example
2.0 Finite element mass matrix
2.1 Bar element
2.2 Beam element
2.2.1 Bernoulli‘s beam, diagonal mass matrix
2.2.2 Thimoshenko‘s beam, the second spectrum of natural frequencies
2.3 Plane and space frame finite element
2.4 Selected types of finite elements
3.0 Natural frequencies and mode shapes of un-damped vibration
3.1 Matrix equation for solving natural frequencies and mode shapes (eigenvectors)
3.2 Normalization of the eigenvectors
3.3 Solution methods
3.3.1 Solutions using determinant, disadvantages
3.3.2 Power method (method of inverse iterations)
3.3.3 Subspace method (method of simultaneous iterations)
3.3.4 Lanczos method
4.0 Reduction method in dynamics
5.0 Damping matrix
6.0 Solving response of the linear mechanical system by using mode shapes (Modal analysis method)
6.1 Self-induced oscillations by changing the initial conditions
6.2 Harmonic excitation
6.3 General continuous excitation
7.0 The response solution of nonlinear dynamical systems
7.1 Implicit method
7.2 Explicit method
8.0 Buckling (collapse of structures shape)
8.1 Introduction
8.2 Geometric stiffness matrix of bar FE
8.3 Geometric stiffness matrix of plane frame FE (compression-tension + bending)
8.4 Practical examples
9.0 Solution of nonlinear static tasks
9.1 Introduction
9.2 Newton-Raphson method
10. Contacts in FEM
10.1. Introduction
10.2. Penalty method
10.3. Langrange multiplier method
10.4. Augmented Lagrange method
10.5. Partitioning (Semi-analytical) method
10.6. Example