Objectives of the course
- Understanding concepts and results of advanced engineering mathematics and the ability to apply them to engineering problems
- Grasp of matrices, tensors, integral theorems, Fourier series, partial differential equations and basics of probability and statistics
- Understanding optimization concepts
- Ability to apply optimization methods in a given environment, e.g., FEM
- Selection of 'best' optimization tool
Recommended preliminary requirements
- Basic knowledge of linear algebra, calculus and numerical analysis, i.e., vectors and matrices; inner products; systems of linear equations; derivatives of real-valued functions; line, surface and volume integrals; permutations and combinations
Objectives of the course
- Good knowledge of the Computational Methods and the related most important algorithms
- Comprehension of the application of major algorithms in computational methods
- Ability to apply computational methods to engineering problems
- Comprehension of linear and nonlinear computational methods
- Ability to check and to interpret computational results
Recommended preliminary requirements
- Basic knowledge of mathematics such as ordinary and partial differential equations, and basic vector analysis
- Basic knowledge of computer programming
- Linear algebra: Vectors and matrices; addition and multiplication; transformation; determinant; symmetry; systems of linear equations; linear eigenproblem; eigensolution, characteristic polynom; eigenvalue; eigenvector; symmetry of linear equations systems and linear Eigenproblems
- Basics in vector field analysis: basics in vector analysis; vector field; gradient, divergence and vorticity; nabla operator
Objectives of the course
- Good knowledge of the fundamentals of FEM
- Ability to apply the FEM to engineering problems, especially to stress analysis
- Ability to solve problems in this field, including correct modeling, selection of appropriate Finite Elements, checking and discussion of results
- Ability to realize the potential and the limits of FEM
Recommended preliminary requirements
- Basic knowledge of mathematics, solid mechanics and stress analysis
- Basic knowledge of FEM is recommended
Objectives of the course
- Good comprehension of the fundamentals of continuum mechanics
- Good grasp of stress and strain state and the constitutive equations for linear problems
- Comprehension of energy principles
- Ability to solve problems in the field of elastostatics
- Ability to check FEM solutions and to interpret results in the field of elasticity
Recommended preliminary requirements
- Basic knowledge of mathematics and strength of materials
Objectives of the course
- Getting to understand the basic principles underlying heat transfer
- Ability to recognize applications in which heat transfer is involved
- Developent of skills to identify, formulate and solve engineering problems in heat transfer with special stress on the limitations of the models
- Comprehending the complexity of the multimode heat transfer
- Promoting creativity through the application of heat transfer principles to situations
Recommended preliminary requirements
- Basic knowledge of mathematics, thermodynamics, Finite elements and heat transfer
Objectives of the course
- Comprehension of the physical phenomena of damage and its mathematical descriptions
- Ability to do life time estimations within the crack initiation and the crack propagation phase
- Ability to comprehend all stages of creep and fatigue damage: crack nucleation, growth of short and long cracks and final fracture
- Capability to perform life time estimations for the crack initiation and the crack propagation stage taking into account various factors influencing fatigue life (load histories, shape and state of the components under consideration, material, environmental aspects, etc.)
Recommended preliminary requirements
- Basic knowledge of solid mechanics and material sciences
- Basic knowledge of FEM
