Czech

Not applicable.

Institute of Structural Mechanics (STM)

Students will learn fundamentals of nonlinear mechanics. They will understand quality and quantity of differences between linear and nonlinear analysis of structures. They will learn different formulations and methods of nonlinear analysis. Use of nonlinear analysis of structures in design praxis is increasing, therefore the knowledge gained in this subject will be very appreciated in praxis.

Linear mechanics, Finite element method, Matrix algebra, Fundamentals of numerical mathematics, Infinitesimal calculus.

In the subject Nonlinear mechanics the konwledge of fundamentals of the tensor calculus are needed. These should be learned in the subject of mathematics.

Lectures are theoretical. They start from the fundamentals of the tensor calculus and then there are lectured the strain and stress measures, basic formulations of the geometrical nonlinearity, fundamentals of the material nonlinearity, methods of solution of nonlinear algebraic equations and postcritical analysis. In the seminaries students work on computers uner the leadership of the teacher. They practically analyze what was theoretically lectured.

The attendance of lectures is not mandatory, but serves as one of the bases for evaluation of students. Attendance of exercises is mandatory. The theoretical knowledge which is presented on lectures is needed to pass the written and oral exam.

1. Index, tensor and matrix notation, vectors and tensors, properties of tensors, transformation of physical quantities.
2. Fundamental laws i mechanics, kinds of ninlinearities by their sources, Eulerian and Lagrangian meshes, material and space coordinates, fundamentals in geometrical nonlinearity.
3. Srain measures (Green-Lagrange, Euler-Almansi, logarithmick, infinitesimál), their behaviour in large rotation and large deformation.
4. Stress measures (Cauchy, 1st Piola-Kirchhoff, 2nd Piola-Kirchhoff, corotational, Kirchoff) and transformatio between them.
5. Energeticaly konjugate stress and strain measures, two basic formulations in geometyric nonlinearity.
6. Influence of stress on stiffness, geometrical stiffness matrix.
7. Updated Lagrangian formulation, basic laws and tangential stiffness matrix.
8. Total Lagrangian formulation, basic laws and tangential stiffness matrix.
9. Objective stress rates, constitutive matrices, fundamentals of material nonlinearity.
10. Numerical methods of solution of the nonlinear algebraic equations, Picard method, Newton-Rapson method.
11. Modified Newton-Raphsonmethod, Riks method.
12. Linear and nonlinear stability.
13. Postcritical analysis.

Not applicable.

Students will learn various types of nonlinearities that occur in the design of structures. They will understand the basic differences in the attitude to linear and nonlinear solution of structures. They will learn more general definitions of stress and strain measures, the two main formulation of geometrical nonlinearity the same as the fundamentals of material nonlinearity. The main numerical methods of solution of nonlinear algebraic equation will be also explained.

Extent and forms are specified by guarantor’s regulation updated for every academic year.

Deeper knowledge of nonlinear mechanics including its applications in analysis of structures should be gained on a nonmandatoru specialised seminar.

Not applicable.

Bittnar, Z., Šejnoha, J.: Numerické metody mechaniky. Vydavatelství ČVUT, 1992.
Servít, R., Drahoňovský, Z., Šejnoha, J. Kufner, V.: Teorie pružnosti a plasticity II. STNL/ALFA Praha, 1984. (CS)

Bathe, K-J.: Finite Element procedures. Prentice - Hall, 1996.
Desai, C. S, Siriwardane, H. J.: Constitutive Laws for Engineering Materials. Prentice - Hall, 1984.