Czech

5

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.

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

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 nonlinerity, 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.Introduction to nonlinear mechanics. Physical and geometrical nonlinearities. Eulerian and Lagrangian nesnes.
2.Strain measures (Green-Lagrange, Euler-Almansi, engineering, logarithmic), their behavior in large strain and large rotation. Stress measures (Cauchy, 1. Piola-Kirchhoff, 2. Piola-Kirchhoff, Biot). Energeticaly conjugate stress and strain measures.
3.Tangent stiffness matrix, Material stiffness, Geometrical stiffness. Influence of nonlinear members of the strain tensor. Newton-Raphson method. Calculation of unbalanced forces.
4.Modified Newton-Raphson method. Postcritical analysis. Deformation control. Arc length method
5.Linear and nonlinear buckling. Von Mises truss, snap through. Physical nonlinearity (supports, beams, concrete, subsoil).
6.Types of materials, introduction into constitutive material models. Linear and nonlinear fracture mechanics. Fracture mechanical material parameters.
7.Problem of strain localization, false sensitivity on the mesh. Restriction of localization. Crack band model. Nonlocal continuum mechanics.
8.Constitutive equations for concrete and other quasi-fragile materials. Fracture-plastic model. Mircroplane model.
9.Influence of size to bearing capacity (size effect). Energetical and statistical causes. Analysis of the influence of size on strength in tension in bending.
10.Presentation of modeling by a software on nonlinear fracture mechanics. Examples of applications. Mechanics of damane.

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 new definition of stress and strain measures and the principles that are necessary for nonlinear solution of structures by the Newton-Raphson method.

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

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

Not applicable.

Not applicable.

Not applicable.

26 hours, compulsory

1. Demonstration of the differences between linear and nonlinear calculations.
2. Demonstration of the problems with a big rotations. Demonstration of the differences between the 2nd order theory and the large deformations theory.
3. Examples on bending of beams with a big rotations of the order of radians.
4. Examples on calculations of cables and membranes.
5. Examples on calculations of mechanismes.
6. Examples on calculations of stabilioty of beams.
7. Examples on calculations of stability of shells.
8. Comparison of the Newton-Raphson, modified Newton-Raphson and Picard methods.
9. Examples on postcritical analysis of beams and shells.
10. Demostration of the explicit method in nonlinear dynamics.