Course Details

Nonlinear Mechanics

Academic Year 2025/26

NDA028 course is part of 1 study plan

​ NPC-SIK Winter Semester 1st year

Course Guarantor

Ing. Rostislav Lang, Ph.D.

Institute

Institute of Structural Mechanics

Language of instruction

Czech

Credits

4 credits

Semester

winter

Forms and criteria of assessment

graded course-unit credit

Offered to foreign students

Not to offer

Course on BUT site

https://www.vut.cz/en/students/courses/detail/295911

Lecture

13 weeks, 2 hours/week, elective

Syllabus

  • 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.

Exercise

13 weeks, 1 hours/week, compulsory

Syllabus

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