Course Details

Nonlinear Mechanics

Academic Year 2024/25

NDA028 course is part of 1 study plan

NPC-SIK Winter Semester 1st year

Course Guarantor


Language of instruction



4 credits



Forms and criteria of assessment

graded course-unit credit

Offered to foreign students

Not to offer

Course on BUT site


13 weeks, 2 hours/week, elective


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.


13 weeks, 1 hours/week, compulsory


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.