DDB033 course is part of 4 study plans
Ph.D. full-t. program DPC-K compulsory-elective Summer Semester 1st year 8 credits
Ph.D. combi. program DKC-K compulsory-elective Summer Semester 1st year 8 credits
Ph.D. full-t. program DPA-K compulsory-elective Summer Semester 1st year 8 credits
Ph.D. combi. program DKA-K compulsory-elective Summer Semester 1st year 8 credits
Advance topics on FEA. Introduction to nonlinear mechanics. Tensors, strain and stress measures, coordinate systems, solution methods tangent stiffness matrix, material and geometrical stiffness, two basic formulations of geometrical nonlinearity, numerical methods of solution of nonlinear algebraic equations. Energetical principles in statics, static stability, static nonlinear models, collapse, loss of stability, bifurcations and catastrophes, loss of symmetry. Energetical principles in dynamics, dynamic nonlinear models, conservative/dissipative system, solution and monitoring of dynamical systems, phase space and trajectory of dynamical system, nonlinear symptoms in dynamics.
Basic knowledge of structure mechanics, matrix and vector algebra, infinitesimal calculus, fundamentals of numerical mathematics.
Planned educational activities and teaching methods
Teaching methods depend on the type of course unit as specified in the article 7 of BUT Rules for Studies and Examinations.
Lectures are oriented to post gradual students with aim to make their knowledge in structure mechanics deeper. The topics are selected from the point of view of their application in advance structure analysis.
Specification of controlled instruction, the form of instruction, and the form of compensation of the absences
Vymezení kontrolované výuky a způsob jejího provádění stanoví každoročně aktualizovaná vyhláška garanta předmětu.
3 hours/week, 13 weeks, elective
Syllabus of lectures
1. Interesting problems in structural mechanics; equalizing of bending moments between supports and on the support; optimal and variable beam section; design of the beam shape dependent on load.
2. Assumptions of linear mechanics; plane section remain plane and undeformed (plasticity, wall, torsion, shear lag), small deformations (loading by bending moment and by force), linear material.
3. Exception cases; mechanism; follower load.
4. Measurement of loading diagrams of nonlinear materials.
5. Measurement of deflection of cantilever beam, von Mises truss, catastrophic machines.
6. Energetical principles in statics, static stability.
7. Design of static nonlinear models and its solution.
8. Nonlinear symptoms in structural statics - collapse, loss of stability (beam buckling, bending of cantilever beam, frame, von Mises truss), bifurcations and catastrophes (beam buckling), loss of symmetry (beam buckling, torsion).
9. Energetical principles in dynamics (Lagrange and Hamilton function).
10. Design of dynamic nonlinear models, dynamical systems (definition, conservative/dissipative system).
11. Solution and monitoring of dynamical systems, numerical methods.
12. Phase space and trajectory of dynamical system.
13. Nonlinear symptoms in dynamics.