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Numerical methods of mechanics and dynamics

Course Code:
18NMMD
Academic Degree:
doctoral
Study Programme:
Transportation Systems and Technology (P1041D040003)
language
czech, english flag
Form of Study:
full-time and part-time
Type of Course:
optional
Course Completion:
exam
Supervisor:
prof. Ing. Ondřej JIROUŠEK, Ph.D.
v DB je chyba..
Supervising Department:
Department of Mechanics and Materials (16118)
Abstract:
• Direct stiffness method. Application to truss structures. Tension/compression beam. Solution of truss structures. Variational formulation of tesion/compression beam. • Variational formulation of beam loaded in bending. Beam with shear effects (Timoshenko). Beam on elastic foundation (Timoshenko-Winkler). Beam loaded with M+N+T combination. • Isoparametric elements. Natural coordinates. • Isoparametric elements. Triangular and quadrilateral elements. Linear and quadratic elements T3 and T6, Q4 and Q8. Plane stress, plane strain. • Plane deformation, plane strain. Elements for plane problems. • Plane strain, plane strain. Derivation of element stiffness matrix. • Spatial elements. Summary of 2D and 3D elasticity in FEM. Use of symbolic algebra tools. • Linear dynamics and FEM. Hamilton's variational principle. Consistent and diagonal mass matrices. Solutions for natural shapes and natural frequencies solution. • Direct time integration of equations of motion. Implicit and explicit methods. Newmark's method. • Numerical integration. Solution of nonlinear problems.