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DG20RNAK - Nonlinear analysis of structures

Course specification
Type of study Doctoral studies
Study programme
Course title Nonlinear analysis of structures
Acronym Status Semester Number of classes ECTS
DG20RNAK elective 2 4L + E 10.0
Lecturers
Lecturer
Lecturer/Associate (practicals)
    Prerequisite Form of prerequisites
    -
    Learning objectives
    To understand fundamental mathematical and mechanical formulations of the nonlinear structural analysis.
    Learning outcomes
    Student is able to independently create and analyze geometrically and materially nonlinear models of continua and structures.
    Content
    Introduction to the nonlinear analysis. Sources of nonlinear behavior of structures. Lagrange and Euler description of displacement. Lagrangian finite one-dimensional elements - description of deformation and stress fields. Geometric nonlinearity of structures - Total Langrangian and Updated Langrangian. Formulation of geometrically nonlinear problems - nonlinear analysis of beams and shells. Bifurcation stability of beams and shells. Procedures for solving nonlinear equations (Newton-Rapson, modified Newton-Rapson, Arc length method). Review of models for the analysis of material nonlinearity (nonlinear elasticity, one - dimensional plasticity, multiaxial plasticity, viscoelasticity ...). Solution procedures and stability of a solution.
    Teaching Methods
    Auditory lectures and individual work with students
    Literature
    1. K.J. Bathe, „Finite Element Procedures”, Prentice-Hall, 1996 (Original title)
    2. T. Belytschko,W.K. Liu, B. Moran, „Nonlinear Finite Elements for Continua and Structures”,Wiley, 2000 (Original title)
    3. M.A. Crisfield, „Non-Linear Finite Element Analysis of solids and Structires”,Wiley, 1991 (Original title)
    4. J. Jarić, „Mehanika kontinuuma”, Građevinska knjiga, 1988 (Original title)
    5. G. Radenković, „Konačne rotacije i deformacije u izogeometrijskoj teoriji nosača”, Univerzitet u Beogradu-Arhitektonski fakultet, 2017 (Original title)
    Evaluation and grading
    Calculation and defence of the semestral assignment (50%) Oral exam (50%)
    Specific remarks
    The course can be conducted in English.