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DG20IAK - Isogeometric analysis of structures

Course specification
Type of studyDoctoral studies
Study programme
Course titleIsogeometric analysis of structures
AcronymStatusSemesterNumber of classesESPB
DG20IAKelective34П + В10.0
Lecturers
Lecturer (for classes)
Lecturer/Associate (for practice)
    ConditionОблик условљености
    --
    The goal
    To learn fundamental concepts of the isogeometric approach to the for the structural analysis. Develop ability and creativity to independently formulate and solve problems of elastostatics and elastodynamics of structural systems.
    The outcome
    Student is able to analyze and solve basic problems of the structural mechanics using the Isogeometric approach. Student is able to continue independent research work for the modeling of complex structures.
    Contents
    Introduction to IGA. B-spline curve. Affine transformations of B-spline curves and surfaces. Knot insertion. Elevation of B-spline curves. Non-uniform rational B-spline. Knot insertion and elevation of NURBS. Rational spline surfaces. Boundary value problem problem of elastostatics. Strong form of BVP. Weak form of BVP. Galerkin solution to the BVP. The principle of virtual displacements. Beam axis geometry in NURBS parametric coordinates: base vectors and beam axis metric tensor, beam axis curvature, metric of arbitrary point. Bernoulli-Euler beam theory: strain of the rod axis, strain at an arbitrary point, bending strains. Timoshenko beam theory. Isogeometric finite element of the beam. Stress-strain relations. Section forces. Formulation of linear and nonlinear stiffness matrix. Equivalent control forces. Equilibrium equation. Bernoulli-Euler beam element. Linear beam in plane. Bezier beam element. Hermite cubic spline. Hermit beam element. Relation between Hermit and Bezier beams. Shell geometry: base vectors and metric tensor of the midsurface of a shell, Christoffel coefficients of the second kind, metric of the equidistant surface. Kirchhoff-Love theory of thin elastic shells. Mindlin-Reissner shell theory. Stress strain relations. Formulation of isogeometric finite element of a shell - linear theory. Total Lagrangian formulation. Bezier plate elements.
    Methods of teaching
    Auditory lectures and individual work with students
    Literature
    1. G. Radenković, „Izogeometrijska teorija nosača”, Univerzitet u Beogradu-Arhitektonski fakultet, 2014 (Original title)
    2. G. Radenković, „Konačne rotacije i deformacije u izogeometrijskoj teoriji nosača”, Univerzitet u Beogradu-Arhitektonski fakultet, 2017 (Original title)
    3. J.A. Cottrell, T.J.R. Hughes, Y. Bazilevs, „Isogeometric Analysis: Toward Integration of CAD and FEA”, Wiley, 2009 (Original title)
    4. T.J.R. Hughes, „The Finite Element Method: Linear Static and Dynamic Finite Element Analysis”, Prentice-Hall, 1987 (Original title)
    Облици провјере знања и оцјењивање
    Calculation and defence of the semestral assignment (50%) Oral exam (50%)
    Посебна назнака
    Предмет се може изводити на енглеском језику.