CIE4180 Plate Analysis, Theory and Application

Course 2021/2022
prof.dr.ir. M.A.N. Hendriks, dr.ir. P.C.J. Hoogenboom (email p.c.j.hoogenboom@tudelft.nl)
4 Credits (EC)

Plates loaded in plane (IP)

Derivation of the basic equations (kinematic, constitutive, equilibrium); differential equations and boundary conditions; several analytical solutions; introduction to the finite element method; derivation of a rectangular plane stress/strain finite element; constant shear element.

Plates loaded out of plane (OOP)

Derivation of the basic equations including shear deformation (Reissner-Mindlin theory); reduction to thin plates (Kirchhoff theory); differential equation and boundary conditions; concentrated shear force, several analytical solutions; derivation of a rectangular slab finite element.

Checking finite element results; recommended element size; singularities and their interpretation; design and checking of reinforcement.

Scope

  • A slab is a reinforced concrete plate loaded out of plane.
  • The application examples are on reinforced concrete and steel structural parts.
  • The course is on linear elastic analysis, therefore, plate buckling and non-linear analysis are not covered.
  • The course does not include shell structures.

    Readers

  • Plate analysis, theory and application, Volume 1 Theory
  • Plate analysis, theory and application, Volume 2 Numerical methods
  • Plates and FEM, Surprises and Pitfalls, Chapter 16

    Schedule

    When and where Subject Reader Slides Collegerama
    . 8 Nov. 15:45 D IP .... Introduction Vol. 1, Ch. 1 1, 2 13 Nov. 2017
    10 Nov. 13:45 D IP .... Theory Vol. 1, Ch. 1 3 15 Nov. 2017
    12 Nov. 13:45 C IP .... Applications Vol. 1, Ch. 2 22 Nov. 2017
    17 Nov. 15:45 D IP .... Applications Vol. 1, Ch. 2 4 24 Nov. 2017
    19 Nov. ........ Assignment 1 published on Brightspace
    22 Nov. 15:45 D IP .... Approximations Vol. 2, Ch. 1, 2 5, 6, 7, 8, 9 27 Nov. 2017
    24 Nov. 13:45 D IP .... Finite element method Vol. 2, Ch. 3 10, 11 29 Nov. 2017
    29 Nov. 15:45 D OOP Thick plates Vol. 1, Ch. 3 12 . 4 Dec. 2017
    . 1 Dec. 13:45 D OOP Thin plates Vol. 1, Ch. 4 13, 14 . 6 Dec. 2017
    . 6 Dec. 15:45 D OOP Boundary conditions Vol. 1, Ch. 4 15, 16 11 Dec. 2017
    . 8 Dec. 13:45 D OOP Applications of the thin plate theory Vol. 1, Ch. 5 17, 18 13 Dec. 2017
    . 9 Dec. ........ Due date of assignment 1
    10 Dec. ........ Assignment 2 published on Brightspace
    13 Dec. 15:45 D OOP Approximations and FEM Vol. 2, Ch. 6, 7, 8 19, 20 18 Dec. 2017
    15 Dec. 13:45 D ........ Reinforcement design Ch. 16 21 20 Dec. 2017
    20 Dec. 15:45 D ........ Recap, questions and answers 22, 23, 24
    24 Dec. ........ Due date of assignment 2
    27 Jan. 13:30 L&R K and J........ Exam, 3 hours
    . 8 Apr. .. 9:00 3ME J ........ Exam, 3 hours

    Assignments

    Apply the finite element method to a plate loaded in plane and a plate loaded out of plane. The software DIANA is available but you can use any suitable finite element program. Make sure the program can analyse plates loaded in plane (plane stress elements or membrane elements) and plates loaded out of plane (plate elements or plate bending elements). Do not use solid elements for the assignments. The assignments and the exam need to be done in the same academic year. So, you cannot do the assignments in 2020/2021 and take the exam in 2021/2022.

  • Assignment 1, Parameter sheet 1, Answer sheet 1 (10% of the course grade)
  • Assignment 2, Parameter sheet 2, Answer sheet 2 (10% of the course grade)

    Diana

  • Download from https://dianafea.com/diana-downloads
  • Install Diana
  • For the license, ensure that you are connected to the TU Delft network (e.g. via VPN). Follow this procedure
  • Tutorials at https://dianafea.com/diana-tutorials -- Elastic analysis of a deep beam with web opening -- Elastic analysis of a bending plate

    Exam

    Three hour written examination (80% of the course grade). You are allowed to bring a calculator and an A4 formula sheet (can be two sided) which is in your handwriting (and does not need a magnifying glass to read).

    Further reading

    J. Blaauwendraad, Plates and FEM, Surprises and Pitfalls, 2010, Springer, pp. 413

    Previous exams

    21 April 2023 (432 KB)
    . 2 February 2023 (614 KB)
    . 8 April 2022 (865 KB)
    27 January 2022 (786 KB)
    . 9 April 2021 (881 KB)
    28 January 2021 (899 KB)
    30 January 2020 (888 KB)
    10 April 2019 (805 KB)
    31 January 2019 (951 KB)
    11 April 2018 (603 KB)
    . 1 February 2018 (666 KB)
    12 April 2017 (661 KB)
    . 2 February 2017 (699 KB)
    . 6 April 2016 (834 KB)
    28 January 2016 (981 KB)

    Previous assignments

    15 December 2022 (214 KB)
    24 November 2022 (232 KB)
    10 December 2021 (112 KB)
    19 November 2021 (104 KB)