Please note! Course description is confirmed for two academic years, which means that in general, e.g. Learning outcomes, assessment methods and key content stays unchanged. However, via course syllabus, it is possible to specify or change the course execution in each realization of the course, such as how the contact sessions are organized, assessment methods weighted or materials used.


1. Understanding of the role of the three-dimensional elasticity theory in (bar, beam, membrane,) plate and shell models in analyzing the mechanics of structures.
2. Understanding of the energy and equilibrium approaches in deriving and formulating (bar, beam, membrane,) plate and shell models.
3. Ability to derive the (beam and) plate models of statics and free vibrations within the theory of elasticity.
4. Ability
to apply plate and shell models to various types of structural analyses and to solve the corresponding partial differential equations by the most crucial analytical solution methods.

Credits: 5

Schedule: 11.01.2022 - 27.02.2022

Teacher in charge (valid for whole curriculum period):

Teacher in charge (applies in this implementation): Jarkko Niiranen

Contact information for the course (applies in this implementation):

CEFR level (valid for whole curriculum period):

Language of instruction and studies (applies in this implementation):

Teaching language: English. Languages of study attainment: English


  • valid for whole curriculum period:

    Week 1:
    2D and 3D theories of elasticity (and bar model)
    Week 2:
    Kirchhoff plate model (and Euler--Bernoulli beam model)
    Week 3:
    Reissner--Mindlin plate model (and Timoshenko beam model)
    Week 4:
    Models for orthotropic, stiffened, sandwich and laminate plates
    Week 5:
    Vibrations of (bars, beams,) membranes and plates
    Week 6:
    Shells models
    Week 7:

    (The actual order of some of the weeks 1--6 may vary.)

Assessment Methods and Criteria
  • valid for whole curriculum period:

    1. Theoretical home assignments:
    - returned according to weakly deadlines (assessed weekly by assistants)

    2. Final exam:
    - on week 7 (assessed by the lecturer)

    The final grade (0 5) is composed of the points collected from the final examination (67% = 18 pts) and exercise assignments (33% = 9 pts). The passing grade 1 can be achieved by about 50% (14 pts) of the total maximum (27 pts).

  • valid for whole curriculum period:

    Lectures: 2 double-hours per week (24 h = 18%)
    - contact teaching: attending the lectures (pre-browsing, listening, writing notes, asking etc.)

    Reading: 2 double-hours per week (24 h = 18%)
    - self-studies: reading and writing the derivations in the lecture slides and/or textbook

    Theoretical Exercises: 1--2 double-hours per week (12--24 h = 9--18%)
    - contact teaching: advice hours for theoretical hands-on exercises instructed by assistants

    Theoretical Home Assignments: 6--8 hours per week (36--48 h = 27--36%)
    - 4-6 per week
    - self-studies for theoretical hands-on exercises: problem solving, calculating, writing solution documents

    Final exam and preparation: 3 + 22 hours (25 h = 19%)


Study Material
  • valid for whole curriculum period:

    Primary course material:
    - Lecture slides and home assignments
    - Text book by Eduard Ventsel and Theodor Krauthammer: Thin Plates and Shells: Theory: Analysis, and Applications. CRC Press, 2001 (available as an E-book in the university library)

    Secondary course material:
    1. Arbind Kumar Singh: Mechanics of Solids, PHI Learning Private Limited, 2007.
    2. Clive L. Dym and Irving H. Shames: Solid Mechanics, A Variational Approach, Augmented Edition, Springer, 2013.

Substitutes for Courses
SDG: Sustainable Development Goals

    9 Industry, Innovation and Infrastructure

    11 Sustainable Cities and Communities


Further Information
  • valid for whole curriculum period:

    Buckling of plates and shells is covered by course CIV-E4100 Stability of Structures; Finite element methods for plates and shells is covered by course CIV-E4010 Finite Element Methods in Civil Engineering; Material nonlinearities (of plates and shells) are covered by course CIV-E4080 Material Modelling in Civil Engineering.

    Teaching Period:

    2020-2021 Spring III

    2021-2022 Spring III

    Course Homepage:

    Registration for Courses: In the academic year 2021-2022, registration for courses will take place on Sisu ( instead of WebOodi.