Course syllabus for Structural analysis using the finite element method

Course syllabus adopted 2021-08-31 by Head of Programme (or corresponding).

Overview

  • Swedish nameStrukturberäkningar med finita elementmetoden
  • CodeMMS145
  • Credits7.5 Credits
  • OwnerFRIST
  • Education cycleFirst-cycle
  • Main field of studyArchitecture and Engineering, Mechanical Engineering, Mathematics, Civil and Environmental Engineering, Industrial Design Engineering, Engineering Physics
  • DepartmentMECHANICS AND MARITIME SCIENCES
  • GradingUG - Pass, Fail

Course round 1

The course round is cancelled. For further questions, please contact the director of studies
  • Teaching language Swedish
  • Application code 99128
  • Open for exchange studentsNo

Credit distribution

0119 Examination 3 c
Grading: UG		 3 c
0219 Written and oral assignments 4.5 c
Grading: UG		 4.5 c

    Examiner

    Information missing

    Eligibility

    General entry requirements for bachelor's level studies

    Specific entry requirements

    English language proficiency + strength of materials/solid mechanics, linear algebra, multivariable analysis

    Aim

    The finite element method (FEM) is a numerical method, to solve partial differential equations, enabling the analysis of many fields of engineering. This course provides the theoretical basis of FEM as well as, on an overall level, introduction to several advanced topics such as contact. Focus of the course is practice in performing finite element simulations, using industrial software (ANSYS), to analyze and design structural components.

    Learning outcomes (after completion of the course the student should be able to)

    • Summarize what the Finite Element Method (FEM) is and exemplify what it could be used for.
    • Describe the theoretical basis of FEM and explain strong form, weak form, and FE-form.
    • Construct FE-models and perform:
      • static structural analysis to determine deformations, stresses, strains, fatigue life and safety factors.
      • linearized buckling analysis to estimate critical buckling loads and buckling modes.
      • modal analysis, without external loads, to estimate natural-frequencies and modal shapes.
      • steady-state thermal analysis to determine temperature and heat flow.
      • sequential thermo-mechanical analysis to determine thermal stresses.
      • topology optimization to find geometries that maximizes stiffness under constraints.
    • Compare FEM to Finite Element Analysis (FEA) and illustrate the steps involved in each (assembling, numerical integration, etcetera).
    • Identify, motivate and select relevant boundary conditions for a given problem.
    • Select and motivate the appropriate choice of element type for a given analysis.
    • Create a mesh and judge the quality of a given mesh. Can also identify and motivate regions where the mesh density must be high and where it can be low.
    • Explain essential and natural boundary conditions, also list these conditions for all studied elements. Exemplify boundary conditions of mixed type.
    • Recognize the governing equations for different structural models and explain their terms.
    • Perform convergence studies and evaluate the results. Can also describe the use of p-refinement and h-refinement.
    • Use FEA to guide the design of a component, with respect to given criteria.
    • Perform parametric studies for simpler optimization tasks.
    • Summarize the following element types: bars, beams, plates, shells, 2D solids (plane stress/strain, axisymmetry) and 3D solids.
    • Explain the difference between linear and nonlinear problems and how they are solved. List sources leading to a nonlinear FE-problems.
    • Solve and evaluate results from FE-models containing:
      • Contact formulations (Penalty, Lagrange, Augmented-Lagrange) with and without friction.
      • Linear material models (Hooke's law, Fourier's law), elastic-plastic models (elastic-ideally-plastic, linear hardening).
    • Prepare CAD-geometry for FEA (defeaturing and repairing).

    Content

    • Theoretical basics of the Finite Element Method (FEM).
    • Practice using industrial software to set up and perform Finite Element Analysis (FEA).
    • Common types of FEA: static structural analysis, steady-state heat flow, linearized buckling, modal analysis, high cycle fatigue.
    • Iterative design based on one or more criteria: stiffness/deformation, allowable stress, fatigue, weight, etcetera.
    • Introduction to non-linear problems.
    • Modeling aspects: choosing boundary conditions (loads and supports), preparing CAD geometry, meshing, choosing element types, contact formulations.
    • Topology optimization

    Organisation

    The course consists of a number of lectures, which cover the theory and exemplify practical aspects of using a FE software (ANSYS). A large part of the course consists of self-study where you work on you hand-in assignments. For hands-on support and answering of questions, there will be scheduled consultation hours.

    Literature

    Will be made available on the course homepage at the beginning of the course.

    Examination including compulsory elements

    Home-exam and hand-in assignments. The assignments are solved individually and are presented on Zoom.

    The course examiner may assess individual students in other ways than what is stated above if there are special reasons for doing so, for example if a student has a decision from Chalmers about disability study support.

    Structural analysis using the finite element method | Chalmers