Skip to content
All courses
0542-4223

Introduction to finite elements

Also listed as: מבוא לאלמנטים סופיים

The most transferable single course in the catalogue. Direct stiffness through weak forms to isoparametric elements and numerical integration, so that a mesh and a contour plot mean something.

Semester
Semester A
Weekly hours
4h
Counts as
Core: solids
Interest areas
Structures and computational mechanics · Mechanical design

What it covers

Foundations

  • Direct stiffness method for springs, bars and trusses, assembly and boundary conditions
  • Strong form against weak form, method of weighted residuals, Galerkin
  • Variational and energy principles, Rayleigh–Ritz, minimum potential energy
  • One-dimensional elements: bar, Euler–Bernoulli beam with Hermite shape functions, frames

Element technology

  • Shape functions and interpolation, convergence requirements, the patch test
  • Two-dimensional elements: constant-strain triangle, quadratic triangles, bilinear quads
  • Plane stress, plane strain and axisymmetric formulations
  • Isoparametric formulation, natural coordinates, the Jacobian
  • Gauss quadrature, and the failure modes: locking and hourglassing
  • Three-dimensional solids, plates and shells

Using the results

  • Stress recovery, error estimation, h- and p-refinement
  • Steady heat conduction with the same machinery
  • Introduction to eigenvalue and transient analysis

Results worth carrying out

  • The system you are solving

    [K]{d}={F}[K]\{d\} = \{F\}
  • Element stiffness

    Ke=VeBTEB  dVK_e = \int_{V_e} B^{\mathsf{T}} E\, B \; dV
  • Isoparametric mapping

    x=i=1nNi(ξ,η)xix = \sum_{i=1}^{n} N_i(\xi,\eta)\, x_i
  • Gauss quadrature

    ΩfdΩi=1nwif(ξi)\int_\Omega f \, d\Omega \approx \sum_{i=1}^{n} w_i\, f(\xi_i)

Figures worth knowing

  • Mesh diagrams
  • Shape-function plots
  • von Mises stress contours
  • Jacobian mapping between natural and physical coordinates
  • Convergence curves under refinement

Related courses

We also write the summaries.

This map tells you what a course contains. The summaries, the tutoring and the people who already took it are the part you get by joining.

The topic outlines are not official syllabi. The university publishes a catalogue blurb per course, not lecture-by-lecture material, so each outline describes what a course of that name, at those hours, with those prerequisites teaches at engineering schools generally, cross-checked against the standard textbook for the subject. Treat it as an informed map, not as a transcript of the lectures.