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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

Comes after

  • Mechanics of solids 1

Opens up

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=∫VeBTE B  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

    ∫Ωf dΩ≈∑i=1nwi f(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

Quick answers

When is Introduction to finite elements taught?

Introduction to finite elements (0542-4223) is taught in Semester A (fall), 4 weekly hours. It counts toward “Core: solids” in the Tel Aviv University Mechanical Engineering elective requirements.

What do I need before 0542-4223?

Before Introduction to finite elements you need: Mechanics of solids 1.

What software is used in Introduction to finite elements?

Introduction to finite elements is normally taught with ANSYS, ABAQUS, COMSOL, MATLAB PDE Toolbox, Nastran.

Which jobs does Introduction to finite elements prepare you for?

Introduction to finite elements is part of the preparation for these roles: Simulation and FEA engineer, Additive manufacturing engineer, Medical device engineer, Aerospace structures engineer.

Which interest areas include Introduction to finite elements?

Introduction to finite elements sits in these interest areas: Structures and computational mechanics, Mechanical design.

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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.