Introduction to theory of elasticity
Also listed as: מבוא לתורת האלסטיות
The theory floor under every serious solid-mechanics result. Stress and strain as tensors, boundary-value problems formulated and solved, and the classical two-dimensional solutions.
- Semester
- Semester B
- Weekly hours
- 4h
- Counts as
- Core: solids
- Interest areas
- Structures and computational mechanics · Aeronautics and space
Comes after
- Mechanics of solids 1
What it covers
Formulation
- Index and tensor notation, vectors and second-order tensors
- Strain analysis: displacement gradient, infinitesimal strain tensor, compatibility
- Stress: traction vector, Cauchy stress tensor, equilibrium, principal stresses, invariants
- Generalised Hooke's law, isotropic elasticity, Lamé constants, E, ν, G, K
- Navier displacement equations, Beltrami–Michell stress equations, Saint-Venant's principle
Two-dimensional elasticity
- Plane stress and plane strain, and when each is the right idealisation
- Airy stress function and the biharmonic equation
- Cartesian solutions: beam bending
- Polar solutions: thick cylinder (Lamé), stress concentration at a hole (Kirsch), the wedge and Flamant problems
Torsion and energy methods
- Torsion of non-circular bars, Prandtl stress function, warping
- The membrane analogy
- Energy methods and an introduction to three-dimensional problems
Results worth carrying out
Infinitesimal strain tensor
Equilibrium
Hooke's law, isotropic
Airy stress function
Kirsch, stress at a hole edge
Figures worth knowing
- Three-dimensional Mohr's circle
- Stress-concentration contours around a hole
- Airy-function stress fields
- Membrane analogy for torsion
- Photoelastic fringe patterns
Related courses
- 0542-4220Semester A · 4h
Theory of vibrations
תורת התנודות
From one degree of freedom to continuous systems, with modal analysis in the middle. It is the course that turns "the machine shakes" into a number you can design against.
Structures and computational mechanicsMiniaturised systems and materialsAeronautics and space - 0542-4224Semester B · 4h
Mechanics of solids 2
מכניקת המוצקים 2
The bridge from strength of materials to failure analysis. Yield criteria, unsymmetric bending, thin-walled torsion, energy methods, buckling. It counts toward three interest areas at once.
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Research project for honours students 1
פרויקט מחקר למצטיינים 1
The honours research project, and the most direct on-ramp to a thesis in the catalogue. You pick a supervisor, produce results, and frequently continue the same problem into a masters.
Structures and computational mechanicsMechatronics and roboticsMiniaturised systems and materialsAeronautics and spaceEnvironment and energyFlow and thermal designMechanical design - 0542-4012Semester B · 3h
Research project for honours students 2
פרויקט מחקר למצטיינים 2
The continuation of the honours project, where the results get deep enough to defend. Under the direct track this is already the first part of the masters thesis.
Structures and computational mechanicsMechatronics and roboticsMiniaturised systems and materialsAeronautics and spaceEnvironment and energyFlow and thermal designMechanical design
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