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Continuum solid mechanics

Presentation

Programme (detailed contents):

Stress theory, strain theory, displacement-strain relation, constitutive relation in linear elasticity, formulation of the elasticity problem, analytical methods in elasticity, Case of slender structures.

 

 

Organisation:

Despite two plenary lectures and one plenary restitution lecture, this course is done as small class with both lectures and applications. There is also two small projects on computer.

Objectives

At the end of this module, the student will have understood and be able to explain (main concepts) continuum mechanics, the notions of stress, strain and displacement fields, and the constitutive relation in linear elasticity.

 

 

The student will be able to:

- Analyse the stress and strain states of a solid submitted to a loading.

- Compute the stress, given the strain and conversely.

- Compute the strain state given the displacement field.

- Write the equations of the local equilibrium.

- Translate into equations the boundary conditions of a model.

- Propose a relevant model of a real problem with particular attention to boundary conditions.

- Compute the stress, strain and displacement fields of some simple problems of elasticity.

Needed prerequisite

Analysis, function of multiple variable, Taylor expansion, partial derivatives

Linear algebra, vectors, matrix, eigenvectors and eigenvalues

Algorithms, bases of programming in Python

Rigid solid mechanics, equilibrium, resultant force and moment.

Form of assessment

The evaluation of outcome prior learning is made as a continuous training during the semester. According ot the teaching, the assessment will be different: as a written exam, an oral exam, a record, a written report, peers review...