Association des Parents d'Elèves du Conservatoire de musique agréé et de danse de Châlons en Champagne

Application to elasticity

The historical application of the Virtual Fields Method was elasticity. In this case, it can be shown that what is usually considered as an inverse problem can be solved directly. The method relies on the principle of virtual work. The following slideshow illustrates how this principle can be used to derive specific equilibrium equations. The principle of virtual work

Principle of the method in the case of linear elasticity

The following slideshow describes the application of the VFM in the case of elasticity. The VFM in linear elasticity

Principle of the method in the case of non-linear elasticity

Another very simple situation concerns non-linear elasticity, particularly when the stress can be expressed as a polynomial function of the strain. It is the case for a composite non-linear in-plane shear behaviour with a softening terms expressed as a cubic function of the shear strain, as illustrated in the following slideshow. The VFM in non-linear elasticity: an example