# 3.7.2: Deformation-Energy

In mechanics, energy is equal to force times displacement parallel to its direction. Think of a rubber band: If you stretch it, you do work on it. This work gets stored inside the rubber and can be transformed into other kinds of energy. You may for example launch a small toy airplane with it: Then the elastic energy in the rubber gets transformed into kinetic energy. When stretching an elastic material the force to be applied at the beginning is zero and then grows proportionally to the stiffness and the increase of length of the material. The mechanical work is equal to the area beneath the curve that results from drawing the magnitude of the applied force over its corresponding displacement. In case of linear elastic materials this gives a rectangular triangle with the final displacement forming one leg and the final force being its other leg. From this one sees, that for equal final forces the elastic energy stored in a material decreases with decreasing displacements which corresponds to increasing stiffness.

Fig. 3.7.2.1: Simply supported beam under axial and transversal point-load

Via the input

**“Elems|Ids”**one can supply identifiers od elements of those parts for which the deformation energy shall be calculated. An empty list means that all elements are considered. The**“LCase”**-input lets one select the load-case for which results shall be retrieved. The structure of the data trees returned from the**“D-Energy”**-component (see fig. 3.7.2.1) contains one branch per element. A list of axial deformation energy and bending energy for each element is displayed. In case of shells the branches contain the in-plane or bending energy of each face of the shell.

Shell_BendingEnergy.gh

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Shell_DeformationEnergy.gh

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