What is meant by Non-Linearity?

First of all, let us examine the term 'linear' finite element stress analysis. In the linear analysis, two assumptions are involved. Firstly the stress in the material is exactly proportional to strain.

Secondly, the structure deforms exactly proportional to the loads, as long as the supports are the same. The second assumption may be mistaken to derive from the first - it does not. (Fishing rod is an example of a non-linear structure made of linear material).

A stress analysis problem is linear only if both conditions hold. If any one of them is violated, then we have a Non-Linear problem. Most real life structures, especially plastics, are non-linear, perhaps both in structure and in material.

Most plastic materials have a non-linear (see figure) stress strain relationship. The non-linearity arising from the nature of material is called 'Material Non-linearity'. Furthermore, due to the generally thin walls, plastic structures exhibit a non-linear load-deflection relationship, which ... more.

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