On rigid origami III: static rigidity, pre-stress stability and second-order rigidity

The foldability of rigid origami has been widely studied and applied to many engineering fields. In this article we introduce the statics of rigid origami, find the form of stress and load, and prove the equivalence of static rigidity and first-order rigidity. Another concept introduced here is the pre-stress stability. We concern what is the stability of a creased paper when it is rigid but not statically rigid and how would the pre-stress contribute to the stability. The answer to these questions is also linked with the second-order rigidity. A brief discussion on the numerical methods to determine these rigidity concludes the article.