A tessellated continuum approach for the static analysis of perforated structures

Pre-fractals have the capacity to represent structures of different levels of complexity and have recently been shown to be suitable for continuum analysis using a method called tessellated continuum mechanics. Tessellated continuum mechanics is an analytical theory for the analysis of porous/perforated structures but presently has only been tested to any extent on heat transfer problems. This paper is concerned with extending the implementation of the tessellated approach to static structural analysis of one and two dimensions with a particular emphasis on perforated plates. The principal objective of the work is to establish that the structural analysis of perforated structures is possible to a very high degree of accuracy in a continuum mechanics framework. The tessellated approach involves the local expansion of space to close perforations and invokes the concept of finite similitude, which has appeared in the recent literature. The consequences of local-space scaling are examined and static testing for beams and plates, constrained by different boundary conditions are presented.