Continuum and truss models in optimal topology design of structures

This article issues from the present state of knowledge in mechanics, characterized by general approaches of analysis and optimal design on the macrolevel. In case of the analysis, the matter is in the finite element method, in case of optimization - in methods of mathematical programming. Homogenization allows to use these approaches also for non-homogeneous models of materials (e.g, micro-structures). Designing an optimal topology of structures, different approaches are used concurrently in modeling and optimization of truss and continuum models. While optimization of truss model topology varies connections of nodes by truss elements, using mostly discrete optimization, in continuum structures the model of the microstructure is homogenized and effective material constants are used in classic equations of discretized continuum, where parameters of the microstructure are optimized. The article proposes a crystal model having its background in real microstructures, applicable when considering its characteristics through truss and continuum models. This model is of interest especially in the problems of an optimal three-dimensional topology.