Coordinated synthesis of hierarchical engineering systems

In this paper, we develop a formal procedure for the coordinated synthesis of hierarchically described engineering systems. By using an iso-parametric or iso-geometric mapping of the geometrical model, material description and behavioral fields, a natural correspondence is established between the physical hierarchy of the system and its behavioral hierarchy. This geometry-centric philosophy, together with an appropriately defined adjoint problem allows the evaluation of arbitrary system-level functions locally on the sub-systems by capturing interactions between the subsystems without exchange of geometrical and material data (CAD models). The systematic development of the procedure for analysis and synthesis of hierarchically described engineering systems is the focus in the first part of the paper. This includes the development of a procedure to assess the sensitivity of system functions to changes in sub-system designs. A NURBS based numerical solution procedure is then demonstrated to solve the obtained solution system. The solution procedure involves the development of matrix systems for interacting sub-systems and their solution using methods inspired by domain decomposition techniques. The developed procedures are demonstrated through a detailed example involving a particulate composite material system in which the effective thermal conductivity is evaluated in a partitioned manner. To carryout this latter evaluation, a three-dimensional meshless synthesis procedure termed Hierarchical Partition of Unity Field Compositions (HPFC) developed in our prior research is employed. The techniques developed in this paper are expected to be of value in “top–down” synthesis of complex assembly of components as well as in synthesizing material microstructural arrangements to effect behavior at larger length-scales.