New developments in the optimal analysis of regular and near-regular structures: decomposition, graph products, force method

In this paper, advances on the optimal analysis of regular and near-regular structures are presented. Some new mathematical conditions for the decomposition of regular structures are provided. Decomposed regular structures are solved using divide and conquer algorithms (Kaveh in Optimal analysis of structures by concepts of symmetry and regularity. Springer, New York, 2013). Moreover, some allowable matrix operations for finding the eigenvalues of the regular structures are studied. Using the obtained results of the regular structures, a combined force method for the analysis of near-regular structures is presented. Previously, the displacement method of the analysis of near-regular structures (second group) was presented by our research group (Rahami et al. in J Comput Civ Eng, ASCE, 2014, doi:10.1061/(ASCE)CP.1943-5487.0000375). The merits and demerits of the present force method over the previously applied displacement method are similar to those in the general force and displacement methods.