دانلود کتاب تبدیل های توپولوژیکی برای تحلیل سازه ای کارآمد

In this book, a number of topological transformations are proposed for simplifying certain problems in the mechanics of structures. For each case, the main problem is stated, and then, the transformation is established. Once the required topolog-ical analysis is performed, a back transformation results in the solution for the main problem. The topological transformations studied here employ (1) models drawn on lower-dimensional spaces, (2) models embedded onto higher-dimensional spaces, (3) interchange models defined which have more suitable connectivity prop-erties than the corresponding original structural model, (4) other relevant studies are made using graph theory, and finally, metaheuristic algorithms are utilized for graph decomposition and the selection of cycle bases of graphs.

The aim of the present work is twofold. On the one hand, it shows to mathe-maticians how apparently pure mathematical concepts can be applied to the efficient solution of problems in structural mechanics. On the other hand, it illustrates to engi-neers the important role of mathematical concepts for the solution of engineering problems.