Machi Zawidzki - Böcker

Ario and Zawidzki show readers how to handle symmetric structures in engineering using group-theoretic bifurcation theory as a mathematical tool for the finite element analysis of symmetric structures.They guide the reader from the initial mathematical concepts through to application examples. Readers will gain a solid theoretical grounding in group theory and strong working knowledge of the use of computational frameworks for structural analysis using mathematical representations of symmetry and physical symmetry. First, the authors elaborate an outline of symmetric structures in engineering and then describe the representation of symmetry and group theory. They then discuss block diagonalization theory and finite element analysis models. This provides readers with the base knowledge needed for Chapter 6, which is based on numerical analysis examples of invariant, static FEM model systems and dynamic model systems of the dihedral group. This unique approach is a vital method that will enable readers to reduce the time and computation needed for accurate analysis so that they can better design such structures. The focus on finite element methods and practical examples and case studies throughout provides a strong practical foundation for anyone studying or working in this field.The book is a valuable resource for undergraduate and postgraduate students on various courses such as civil and mechanical engineering, architecture, structural engineering, applied mathematics, and physics. Additionally, it describes vital practical solutions for structural engineers, structural system manufacturers, fabricators of prefabricated elements, and developers of computational mechanics and so on.

This book presents three projects that demonstrate thefundamental problems of architectural design and urban composition – the layoutdesign, evaluation and optimization. Part I describes the functional layoutdesign of a residential building, and an evaluation of the quality of a townsquare (plaza).The algorithm for the functional layout design is based onbacktracking using a constraint satisfaction approach combined with coarse griddiscretization. The algorithm for the town square evaluation is based ongeometrical properties derived directly from its plan.Part II introduces a crowd-simulation application for theanalysis of escape routes on floor plans, and optimization of a floor plan forsmooth crowd flow. The algorithms presented employ agent-based modeling andcellular automata.

This book is comprised of two parts, both of which exploremodular systems: Pipe-Z (PZ) and Truss-Z (TZ), respectively. It presents severalmethods of creating PZ and TZ structures subjected to discrete optimization.The algorithms presented employ graph-theoretic and heuristic methods. Theunderlying idea of both systems is to create free-form structures using theminimal number of types of modular elements. PZ is more conceptual, as it formssingle-branch mathematical knots with a single type of module. Conversely, TZis a skeletal system for creating free-form pedestrian ramps and ramp networksamong any number of terminals in space. In physical space, TZ uses two types ofmodules that are mirror reflections of each other. The optimization criteriadiscussed include: the minimal number of units, maximal adherence to the givenguide paths, etc.