Current architecture is characterized by specifying new typologies but not experienced until now in the engineering and architecture disciplines. Architectural free forms with non-euclidean geometries are being developed, which answer to logical analysis and parametric design, and which are tending to the mimesis of behaviour with the nature. Innovative research is developing advanced constructions of complex geometries and free forms by architects like Yushang

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Architecture is totally linked to the knowledge and study of geometry. The re-entrant hexatruss structure is part of the auxetic structures. These structures, characterized by its negative Poisson's ratio, change their geometric configuration from a line to a surface and from a surface to a volume or spatial framework. This project is based on establishing those re-entrant hexatruss geometries to be able to build new spaces in architecture, studying analytically geometric and structural properties of auxetic materials and structures that can be a part of the architecture construction.

The following article extends and tests computational methodologies of design to consider Finite Element Analysis in the creation of optimized infill structures based on regular and semi-regular patterns that comply with the geometrical constraints of deposition. The Stress-Deformation relationship manifested in Finite Element Analysis is structured in order to influence the geometrical arrangement of the complex spatial infill. The research presents and discusses a program of performance informed infill design, and validates the generalizability of a method of internalizing and automating Finite Element Method (FEM) processing in Fused Deposition Modeling (FDM) workflows, and tests manufacturability of the methods through its ability to handle the FDM process constraints of FEM influenced intricate geometries.

En este artículo, se aborda la determinación de las condiciones de equilibrio de Superficies de Geometría Variable definidas por Estructuras Recíprocas mediante el estudio de un campo de fuerzas actuantes y del lugar geométrico que describen los elementos de tales estructuras a través de los diferentes estados de transformación. Se establecen las propiedades geométricas y estructurales de un Nodo Recíproco de estas estructuras con tres barras cilíndricas iguales, mediante el desarrollo de una formulación matemático-paramétrica, con el objetivo de deducir el proceso de equilibrio para la obtención analítica de sistemas de estabilización de Superficies de Geometría Variable conformadas por Estructuras Recíprocas Transformables. La finalidad de la investigación presentada aquí es la aplicación de dicho sistema de estabilización mediante un software geométrico-estructural de nueva creación, al diseño y cálculo de distintas tipologías de superficies en la configuración de arquitecturas de geometría transformable.