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This paper presents the evolution of and influence that the use of a triangular grid has had on the transformation of layered grid structures during the last two centuries. Historical facts, technological advances, economic and social crises among other factors influence the process of change and evolution of the grid systems in architecture to make construction processes more efficient by reducing the consumption of materials and qualified labor. Geometry and structure innovate styles and processes that are perfected over the years, achieving lighter and more stable structures. For the purpose of this paper historical data will be collected that allows the development of a theory that shows the influence of various periods based on technological advances. This research shows four historical periods in the evolution of layered grid structures. Being the triangular grid a widely used methodology in the construction of a diversity of geometric proposals and innovative construction systems for the solution of a diversity of buildings from the first domes built in the early 19th century to the free-form structures built from the late 20th century to the present day.

The use of self-organizing maps and artificial neural networks for structural health monitoring is presented in this paper. The authors recently developed a nonparametric structural damage detection algorithm for extracting damage indices from the ambient vibration response of a structure. The algorithm is based on self-organizing maps with a multilayer feedforward pattern recognition neural network. After the training of the self-organizing maps, the algorithm was tested analytically under various damage scenarios based on stiffness reduction of beam members and boundary condition changes of a grid structure. The results indicated that proposed algorithm can successfully locate and quantify damage on the structure. Scopus

The arrangement and form of the image sensor have a fundamental effect on any further image processing operation and image visualization. In this paper, we present a software-based method to change the arrangement and form of pixel sensors that generate hexagonal pixel forms on a hexagonal grid. We evaluate four different image sensor forms and structures, including the proposed method. A set of 23 pairs of images; randomly chosen, from a database of 280 pairs of images are used in the evaluation. Each pair of images have the same semantic meaning and general appearance, the major difference between them being the sharp transitions in their contours. The curviness variation is estimated by effect of the first and second order gradient operations, Hessian matrix and critical points detection on the generated images; having different grid structures, different pixel forms and virtual increased of fill factor as three major properties of sensor characteristics. The results show that the grid structure and pixel form are the first and second most important properties. Several dissimilarity parameters are presented for curviness quantification in which using extremum point showed to achieve distinctive results. The results also show that the hexagonal image is the best image type for distinguishing the contours in the images. © 2018 by the authors. Licensee MDPI, Basel, Switzerland. open access

Spatial structures have shown a great development, mainly since the post-war years from the middle of the twentieth century. They have become a constructive solution which provides lightness and stiffness, while achieving longer spans and reducing energy and used material. In Mexico City, the Sports Palace was completed in 1968 to become a landmark of Mexican architecture and an example of a low-cost, lightweight, dome. This essay shows the geometric influences and foundation behind its design, as well as the development and typological transformation of its structural elements and materials in the finally adopted constructive solution ─the crossed arch. Such solution transformed material and its geometry into a structural typological solution of its own. Here, Félix Candela used constructive and structural elements, previously experienced in other typologies, into solutions to form new types. This way, Candela developed the hyperbolic paraboloid, employing new materials and applying geometry for the structural typological development of the shape of the Sports Palace, achieving a dome which would become a typological model of international architecture.

The minimum mass designs of state of the art helical circumferential grids are compared to axial helical grids. Analytical models based on the classical laminate theory deliver optimization results in less than one second. Using finite element models the obtained results are validated and adjusted in a second optimization step. Studies on the influence of rib heights and Young’s modulus show potential to create lighter grids in axial helical design than in helical circumferential design. This is shown for medium length cylinders from relatively low up to very high load levels.