The main contribution of the present paper is to train efficient neural networks for seismic design of double layer grids subject to multiple-earthquake loading. As the seismic analysis and design of such large scale structures require high computational efforts, employing neural network techniques substantially decreases the computational burden. Square-on-square double layer grids with the variable length of span and height are considered. Back-propagation (BP), radial basis function (RBF) and generalized regression (GR) neural networks are trained for efficiently prediction of the seismic design of the structures. The numerical results demonstrate the superiority of the GR over the BP and RBF neural networks.

Performance control (PC) is a recently developed, observation based, design process that aims at rational and efficient selection of structural elements rather than investigating their usefulness through iterative processes. The basic notion behind PC is that structural response is mainly a function of design and detailing, rather than numerical computations. The design concept uses pre-selected target displacements and failure mechanisms as key control objectives. While elastic analysis is still the predominant design methodology for double-layer grids (DLG) and similar structures under service conditions, performance-based procedures could further enhance their functional uses up to plastic limit states. The current contribution presents a general technique for the estimation of maximum plastic displacements of twistless, orthotropic, DLG of regular formation, simply supported along the sides of a parallelogram, and subjected to monotonically increasing uniform distribution of normal nodal forces. In the interim, a new application for the uniqueness theorem has also been discussed. The proposed methodology is ideally suited for preliminary design as well as capacity analysis purposes. It lends itself well to both manual and spreadsheet computations. The applications of the proposed solutions have been illustrated through a number of generic examples. The paper does not address seismic conditions.

This paper studies the increase in strength and stiffness of the composite double-layer grids, whose top-layers combine the steel frame elements with concrete decks. Firstly, the paper obtains the ultimate load capacities of square concrete decks with and without ribbed edges under various support and load conditions. Then, the load capacity of a composite double-layer grid is obtained under various loads, geometric and support conditions. A comparison of the results indicates that: the composite grid exhibits 2 to 5 times higher load capacity than the corresponding non-composite grid. In addition, a composite grid with (roller+pin) supports has about 20% of the load capacity of the identical grid with (pin+pin) supports.

A two-stage optimization method is presented by employing the evolutionary structural optimization (ESO) and ant colony optimization (ACO), which is called ESO-ACO method.To implement ESO-ACO, size optimization is performed using ESO, first. Then, the outcomes of ESO are employed to enhance ACO. In optimization process, the weight of double layer grid is minimized under various constraints which artificial ground motion is used to calculate the structural responses. The presence or absence of elements in bottom and web grids and also cross-sectional areas are selected as design variables. The numerical results reveal the computational advantages and effectiveness of the proposed method.

For reliability-based topology optimization (RBTO) of double layer grids, a two-stage optimization method is presented by applying" Solid Isotropic Material with Penalization "and" Ant Colony Optimization" (SIMP-ACO method). To achieve this aim, first, the structural stiffness is maximized using SIMP. Then, the characteristics of the obtained topology are used to enhance ACO through six modifications. As numerical examples, reliability-based topology designs of typical double layer grids are obtained by ACO and SIMP-ACO methods. Their numerical results reveal the effectiveness of the proposed SIMPACO method for the RBTO of double layer grids.