Single-layer Grid Research Articles

Static performance of double-ring joints for freeform single-layer grid shells subjected to a bending moment and shear force

This paper discussed a new type of bolted joint named a double-ring joint used in freeform single-layer grid shells. Prototype static tests and numerical simulations were undertaken to investigate the mechanical behavior of the bolted joint subjected to the bending moment and shear force. The main conclusions of this study are as follows. There are two primary failure modes of double-ring joints. One is the fracture of the bolt, and the other is the instability of the central ring. The failure mode depends only on the ratio of the ring thickness to the ring diameter when the height of the ring and the diameter of the bolt match. Ultimately, the simplified formulae for the load-bearing capacity of a double-ring joint in different failure modes were proposed as a reference for joint design.

Buckling and Reliability Analysis of Single Layer Grid Dome with Diagonal Brace under Snow Load

Buckling and Reliability Analysis of Single Layer Grid Dome with Diagonal Brace under Snow Load

Design of a Linear Bistable Compliant Crank–Slider Mechanism

This paper presents a new model for a linear bistable compliant mechanism and design guidelines for its use. The mechanism is based on the crank–slider mechanism. This model takes into account the first mode of buckling and postbuckling behavior of a compliant segment to describe the mechanism's bistable behavior. The kinetic and kinematic equations, derived from the pseudo-rigid-body model (PRBM), were solved numerically and are represented in plots. This representation allows the generation of step-by-step design guidelines. The design parameters consist of maximum desired deflection, material selection, safety factor, compliant segments' widths, maximum force required for actuator selection, and maximum footprint (i.e., the maximum rectangular area that the mechanism can fit inside of and move freely without interfering with other components). Because different applications may have different input requirements, this paper describes two different design approaches with different parameters subsets as inputs. The linear bistable compliant crank–slider mechanism (LBCCSM) can be used in the shape-morphing space-frame (SMSF) as potential application. The frame's initial shape is constructed from a single-layer grid of flexures, rigid links, and LBCCSMs. The grid is bent into the space-frame's initial cylindrical shape, which can morph because of the inclusion of LBCCSMs in its structure.

Effects of the Equivalent Geometric Nodal Imperfections on the stability of single layer grid shells

The present paper discusses the sensitivity of the global and local stability of a hybrid single layer grid shell to a set of Equivalent Geometric Nodal Imperfections representative of the actual structural and construction imperfections. Since imperfections are hard to be measured and controlled in experimental facilities, the stability of the structure is extensively investigated in numerical experiments. The imperfections are set by means of the so-called Eigenmode Imperfection Method. The method parameter space is densely sampled, and different structural models are adopted. The results are given in terms of two bulk parameters: the well established Load Factor and the proposed Buckling Shape Length, the latter being introduced to provide a continuous measure of the degree of “globalness” of the instability. Significant and non monotonic changes in both the Load Factor and Buckling Shape Length are observed versus the growth of the imperfection amplitude. Further, a local metrics of the grid shell geometry, named nodal apex, is introduced for each structural node. Special emphasis is given to the analysis of the correlation between the apex of the initial imperfect geometry and the apex of the deformed shape at collapse. The observed high correlation suggests that the mechanical behavior of the imperfect grid shell is significantly influenced by this local geometrical feature.

Theoretical and experimental study of robustness based design of single-layer grid structures

Structural robustness refers to the ability of a structure to avoid disproportionate consequences to the original cause. Currently attentions focus on the concepts of structural robustness, and discussions on methods of robustness based structural design are rare. Firstly, taking basis in robust <TEX>$H_{\infty}$</TEX> control theory, structural robustness is assessed by <TEX>$H_{\infty}$</TEX> norm of the system transfer function. Then using the SIMP material model, robustness based design of grid structures is formulated as a continuum topology optimization problem, where the relative density of each element and structural robustness are considered as the design variable and the optimization objective respectively. Generalized elitist genetic algorithm is used to solve the optimization problem. As examples, robustness configurations of plane stress model and the rectangular hyperbolic shell model were obtained by robustness based structural design. Finally, two models of single-layer grid structures were designed by conventional and robustness based method respectively. Different interference scenarios were simulated by static and impact experiments, and robustness of the models were analyzed and compared. The results show that the <TEX>$H_{\infty}$</TEX> structural robustness index can indicate whether the structural response is proportional to the original cause. Robustness based structural design improves structural robustness effectively, and it can provide a conceptual design in the initial stage of structural design.

Total Absorption of Electromagnetic Waves in Ultimately Thin Layers

We consider single-layer arrays of electrically small lossy bi-anisotropic particles that completely absorb electromagnetic waves at normal incidence. Required conditions for electromagnetic properties of bi-anisotropic particles have been identified in the most general case of uniaxial reciprocal and nonreciprocal particles. We consider the design possibilities offered by the particles of all four fundamental classes of bianisotropic inclusions: reciprocal chiral and omega particles and nonreciprocal Tellegen and moving particles. We also study the reflection/transmission properties of asymmetric structures with different properties when illuminated from the opposite sides of the sheet. It has been found that it is possible to realize single-layer grids which exhibit the total absorption property when illuminated from one side but are totally transparent when illuminated from the other side (an ultimately thin isolator). Other possible properties are co-polarized or twist polarized reflection from the side opposite to the absorbing one. Finally, we discuss possible approaches to practical realization of particles with the properties required for single-layer perfect absorbers and other proposed devices.

Coupled form-finding and grid optimization approach for single layer grid shells

This paper demonstrates a novel two-phase approach to the preliminary structural design of grid shell structures, with the objective of material minimization and improved structural performance. The two-phase approach consists of: (i) a form-finding technique that uses dynamic relaxation with kinetic damping to determine the global grid shell form, (ii) a genetic algorithm optimization procedure acting on the grid topology and nodal positions (together called the ‘grid configuration’ in this paper). The methodology is demonstrated on a case study minimizing the mass of three 24×24m grid shells with different boundary conditions. Analysis of the three case studies clearly indicates the benefits of the coupled form-finding and grid configuration optimization approach: material mass reduction of up to 50% is achieved.

Research on Mechanism of Consolidating the Saturated Soft Clay with the Application of Pile-Supported Composite Foundation

In order to reduce both uneven settlements and construction duration, researches on pile-supported composite foundation of highway were carried out. When the groundfill is higher than the critical height（1.35 times space between piles）, a complete geostatic arch is formed in the pile-supported composite foundation, which could significantly reduce the uneven settlement. Grids installed at the bottom of embankment could markedly reduce the side displacement and increase the stability of embankment, multilayer grids with layout of loose on the top and dense at the bottom prefer to single layer grids. Plastic drainage board makes up well-functioned drainage system, which can shorten the dispersal time of pore water pressure and accelerate the consolidation of soft soil to shorten the construction duration.

Construction process analysis for a single-layer folded space grid structure in considering time-dependent effect

A new long-span space grid structure system, “single-layer folded space grid” (SFSG), is applied in the Shenzhen Universiade Stadium. Compared with regular single-layer grid, the out-of plane stiffness and bearing capacity of the structure is improved with bending and uplifting of the structural units in SFSG, and the span capacity of the structure is then enhanced. Because of the large structural dimension, the construction process including assembling, closure and brace-unloading should be divided into many stages. As a result, there is very strong time-dependent effect for the structural stress state in construction. In this paper, based on matrix mechanics model of space grid structures, a time-dependent analysis method considering temperature variation during construction is presented based on matrix mechanics model to optimize the closure scheme. A combined brace element is presented to accurately simulate the mechanic character of temporary braces. In this way, the whole construction process of assembling, closure and brace-unloading are effectively and accurately analyzed for the SFSG structure of Shenzhen Universiade Stadium. The displacement state, stress distribution, and force changes in temporary braces are obtained to provide instruction for the design and control of construction process.

Recent Developments in the Design of Glazed Grid Shells

Free-form geometries are very popular in today's architecture. Computer controlled fabrication methods allow for structures, which would not have been possible a few years ago. But how does one transfer 3D geometries into a load bearing structure without loosing the architectural vision of smoothly shaped building envelopes? An intense discussion is necessary to navigate architectural visions of elegant 3D shapes through the technical and economic constraints of realization. The role of the engineer is conceived as that of a mediator between the aesthetic ambitions of the architect, the budget of the client and the technical capabilities of the contractor. From the very early stages of form finding to the assembly on site, a consistent design process is absolutely necessary to achieve high quality free formed structures. In this paper different examples are presented to demonstrate this. The projects vary from a single layer grid shell for Westfield's new shopping centre at White City, London and a large space structure in Frankfurt to a timber shell for a department store in Cologne

Impedance characteristics of power distribution grids in nanoscale integrated circuits

The essential design characteristic of nanoscale integrated circuits is increased interconnect complexity. Conductors at different levels of the interconnect hierarchy have highly different physical and, consequently, electrical characteristics. These interconnect lines also exhibit inductive behavior due to enhanced switching speed of nanoscale devices, making interconnect design and analysis difficult. The design of robust and area efficient power distribution networks for high-speed integrated circuits has therefore become a challenging task. The impedance characteristics of multilayer power distribution grids and the relevant design implications are the subject of this paper. The power distribution network spans many layers of interconnect with disparate electrical properties. Unlike single-layer grids, the electrical characteristics of multilayer grids vary significantly with frequency. As the frequency increases, a large share of the current flow is transfered from the low-resistance upper layers to the low-inductance lower layers. The inductance of a multilayer grid therefore decreases with frequency, while the resistance increases with frequency. The lower layers of multilayer power grids provide a low-inductance current path, significantly reducing the grid impedance at high frequencies. Multilayer power distribution grids extend to the lower interconnect layers, exhibiting superior high-frequency impedance characteristics as compared to power distribution grids built exclusively within the upper, low-resistance metal layers. A significant share of metal resources to distribute the global power should therefore be allocated to the lower metal layers. An analytic model is also presented to determine the impedance characteristics of a multilayer grid from the inductive and resistive properties of the comprising individual grid layers.

Laboratory simulation of direct lightning strokes to a modeled building: measurement of magnetic fields and induced voltages

In IEC 61312-2 equations for the assessment of the magnetic fields inside structures due to a direct lightning strike are given. These equations are based on computer simulations for shields consisting of a single-layer steel grid of a given mesh width. Real constructions, however, contain at least two layers of reinforcement steel grids. The objective of this study was to experimentally determine the additional shielding effectiveness of a second reinforcement layer compared to a single-layer grid. To this end, simulated structures were set up in the high current laboratory. The structures consisted of cubic cages of 2 m side length with one or with two reinforcement grids, respectively. The structures were exposed to direct lightning currents representing the variety of anticipated lightning current waveforms. The magnetic fields and their derivatives at several positions inside the structure as well as the voltage between “floor” and “roof” in the center were determined for different current injection points. From these data the improvement of the shielding caused by a second reinforcement layer is derived.

A comparison of simple hierarchy and grid metaphors for option layouts on small-size screens

Modern, technologically driven society is characterized by an increase in the rate of mobile device use and an increase in the extent to which these devices are used for more complex tasks than search for phone numbers. While direct consequences of screen-size reduction on task performance are well known, data are lacking on the impact of layout of multiple options in a complex task environment. In this paper we describe the results of an end-user study in which we compared two basic interface designs for the layout of multiple options: a simple hierarchy and a single layer grid. These two designs were presented to users on two screen sizes; a larger size approximating the size of a standard laptop or desktop screen and a smaller size approximating the size of a PDA screen. This study illustrates that while task performance in accessing information was superior using the grid interface rather than the simple hierarchy interface, users preferred the simple hierarchy interface. Even as the complexity of the task increased, the physical size of the screen had a significantly bigger impact on task performance than did the task complexity. These findings indicate that the grid layout should be used when task performance is of the paramount concern and the complexity of choices is not expected to be large. When user preference/satisfaction is more important than task performance the appeal of the simple hierarchy layout may supersede the cost in performance it entails.

APPROXIMATE DISCRETE VARIABLE OPTIMIZATION OF FRAME STRUCTURES WITH DUAL METHODS

The purpose of this work is to present an efficient method for optimum design of frame structures, using approximation concepts. A dual strategy in which the design variables can be considered as discrete variables is used. A two-level approximation concept is used. In the first level, all the structural response quantities such as forces and displacements are approximated as functions of some intermediate variables. Then the second level approximation is employed to convert the first-level approximation problem into a series of problems of separable forms, which can be solved easily by dual methods with discrete variables. In the second-level approximation, the objective function and the approximate constraints are linearized. The objective of the first-level approximation is to reduce the number of structural analyses required in the optimization problem and the second level approximation reduces the computational cost of the optimization technique. A portal frame and a single layer grid are used as design examples to demonstrate the efficiency of the proposed method.

Description of a triangular ring-joint on the camden and amboy railroad

This paper discussed a new type of bolted joint named a double-ring joint used in freeform single-layer grid shells. Prototype static tests and numerical simulations were undertaken to investigate the mechanical behavior of the bolted joint subjected to the bending moment and shear force. The main conclusions of this study are as follows. There are two primary failure modes of double-ring joints. One is the fracture of the bolt, and the other is the instability of the central ring. The failure mode depends only on the ratio of the ring thickness to the ring diameter when the height of the ring and the diameter of the bolt match. Ultimately, the simplified formulae for the load-bearing capacity of a double-ring joint in different failure modes were proposed as a reference for joint design.