Double-layer Grids Research Articles

Optimal design of spatial structures by a novel meta-heuristic algorithm: Sound energy optimizer

Sound signals are used by various species of living creaters to commonicate with each other. Scientific experiments have demonstrated that sound energy can travel through media and cause the receiver objects to vibrate or move. The present work simulates such a phenomenon in development of a new meta-heuristic algorithm called: Sound Energy Optimizer (SEO). Concerning physical rules, SEO leverages natural or ambient sounds for optimization. SEO utilizes a tunable virtual machine to control the decaying pattern of the sound energy in a medium representing the search space. Performance of the proposed algorithm is first evaluated on unconstrained optimization of some mathematical test functions. Then, a variety of pin-jointed structural problems are optimized including space tower, double-layer grid, barrel vault, helipad structure and power transmission towers. In this set, performance evaluation is done not only against the previous works but also by running SEO versus eight recent meta-heuristics under fair comparison conditions. New quantitative indices are introduced and traced as well as the common statistical measures and convergence curves. The results demonstrate competitive performance of SEO versus recent meta-heuristics in the discrete and continuous design of spatial structures.

Comparative Study of Optimal Flat Double-Layer Space Structures with Diverse Geometries through Genetic Algorithm

This paper investigates the structural performance of flat double-layer grids with various constitutive units, addressing a notable gap in the literature on diverse geometries. Six common types of flat double-layer grids are selected to provide a comprehensive comparison to understand their structural performance. Parametric models are built using Rhino and Grasshopper plugins. Single- and multi-objective optimization processes are conducted on the considered models to evaluate structural mass and maximum deflection. The number of constitutive units, the structural depth, and the cross-section diameter of the members are selected as design variables. The analysis reveals that the semi-octahedron upon square-grid configuration excels in minimizing structural mass and deflection. Furthermore, models lacking a full pyramid form exhibit higher deflections. Sensitivity analyses disclose the critical influence of the design variables, particularly highlighting the sensitivity of structural mass to the number of constitutive units and cross-section diameter. These findings offer valuable insights and practical design considerations for optimizing double-layer grid space structures.

Sensitivity of optimal double-layer grid designs to geometrical imperfections and geometric nonlinearity conditions in the analysis phase

Sensitivity of optimal double-layer grid designs to geometrical imperfections and geometric nonlinearity conditions in the analysis phase

Geometric Design Methodology for Deployable Self-Locking Semicylindrical Structures

Due to their unique bistable characteristics, deployable self-locking structures are suitable for many engineering fields. Without changing the geometrical composition, such structures can be unfolded and locked solely by the elastic deformation of materials. However, their further applications are hampered by the lack of simple and systematic geometric design methodologies that consider arbitrary structural curvature profiles. This paper proposes such a methodology for double-layer semicylindrical grid structures to simplify their cumbersome geometric design. The proposed methodology takes joint sizes into account to ensure that the design results can be applied to actual projects without further adjustments. By introducing symmetry into the structural units (SUs) and selecting reasonable geometric parameters that describe the structural side elevation profile, a concise set of simultaneous nonlinear geometric constraint equations is established, the solution of which provides the geometric parameter values of the grid shape. On this basis, the remaining geometric parameter values, i.e., the geometric parameter values of the inner scissor-like elements (SLEs) of each SU, can be achieved from the equations derived from general SLEs. Design examples and the assembled physical grid structure indicate the feasibility and wide applicability of the proposed geometric design methodology.

Realization of planar and surface conformal mappings through stress-free growth of hyperelastic plates: Analytical formulas and numerical calculations

Conformal mapping is a well-known concept and has a long research history in mathematics. Accompanying the developments of computational science and 3D digital scanning technology, conformal mapping has also found wide applications in geometric modeling, computer graphics, medical imaging and other fields. In the virtual image or animation world, conformal mapping offers a convenient approach to achieve various shape changes of planar regions and 3D surfaces. In this work, we propose a promising approach, i.e., through the stress-free growth of hyperelastic plates, to realize arbitrary planar and surface conformal mappings in the physical world. The growth field in a hyperelastic plate can be represented by a symmetric tensor field. For any given planar or surface conformal mappings with explicit analytical expressions, the formulas of growth functions in the growth tensor are derived. In the case that the target surfaces of conformal mappings have no explicit analytical expressions, we further propose a numerical scheme to determine the growth data in the hyperelastic plates. The efficiency of the approach proposed in the current work is validated through several typical examples, where the 3D finite element simulations are conducted. The results demonstrate that, by incorporating the obtained growth functions or growth data, the target surfaces can be generated accurately through growth deformations of hyperelastic plates. As an application of the current work, we further propose an approach of shape-control for double-layer grid structures with plate forms. According to any given target shapes, the values of elongation or contraction of the bar elements are determined, then the desired deformations of the grid structures can be realized.

Particle agglomeration via resonant acoustic mixer for dry powder inhalation

The work presented in this paper employed a resonant acoustic mixing (RAM) process to optimize the fine particle agglomeration process for dry powder inhalation to achieve efficient pulmonary delivery of melatonin. The formulation prepared by acoustic mixing with the double layer grids demonstrated superior agglomerate particle size distribution and approximately 90% of the metered dose in the dosing chamber was emitted from Turbuhaler® (90% emitted dose). Acceleration force during acoustic mixing significantly affected the packing fraction of mixtures and mechanical strength of agglomerates resulting in improved fine particle fraction. The particle agglomeration via RAM can improve the efficiency of agglomerate production by utilizing the internal space of the mixer to induce more particle collision. The agglomerates formulation exhibited ideal fine particle fraction of 47.65 ± 1.46% and 56.02 ± 2.55% at flow rates of 30 and 60 L/min, respectively. The fine particle deposition was only slightly affected at the lower air-flow rate, suggesting a reliable inhalation performance in vivo.

Parametric topology optimization design and analysis of additively manufactured joints in spatial grid structures

This paper presents a complete computer-aided workflow for the parametric topology optimization (TO) design, numerical analysis and additive manufacturing (AM) of steel joints in spatial grid structures. A fully parametric TO design framework for steel joints in spatial grid structure was developed based on the Grasshopper platform. The joint models were parametrically established based on subdivision surface technology and further topology optimized through the bi-directional evolutionary structural optimization (BESO) algorithm with the support of cloud computing server. The structural performance of the optimized joints was thoroughly investigated via the parametric finite element analysis. Variables of loading conditions and TO parameters (target volume and filter radius) that affect the compliance, maximum displacement, maximum stress and stress distribution were taken into account. Analysis showed that the target volume governed the joint structural behaviour while the filter radius affected the geometric details of optimized joint. The practicability of proposed workflow was demonstrated through a parametric optimization design framework of a double-layer spatial grid structure with hundreds of steel joints. A typical optimized joint made of 316L stainless steel was additively manufactured using selective laser melting. This workflow is highly automatic and featured by high design flexibility and integration degree as well as good transplanted ability.

Intrinsic Properties of Composite Double Layer Grid Superstructures

This paper examined the opportunities of composite double-layer grid superstructures in short-to-medium span bridge decks. It was empirically shown here that a double-layer grid deck system in composite action with a thin layer of two−way reinforced concrete slab introduced several structural advantages over the conventional composite plate-girder superstructure system. These advantages included improved seismic performance, increased structural rigidity, reduced deck vibration, increased failure capacity, and so on. Optimally proportioned space grid superstructures were found to be less prone to progressive collapse, increasing structural reliability and resilience, while reducing the risk of sudden failure. Through a set of dynamic time-series experiments, considerable enhancement in load transfer efficiency in the transverse direction under dynamic truck loading was gained. Furthermore, the multi-objective generative optimization of the proposed spatial grid bridge (with integral variable depth) using evolutionary optimization methods was examined. Finally, comprehensive discussions were given on: (i) mechanical properties, such as fatigue behavior, corrosion, durability, and behavior in cold environments; (ii) health monitoring aspects, such as ease of inspection, maintenance, and access for the installation of remote monitoring devices; (iii) sustainability considerations, such as reduction of embodied Carbon and energy due to reduced material waste, along with ease of demolition, deconstruction and reuse after lifecycle design; and (iv) lean management aspects, such as support for industrialized construction and mass customization. It was concluded that the proposed spatial grid system shows promise for building essential and sustainable infrastructures of the future.

Seismic Performance Analysis of the Two-Dimensional Isolation Device for Double-Layer Grid Structure

The isolation technologies are adopted to protect the long-span space structures from serious damage under the action of earthquakes. When the isolation system is applied to the space structures, both horizontal and vertical vibration control effects on the structures should be concerned. In this paper, a two-dimensional earthquake isolation and mitigation device (TEIMD) composed of a high-damping viscoelastic (VE) core pad and VE dampers is proposed. Based on the dynamic shear experiment results of the VE damper, the energy dissipation capability of VE material is preferable. Then, the nonlinear equivalent stiffness and equivalent damping ratio of the TEIMD in horizontal and vertical directions are evaluated by using the numerical simulation method. The TEIMDs are arranged on the column top of a double-layer grid structure to assess the isolation effectiveness of the novel device. The dynamic analysis results of the double-layer grid structure with and without TEIMD reveal that this novel device can significantly reduce the acceleration response of the upper grid by relying on the strong energy dissipation performances in the horizontal and vertical directions. This research also verifies the feasibility of applying the TEIMD to the double-layer grid structure, which can effectively dissipate the vertical vibration energy of the structure.

Battery Safety Risk Assessment in Real-World Electric Vehicles Based on Abnormal Internal Resistance Using Proposed Robust Estimation Method and Hybrid Neural Networks

Battery safety issue is developing as one of the main hinders restricting the further application of real-world electric vehicles (EVs). Internal resistance (IR) is one of the important parameters to reflect battery safety, because bigger abnormal IR will cause more heat generation and make the battery easier to cross the critical condition of thermal runway. Safety risk assessment based on abnormal IR can locate this kind unsafe batteries and ensure the safe operation of EVs. Existing studies mostly focus on IR estimation in laboratory, yet is insufficient in real-world abnormal IR detection, which is influenced by random conditions and coupled factors. To cope with this issue, a method is proposed to detect unsafe battery, thereby predicting the thermal runaway. The method can be divided into three parts, i.e., IR estimation, normal IR prediction, and IR evolution law construction and safety risk assessment. First, we analyze the problems of battery IR estimation in real-world scenarios, and propose a robust method to estimate the IR only based on sparse voltage and current. Second, a novel hybrid neural network model is designed and trained to predict normal IRs inputted by temperature, mileage, and state-of-charge. The model combines the advantages of different neural network structures to improve the performance. A double-layer grid searching method is proposed to optimize hyperparameters of the hybrid neural network, aiming to achieve the best accuracy under constructed neural network structure. Finally, the safety boundary indicated by IR is formed by statistic method and the IR evolution law is constructed, then a strategy is proposed to make residual evaluation for safety risk assessment. All the proposed methods are driven by EV historical data to reflect real-world conditions. The results showcase that the method is effective in the cloud for the small IR prediction error with the mean-square-error, mean-relative-error, and max error of 2.45*e-4, 1.78%, and 0.15. In addition, the method can periodically classify the unsafe and normal batteries with 98.6% accuracy for the EVs with the same specification.

A Dynamic Grid Index for CkNN Queries on Large-Scale Road Networks with Moving Objects

As the Internet of Things devices are deployed on a large scale, location-based services are being increasingly utilized. Among these services, kNN (k-nearest neighbor) queries based on road network constraints have gained importance. This study focuses on the CkNN (continuous k-nearest neighbor) queries for non-uniformly distributed moving objects with large-scale dynamic road network constraints, where CkNN objects are continuously and periodically queried based on their motion evolution. The present CkNN high-concurrency query under the constraints of a super-large road network faces problems, such as high computational cost and low query efficiency. The aim of this study is to ensure high concurrency nearest neighbor query requests while shortening the query response time and reducing global computation costs. To address this issue, we propose the DVTG-Index (Dynamic V-Tree Double-Layer Grid Index), which intelligently adjusts the index granularity by continuously merging and splitting subgraphs as the objects move, thereby filtering unnecessary vertices. Based on DVTG-Index, we further propose the DVTG-CkNN algorithm to calculate the initial kNN query and utilize the existing results to speed up the CkNN query. Finally, extensive experiments on real road networks confirm the superior performance of our proposed method, which has significant practical applications in large-scale dynamic road network constraints with non-uniformly distributed moving objects.

A Transparent Tunable Broadband Microwave Absorber Based on Multi-layer Structure by Patterned Graphene

As the increasingly complicated electromagnetic environment, it is crucial to develop the performance of transparent microwave absorbers. Here we proposed a transparent tunable broadband microwave absorber, which is consisted of double-layer graphene rings and metallic grids. The microwave shielding properties can be changed by adjusting the dielectric layer thickness, graphene Fermi energy and relaxation time. Based on the simulated results, the proposed transparent microwave absorber can achieve microwave absorption of over 85% at a frequency range of 4.61–9.75 GHz, indicating a relative absorption bandwidth nearly 71.6% and a normalized transmittance of 88.8% in the visible band.

Nonlinear technique of prestressing spatial structures

One of the crucial aspects of the design of structural space systems is the degree of prestressing since it is involved in the load transferring, deformability and charges. The prestress state can be reached via required member alteration. This paper presents an efficient nonlinear numerical approach based on the force method for prestressing the spatial nonlinear structures to the desired level through computing nonlinear actuation as a function of external nodal displacements. Two equations are derived for indicating the required amount of member alteration eo and prestressing level by using Taylor's series and Pade approximation methods. This technique can be applied to both rigid and flexible spatial structures. The present technique is validated based on three numerical examples, and the computational findings are in well agreement with the compared methods. The results show that the new approach requires less effort and makes greater economic sense. Moreover, the member forces with concern to nonlinear eo of double-layer space grid structure by imposing lack of fit of some members successfully obtained.

A Framework for Optimization of Double Layer Grids with Supporting Cables

Space structures are used when it is required to cover a large unpaved area such as sports stadiums, aircraft factories, bridges, etc. Weight minimization is important in optimizing space structures, having various advantages such as cost reduction, reduction of the deterioration, increasing the possibility of using larger spans, and easy transportation and installation process. The use of meta-heuristic algorithms, inspired by the physics laws of nature, allows us to optimize a variety of complex problems. In this paper, four structures with different spans with and without cables are examined. Optimization is performed using Enhanced Colliding Bodies Optimization (ECBO) and Vibrating Particles System (VPS) optimization algorithms. The optimization is aimed to minimize the weight and the mid-span deflection of the structures. The utilized methods are based on the optimization algorithms in MATLAB (MATrix LABoratory) programming and the SAP2000 (Structural Analysis Program 2000) finite element software. In this way, the results, obtained from the structural analysis in finite element software, are utilized by the optimization algorithms and the operation is repeated until the optimal weight is achieved. In all the investigated examples, the ECBO performed better than the VPS algorithm. The findings indicate that the addition of the cables, in addition of reducing the weight of the structures can reduce the mid-span deflection.

Finite element analysis of the mechanical behavior of a bi-hexagon grid structure

The space grid structure is widely used in large-span and large-scale buildings due to its excellent stiffness and lightweight. However, the joint connection is complicated since many struts emanate from one joint. In this paper, we proposed a novel joint connection with five struts and a space grid structure called the bi-hexagon grid structure (BHGS). The mechanical behavior of the proposed grids was investigated by comparing different double-layer and multi-layer grids by virtue of the Ansys parameter design language. The results show that the proposed structure can significantly reduce material consumption and improve installation efficiency. The comparison results also show the BHGS has a good stress distribution under uniform surface loads. However, the deformation is slightly large, which is acceptable considering the practical application. A configuration method and mechanical behaviors of a double-layer dome based on the bi-hexagon grid structure were presented as a particular application as well as the structural optimization. In addition, an assembly strategy was further given to realize the modular design.

A Numerical Investigation of the Structural Performance of Double-layered Grid Domes Using Software Packages

In the 21th-century, large exhibitions halls covered by domes were constructed. Development of domes promoted by using metal structures, which has opened a new era for civil engineers in connection with the decision of maintenance problems of high strength and weight reduction of structures. Grid domes are a preferred structural form of roofs coverage. The paper aims to study the structural performance of double-layered grid domes using SAP2000 (v.14) and ETABS18. Four different types of double-layered grid domes considered in this work were the Schwedler dome (Type 1), three-way grid dome (Type 2), grid dome with different layers (Type 3), and grid dome with hexagonal patterns (Type 4). The configurations of grid domes were generated by Formian program software. The static linear analysis and design of mentioned grid domes were done and different load cases and their combinations were applied according to ASCE 7-10. It was observed that a double-layered grid dome with different layers (Type 3) was the most efficient in structural performance because the density of members per joint gave a very good distribution of axial forces distribution of the whole dome and then minimized the axial force in members and vertical deflections. The present study indicates that further detailed studies of the subject may lead to a more precise understanding of the performance of grid domes subjected to different load cases and this may bring about increased structural safety and serviceability and the economy in cost constructions.

A New Model for Analysis of the Shielding Effectiveness of Multilayer Infinite Metal Meshes in a Wide Frequency Range

A new analytical model for the calculation of the shielding effectiveness of multilayer infinite metal meshes is proposed. This model is based on the previously developed one for single- and double-layer metal shielding grids. It enables accurate and fast calculations of the shielding effectiveness of multilayer metal meshes with different air interlayers in a wide frequency range. The proposed model considers the ratio of the wire diameter to the aperture size and the layer interspacing. The model is validated by comparison of the results of calculations with the HFSS simulation results. The model validity in a wide frequency range as well as its calculation speed far bigger than that for HFSS is demonstrated. The results of calculations show that the shielding effectiveness of metal meshes can be effectively improved by increasing the distance between the mesh layers and the ratio of the wire diameter to the aperture size.

Optimization of continuous drive friction welding process for AA6061-T6 circular pipe and conical head

Aluminum alloy double-layer grid structure with bolt-ball joint has the advantages of light weight, corrosion resistance, convenient construction, etc. However, when circular pipe and conical head are connected by fusion welding, its strength is low. In order to solve this problem, the continuous drive friction welding (CDFW) process of aluminum alloy circular pipe and conical head and its strength of joint were studied in this paper. Based on the orthogonal experiment scheme, the CDFW experiments were conducted on AA6061-T6 circular pipe, then the tensile tests were completed on the standard samples to obtain joint efficiency under different welding parameters. The optimum welding parameters were determined by the method of variance and range analysis. The microstructure of joints was characterized by hardness test, OM, XRD, SEM, etc. The test results show that parameters affecting joint efficiency are friction pressure, rotational speed and upsetting rotational speed in descending order. Under the optimal welding process, the joint efficiency can reach 87.0%, which is superior to fusion welding. The fracture form of the welded joint is a mixture of intergranular and ductile transgranular fracture. WNZ is the crucial region of the welded joint, where the grain growth is greatly influenced by friction pressure. The friction pressure of the optimal welded joint is moderate, so the grains in WNZ are fine and grow adequately. The hardness softening of the welded joint also has certain influence on its mechanical properties. The solid solubility of the optimal welding sample is high and alloy elements are stable in the Al matrix, so it exhibits good mechanical properties. Finally, the CDFW experiments and tensile tests of circular pipe and conical head were conducted, which verifies the effectiveness of the optimal welding parameters.

Enhanced algorithm of streamline color mapping based on double-layer grid control

2D Flow field streamline visualization, as a classic visualization method, expresses the structure and characteristics of the flow field with continuous streamlines. In this paper, a streamline color mapping enhancement algorithm based on double-layer grid control is proposed, which can better display the flow field and its field intensity distribution. The distance of the streamline is controlled by the double-layer grid, the seed point is scattered in the largest blank seeding area, and the visual streamline diagram of different effects can be obtained by setting the density control parameters, vector illustration with more even color distribution. The results show that the algorithm in this paper can obtain more continuous streamline distribution, and the streamline distribution obtained by regional equalization color mapping can reflect more field intensity distribution characteristics of the flow field.

Damage Detection in Double Layer Grids with Modal Strain Energy Method and Dempster-Shafer Theory

Change in modal strain energy is one of the indicators used to detect damage in structures. However, in structures with high degrees of freedom, such as double-layer grids, this method requires a relatively large number of mode shapes which in practice is difficult to determine. Therefore, it is necessary to reduce the number of required mode shapes. In this study, a damage detection technique based on modal strain energy and Dempster-Shafer evidence theory is presented for locating damage in double layer grids using only a few number of mode shapes. First, by calculating mode shapes of the grid in undamaged and damaged states, the modal strain energy based index for each mode shape is determined. Then, the results obtained from separate mode shapes are combined using Dempster-Shafer theory to achieve better results. In order to investigate the effect of noise on damage detection, 3% random noise is added to mode shapes. To demonstrate the performance of the proposed method, different single and multiple damage cases with different damage intensities are considered. Numerical results show that using 5 mode shapes, the presented technique can detect up to 3 damaged elements with different damage intensities in different parts of the grid with good accuracy (probability of 92.3%). Considering the fact that the classical modal strain energy method fails to distinguish even 1 damaged element in the double layer grid, the result shows significant improvement.