Single-layer Lattice Research Articles

Experimental investigation on energy absorption capability of 3D-printed lattice structures: Effect of strut orientation

This experimental study aimed to investigate the effect of strut orientation in various lattice structures that were created using 3D printers on the energy absorption capabilities of the structures. The experiment involved producing three different lattice structures, namely a cube lattice with vertical and horizontal struts, an octet structure with horizontal and 45˚ angled struts, and a body-centered-cubic (BCC) lattice structure with horizontal, vertical, and 45˚ angled struts using the FDM method. Nylon filament mixed with chopped carbon fiber was utilized as filament, and each lattice structure was designed to contain three units in the x and y directions and one and three units in the z-direction. The study conducted axial crushing tests on single-layer and three-layer lattices to determine the energy absorption capabilities of the various lattice structures. The octet lattice demonstrated the highest energy absorption in both single-layer and three-layer samples, making it the most efficient sample. In single-layer lattice samples, the cube and octet structures absorbed 77% and 94% more energy than the BCC structure, which absorbed only 12.8 J. However, the cube structure demonstrated the lowest energy absorption in three-layer samples. This was attributed to the buckling behavior seen in the strut of the lattice structure under axial load. The octet structure had the highest specific energy absorption value in both layers, making it the most energy-efficient sample.

Seismic vulnerability analysis of single-layer lattice shells with different rise-to-span ratios: Focusing on the selection of Sa(T1)-based intensity measures

This study conducted a detailed examination of seismic vulnerability across different limit states for Schwedler single-layer lattice shells with differing rise-to-span ratios. A comparative analysis of seismic intensity measures, particularly those centered around Sa(T1), was performed to evaluate their effectiveness in vulnerability analysis. To comprehensively address the inherent uncertainties in seismic actions, the study selected a dual set of ground motion scenarios, encompassing both far-field and pulse-type near-field events. A novel approach was employed, integrating a multi-indicator seismic performance assessment model based on the residual seismic safety framework, aiming to thoroughly quantify the cumulative seismic damage to lattice structures. Utilizing the multiple stripes analysis technique enabled the efficient generation of analytical results for vulnerability assessments at various damage thresholds. The findings revealed that lattice shells with larger rise-to-span ratios exhibit increased seismic robustness, notably with far-field seismic events causing more significant damage than their pulse-type near-field counterparts. Furthermore, the study determined that employing seismic intensity measures which consider the effects of higher modes significantly reduces variability in the vulnerability analysis when dealing with pulse-type near-field seismic activity. As a result, the use of the seismic intensity measure IM123 is recommended for assessing the vulnerability of lattice shells with varying rise-to-span ratios, under both far-field and near-field seismic conditions.

Static Stability Behavior-Based Seismic Damage Endurance Assessment of Long-Span Single-Layer Spherical Lattice Shells

ABSTRACT This paper presents a modified evaluation approach for the structural-capacity-reserve (SCR) based on the static stability behavior of single-layer spherical lattice shells to achieve more accurate assessment results of seismic damage endurance. The SCR index in this paper is calculated by integrating the redefined residual structural capacity (RSC) ratio based on post-earthquake static stability behavior within the range of damage degrees caused by strong earthquakes. Compared with the assessment work for seismic damage endurance in the existing literature, the proposed RSC ratio in this paper could take into account both ultimate load-bearing strength and residual deformation. Additionally, the specific quantitative indicator in the proposed assessment method should also be determined according to whether the residual nodal displacement of the lattice shell after an earthquake exceeds the limit value state specified by the design code. The numerical results in the case study indicate that the residual load-bearing strength of the lattice shell remains relatively constant under the same damage state induced by different earthquakes, with residual deformation significantly impacting the assessment of seismic damage endurance. Thereby, the required RSC can be controlled by reducing the residual nodal displacements of the lattice shell under strong earthquakes to achieve a well-balanced design scheme.

Numerical investigation of three-dimensional isolator and mitigation for single-layer lattice shell structure

Three-dimensional (3D) isolators need to have capabilities to support the dead weight of superstructures and mitigate both horizontal and vertical seismic responses of structures. However, the lack of self-centering capability under horizontal loadings and large stiffness under vertical loadings of the 3D isolators might limit their isolation performance in practical engineering. This study presents a novel 3D isolator (hereinafter referred to as DS-SMA-FS) to achieve self-centering capability under horizontal loadings and quasi-zero stiffness under vertical loadings. The self-centering capability is provided by shape memory alloys U-shaped dampers (SMA-UDs), and the quasi-zero stiffness (QZS) property is realized by the negative stiffness of disc spring (DS) isolator and positive stiffness of SMA-UDs. The working mechanism and analytical model of the DS-SMA-FS isolator were developed first. The finite element model of the DS-SMA-FS isolator was furtherly established. Numerical results revealed that DS-SMA-FS can exhibit SC capability under horizontal loadings and QZS property under vertical loadings. Subsequently, single-layer lattice shells were established to explore the isolation performance of the DS-SMA-FS isolator. Structural analysis results indicated that the DS-SMA-FS isolator can prolong the natural vibration periods of the shell and effectively prevent the shells from tri-directional earthquakes.

Equation of State and Thermometry of the 2D SU(N) Fermi-Hubbard Model.

We characterize the equation of state (EoS) of the SU(N>2) Fermi-Hubbard Model (FHM) in a two-dimensional single-layer square optical lattice. We probe the density and the site occupation probabilities as functions of interaction strength and temperature for N=3, 4, and 6. Our measurements are used as a benchmark for state-of-the-art numerical methods including determinantal quantum MonteCarlo and numerical linked cluster expansion. By probing the density fluctuations, we compare temperatures determined in a model-independent way by fitting measurements to numerically calculated EoS results, making this a particularly interesting new step in the exploration and characterization of the SU(N) FHM.

Magnetic behavior of a ferrimagnetic MXene-like lattice: Monte Carlo study

In this study, we performed extensive Monte Carlo simulations to comprehensively analyze the magnetic properties of a single-layer MXene-like lattice. Our investigation involved the exploration of transition temperatures and the behavior of hysteresis cycles, all influenced by a series of key physical parameters. Additionally, we carefully mapped the magnetization as a function of temperature and crystal field, introducing variations in the exchange coupling to unveil their impact on the transition temperature. Furthermore, we investigated the behavior of hysteresis loops, complexly dissecting their responses to changes in exchange coupling, temperature, and crystal field. Significantly, our results highlight the central role of the crystal field in the formation of magnetization plateaus, thus providing promising avenues for applications in nanotechnology and advanced memory storage systems.

Shaking table tests on seismic behaviors of a single-layer spherical lattice shell with shape memory alloy-controlled friction pendulum bearings

An innovative seismic isolation device incorporating a friction pendulum bearing (FPB) and vertically aligned shape memory alloy (SMA) strands is proposed for the seismic control of spherical lattice shells located in strong-earthquake regions. To validate the effectiveness of the proposed SMA-FPBs experimentally, a 1/10-scale single-layer spherical lattice shell test structure and a set of isolators were designed and fabricated. A shaking table was used to apply various three-dimensional seismic excitations to test structures equipped with and without different isolation bearings (SMA-FPBs or bare FPBs). Significant seismic behavior enhancements were observed when such isolation systems were used. However, bare FPBs cannot accommodate excessive displacements induced by high seismic intensities owing to their lack of adaptive control. In contrast, SMA-FPBs exhibited satisfactory control performance in terms of the peak and residual bearing displacements under fortification and rare seismic actions, and the adaptive properties of the SMA-FPBs protected the isolators from disassembly owing to excessive sliding displacements under extremely rare earthquakes, even though their re-centering abilities decreased slightly because of the failure of several SMA wires. Finally, the larger number of SMA wires in an SMA-FPB enhanced its restraining capacity against peak bearing displacement rather than improving the seismic responses of structural nodes and members.

Determining the defect type in a graphene lattice

We consider four common defects that appear in an infinite single-layer graphene lattice, i.e. single vacancy V 1 ( 5 − 9 ) , Stone-Wales SW ( 55 − 77 ) , and double vacancies V 2 ( 5 − 8 − 5 ) and V 2 ( 555 − 777 ) . Investigating the honeycomb pattern of the graphene, we make use of the concept of shortest closed paths (periodic orbits) in the underlying topological structure. Using properties of the shortest closed paths of odd length we present and prove mathematically an algorithm that classifies which one of these defects occurs.

Analysis and Design of Single-layer Lattice Aluminum Domes Using ANSYS Workbench

Analysis and Design of Single-layer Lattice Aluminum Domes Using ANSYS Workbench

Hybrid Lattice Boltzmann Approach for Simulation of High-Speed Flows

A lattice Boltzmann approach utilizing hybrid lattices for accurate simulation of high-speed transonic (TS) flows is presented in this study. Single-layer lattice models, such as D3Q19, are computationally efficient with low numerical dissipation, but are limited to simulate weakly compressible flows within subsonic Mach regime. Multilayer lattice models, such as D3Q33, are capable of simulating thermal and high-speed compressible flows in TS Mach regime, but suffer from a higher numerical dissipation and higher computational cost. To take full advantages of these two types of lattices, a simulation domain is divided into two regions, high-subsonic (HS) flow regions to be solved by single-layer lattices and TS flow regions to be solved by multilayer lattices. The interface connecting the HS and TS flow regions are represented by double-sided surfels to realize smooth flow transition and ensure satisfaction of fundamental conservation laws. The hybrid lattice Boltzmann approach is stable and robust, and it allows multiple HS/TS flow regions with arbitrary shapes. Extensive validation studies demonstrate that the proposed approach is capable of obtaining accurate aerodynamic prediction of flows with a wide range of Mach numbers, and preserving the low numerical dissipation advantage of single-layer lattices in aeroacoustic computations.

A state-of-the-art review of progressive collapse research and guidelines for single-layer lattice shell structures

The importance of progressive collapse analysis of structures has increased significantly due to various structural collapses. Single-layer lattice shell structures are susceptible to progressive collapse, as the failure or instability of a localised region can result in a global collapse due to their lightness and wide span. The geometry of these structures plays a crucial role in the load resistance, and any damage that alters the overall geometry can initiate different instabilities, which may also result in progressive collapse. Therefore, the possibility of progressive collapse is high among these lighter structural forms. However, research on the progressive collapse of single-layer lattice shell structures is limited compared to framed structures, highlighting the need for further investigation. Therefore, this manuscript aims to provide a comprehensive review of research conducted on the progressive collapse of single-layer lattice shell structures, focusing on experimental, numerical, and theoretical investigations. Earlier studies have explored the propagation of local instabilities leading to overall failure. More recent research has primarily focused on two approaches: (1) alternate path analysis, which examines the structure’s response after removing a member, and (2) substructure analysis, which aims to identify collapse-preventive mechanisms. Based on these analyses, various methods to enhance progressive collapse resistance have been discussed, including specific local resistance, alternate load paths, compartmentalisation, and tie forces. This review also highlights the limitations present in the current literature and suggests future research directions, which helps to develop design guidelines that can effectively increase the progressive collapse resistance of single-layer lattice shell structures, making them more reliable for various structural applications.

Measuring the Surface Area Concentration and Specific Surface Area of Mass-Produced Graphene Nanoflakes via Fluorescence Quenching

A primitive cubic lattice composed of 1,000 atoms has 488 surface sites. By definition, every atom in a strictly two-dimensional single-layer lattice composes its surface. These surface atoms are the ones that undergo chemical interactions with the surrounding medium, thereby defining the functionalities of the nanostructure. As such, one of the most important morphological properties of nano-objects is the extremely large specific surface area that enhances their levels of reactivity. Here, we introduce an optical spectroscopy method to measure the surface area concentration, ρA, of mass-produced graphene nanoflakes in liquid dispersions. The information is accessed from the quenching of the fluorescence signal from the dye molecules dispersed in the medium. We found that the quantum efficiency of the fluorescence signal decays exponentially with the concentration of graphene’s surface area, the decay rate being independent of the degree of exfoliation. If the mass concentration ρ is known by other means, the specific surface area can be extracted from the ratio ρA/ρ. The measurements can be performed directly in liquid suspensions of nanoflakes, being highly applicable to the quality control of mass-produced two-dimensional nanomaterials, especially by means of mechanically assisted liquid-phase exfoliation.

Seismic protection of a single-layer spherical lattice shell structure using a separated three-dimensional isolation system

Vertical and three-dimensional (3D) isolation systems are emerging control technologies for spatial grid structures in high seismic intensity regions. Recently, multistage vertical isolation bearings (MVIBs) based on prepressed spring devices (PSDs) have been proposed to support the lattice shell and prevent the transfer of vertical ground motion components to the structure. Seismic dampers can be further combined with an MVIB to develop a hybrid bearing with a damping capacity. In this study, the vertical load-carrying and isolation mechanisms underlying the MVIB configuration were investigated in detail. A series of proof-of-concept tests were conducted on a prototype MVIB comprising four identical PSDs to study its actual mechanical behavior. The test results indicated that the MVIB specimen exhibited multilinear elastic behavior with enhanced load resistance. The key parameters of the tested bearing, such as the transition force and isolation stiffness, increased linearly with the number of PSDs. The MVIB model was subsequently refined using ABAQUS to comprehensively understand the mechanical performance of the spring isolator. Following a device-level study, a single-layer spherical lattice shell was used as the research target. The damped MVIBs and friction pendulum bearings were arranged at the roof supports and column bases, respectively, and the stiffness and energy dissipation properties of these isolators were designed. A system-level seismic analysis was conducted using OpenSees to compare the triaxial dynamic responses of the target structure before and after isolation. The results indicated that the separated 3D isolation system achieved its intended design goals and effectively protected the lattice shell structure from tridirectional seismic shaking.

Computational study on subsonic impact resistance of lattice structures in 3D printed thin Ti6Al4V parts

Additive manufacturing (AM) is a set of digital manufacturing processes which is gaining momentum in the industries for its flexibility, versatility and ability to manufacture complex geometries with limited human interaction. It has enabled relatively fast materialization of a conceptualized design for testing, inspecting and examining the components. AM is highly suitable for fabricating functional gas turbine components owing to its low volume production requirements, lightweight components and geometrical complexity requirements. Laser powder bed fusion (LPBF), is the most common form of metal AM method used. The shape complexity attribute of LPBF can be taken advantage of to fabricate lattice-induced gas turbine inlet components prone to hail or bird impact. In this study, a computational approach was implemented to assess the behaviour of thin Ti6Al4V parts induced with a single-layer lattice subjected to projectile impact. Homogenization of lattice structures was carried out in nTopology to shortlist them for impact studies based on Young’s modulus distribution. The impact analysis was performed on eight lattice structures, two of which were derived from topology optimization, along with a solid plate and hollow plate acting as benchmarks for comparison. The high-velocity impact (250 m/s) was simulated using the “Explicit Dynamics” module in Ansys. It was observed that the lattice geometry directly below the impact site influenced the deformation, stress and energy values. It was concluded that lattices such as isotruss, kelvin cell and FCC, which have more struts interfacing with the impact region, tend to show deformation comparable to solid plates (4.89E-04 m). The equivalent stress values were within the material's elastic limit, indicating elastic deformation. The reduction in kinetic energy of the projectile for lattice-induced plates was also comparable with the values for solid plates (68 %). A correlation coefficient of −0.807 was obtained between packing factor and minimum kinetic energy, indicating denser lattices resulted in higher deceleration.

Enhancement of seismic damage endurance of large-span lattice shells with replaceable fuse-type components

Most large-span public buildings in highly seismic regions are supposed to play the role of post-earthquake emergency relief centers or shelters, in addition to their original functions. As one type of commonly-used structural systems in those buildings, large-span lattice shells are required to retain some post-earthquake seismic damage endurance. To reach this goal, a new replaceable bi-functional stiffness-damping component with the use of low-yield point (LYP) steel element is developed. To determine the placement of fuse-type components in lattice shells rationally, the plastic limit theory of equivalent continuum shell is employed for the classification of primary-secondary structural systems. The proper proportion of fuse-type components and their connection constraints with primary structural system is further clarified by an accompanied parametric study. The assessment on seismic damage endurance and reserve strength of lattice shells with fuse-type components is finalized with the residual seismic capacity ratio and seismic damage model proposed previously. The effectiveness of the proposed seismic damage endurance enhancement strategy for lattice shells with the use of replaceable fuse-type components is fully demonstrated on a case study on a 121.5m-span single-layer Kiewitt lattice shell. In this study, the effects of layout of fuse-type components, V/H ratio and spectral characteristics of ground motion, LYP yield strength, normalized length of ‘fuse’ elements are identified from the aspects of ultimate earthquake resistance, the maximum nodal displacement, seismic damage development, residual seismic capacity and reserve strength. • A seismic damage endurance enhancement strategy for lattice shells is proposed. • A new replaceable fuse-type component using low-yield point steel is developed. • Fuse-type components are replaced using the equivalent continuum shell theory. • Four performance regions are divided by relation between RSC and reserve strength.

Effect of support settlement on ultimate bearing capacity of Zhoukoudian steel structure

In order to study the effect of non-uniform support settlement on global stability ultimate bearing capacity of lattice shell structure, combining with the project of first site protective building in Zhoukoudian Ruins, the finite element software ANSYS is employed to conduct geometric nonlinear and double nonlinear global stability analysis of the single-layer lattice shell respectively based on consistent mode imperfection method and advanced consistent mode imperfection method, thus the global stability ultimate bearing capacity under different settlement cases is obtained and compared. Analysis results show that non-uniform support settlement is beneficial to increase the elastic global stability ultimate bearing capacity of the structure by a small margin, but excessive settlement may have adverse effects on the bearing capacity of the structures with initial imperfections. When considering material nonlinearity, small non-uniform support settlement is conducive to a slight increase in the elastoplastic global stability ultimate bearing capacity of the structure that decreases and is lower than that without settlement with the increase of non-uniform settlement. In addition, non-uniform support settlement will not affect the instability path of the lattice shell.

Wind-induced instability analysis of large-span single-layer lattice domes

This paper addresses the instability behaviour of single-layer lattice domes with a long span subjected to wind action. Two structural configurations with a span of 120 m and a rise-to-span ratio of 1:3 and 1:6 are analysed to compare critical dynamic loads to critical static loads. The Budiansky–Roth and phase-plane criteria are employed for estimating dynamic critical conditions. Wind fluctuation (Cpf) is simulated as a function of the average pressure coefficient (C¯p) over time, and the imperfections are set by means of the so-called “Conformable Imperfection Method”. The parameters considered in this research include the wind fluctuation, fluctuation period, geometric imperfection, and strengthening the members. It is found that the critical wind velocity reduces as the wind fluctuation increases. Furthermore, as the fluctuation period Tf increases, the difference between the static and the dynamic critical loads decreases. The use of Cpf=0.3C¯p and Tf/T1=1.0 (T1 being the fundamental period) produced the lowest amount of critical velocities of 50 and 43 m/s for D1:3 and D1:6 configurations, respectively. The corresponding critical dynamic loads were 29.27 and 15.15 kN giving the dynamic load ratio of 193%, the dynamic to static critical load ratios being 0.67 and 0.68 for these configurations. The D1:3 and D1:6 domes exhibited imperfection sensitivity by as much as about 17 and 82% load reduction, respectively, for an imperfection amplitude of Span/350. Strengthening the critical members of the D1:6 dome subjected to the wind action had the advantage of increasing the static instability load and the dynamic critical load bearing capacity by 20 and 30%, respectively. For estimating the equivalent static wind load, a reduction factor of 0.50 defined as the ratio of dynamic to static load was proposed.

Unidirectional absorption, storage, and emission of single photons in a collectively responding bilayer atomic array

Two-dimensional regular arrays of atoms are a promising platform for quantum networks, with collective subradiant states providing long-lived storage and collimated emission allowing for natural coherent links between arrays in free space. However, a single-layer lattice can only efficiently absorb or emit light symmetrically in the forward and backward directions. Here we show how a bilayer lattice can absorb a single photon either incident from a single direction or an arbitrary superposition of forward and backward propagating components. The excitation can be stored in a subradiant state, transferred coherently between different subradiant states, and released, again in an arbitrary combination of highly collimated forward and backward propagating components. We explain the directionality of single and bilayer arrays by a symmetry analysis based on the scattering parities of different multipole radiation components of collective excitations. The collective modes may exhibit the conventional half-wave loss of fields near the array interface or completely eliminate it. The proposed directional control of absorption and emission paves the way for effective one-dimensional quantum communication between multiple arrays, with single-photons propagating backward and forward between quantum information-processing and storage stages.

Feasibility evaluation of pre-pressed spring devices for vertical isolation of single-layer spherical lattice shell structures

Single-layer spherical lattice shells are typical spatial structures for large-scale landmarks and public buildings. If such buildings are located in strong-earthquake zones, their seismic resilience must be considered. Long-span spatial structures are highly sensitive to multi-component ground motions, and vertical ground shakings lead to strong structural vibrations. Although a few vertical isolators with invariant stiffness have been developed, they are generally too stiff to effectively isolate vertical seismic shakings. In this paper, a nonlinear vertical isolator using pre-pressed and restrained helical springs called pre-pressed spring device (PSD) is proposed. The main advantages of the PSD are that it not only provides a high first stiffness and large bearing force to support the weight of the isolated object but also possesses sufficiently low stiffness to isolate vertical ground motions. In a vertical isolation system, PSDs are employed as basic load-carrying elements, and viscous dampers can be introduced into the system to function as additional energy dissipation devices. The configuration, working principle, and mechanical model of the newly developed PSD are described and explained in detail. Cyclic loading experiments were performed on a prototype PSD to investigate its actual force–displacement relationship. The experimental results showed that the PSD specimen exhibited multilinear elastic behaviors with clear first and isolation stiffness properties. A novel numerical model of the PSD was constructed, and the accuracy of the model was validated by comparing the simulation and experimental results. Subsequently, PSD-damper assemblies and friction pendulum bearings (FPBs) were used to form three-dimensional (3D) isolation bearings for a single-layer spherical lattice shell with surrounding columns. The seismic responses of the controlled structure were evaluated using nonlinear time-history analysis. The numerical results revealed that the PSDs achieved effective static-load support and vertical isolation, and that the entire 3D isolation bearings significantly improved the seismic behavior of the lattice shell structures in all three directions.

Seismic Performance Assessment of a Single-Layer Spherical Lattice Shell Structure with Multifunctional Friction Pendulum Bearings

The dynamic responses of spatial lattice shell structures with friction pendulum bearings (FPBs) under multidimensional seismic excitations are complex. In addition, FPBs may experience uplift and separation of the bearing components owing to excessive displacements. In this study, a novel multifunctional FPB (MFPB) with a multi-defense system was developed, and its effectiveness in reducing and controlling the seismic responses of spherical lattice shell structures was evaluated. The proposed MFPB comprises an FPB, superelastic shape-memory alloy cables, and sleeve restrainers. A mechanical model of the MFPB was established, and its isolation and control behaviors were investigated through numerical simulations. Furthermore, the main characteristics and advantages of the isolation system were analyzed. Subsequently, the MFPB system was applied to a single-layer spherical lattice shell structure with surrounding columns. A computational model of the controlled structure was developed using the OpenSees software. Finally, nonlinear time history analyzes were conducted to analyze the seismic performance of controlled and uncontrolled lattice shells. The results demonstrate that the MFPB isolation system can effectively control the structural responses of isolated spatial lattice shell structures under horizontal and vertical seismic excitations and improve their seismic resilience.