Space Lattice Structures Research Articles

Experimental and numerical investigation on the impact response of bolt-ball joints

The densely populated space lattice structure requires reliable performance under impact loads. The bolt-ball joint serves a crucial role in connecting members at various angles, significantly contributing to the overall safety of the structure. However, there is limited literature available on the impact resistance of the bolt-ball joint. In this study, the drop hammer impact test system was employed to conduct impact tests on 11 specimens of bolt-ball joints. Comprehensive records were maintained, including the final deformation states, video recordings of the impact process, and data on impact force, displacement, and strain. Additionally, numerical simulation analysis was conducted to expand the scope of the study. Five failure modes were observed: global bending deformation, bolt fracture, local denting, coupling deformation of local denting and global bending deformation, bolt and tube fracture. When the impact applied at the bolt ball or conical head and steel tube welding positions, the impact process was categorized into three stages: inertia, global bending deformation, and elastic recovery/bolt fracture. When the impact position was the steel tube, coupling deformation and elastic recovery/ bolt and tube fracture were observed. The energy absorption during the impact test was analyzed, revealing a positive correlation between the degree of specimen failure and the proportion of energy absorbed relative to the work done by the impact force. The effects of impact velocity, impact position, bolt dimension and impact angle on the dynamic response of the specimens were thoroughly analyzed.

Design of Large-Scale Space Lattice Structure with Near-Zero Thermal Expansion Metamaterials

Thermal expansion is inevitable for space structures under the alternating temperature of outer space around the earth. This may lead to the thermal stress and deformation due to the mismatch of the coefficient of thermal expansion. Near-zero thermal expansion (Near-ZTE) is a vitally essential demand for large-scale space telescopes or antennas to preserve their spatial precision and resolution. Recently, mechanical metamaterials with superior and tailorable properties have attracted significant interest with regard to developing negative materials or ultra-property materials. In this paper, the near-ZTE space structure architected by a dual-hourglass bi-material lattice is achieved by the structural optimization method with the gradient-based algorithm. First, an hourglass lattice with adjustable structural parameters is optimized to seek the design of effective negative thermal expansion (NTE) in the thickness direction. Then, two building blocks with both NTE and legacy positive thermal expansion (PTE) are combined as a dual-layered lattice to obtain the near-ZTE. Finally, a structure with near-ZTE of about ~10−9 m/(m·K) is obtained. Furthermore, the various lattice configurations, such as the hexagonal pyramid and triangle pyramid, are investigated in detail. Finally, the natural frequencies of two near-ZTE lattices are calculated by the modal analysis method, and the stiffness is discussed for the optimal solution of space applications. This work demonstrates that the near-ZTE structure can be achieved by utilizing the negative metamaterial and structural optimization method. It provides a novel solution to design the large-scale space structures with the near-zero thermal induced deformation, and may be constructed and assembled by the on-orbit fabrication technology.

Optimized orientation of jointing system in free-form lattice space structures

The recent decades have witnessed the development of a new generation of space structures called free-form space structures. In this new family of space structures, due to the geometric nature of the structure, the orientation of the members varies substantially within the joints, meaning that the members need to be connected to the joints at different angles. The wide distribution of these angles throughout the structure will significantly affect the cost of fabrication. Therefore, accurate and automatic calculation of connection angles and their optimizations have always been of interest to researchers and manufacturers. This article has the following two main objectives. The first objective is to provide geometric calculations and obtain the connection angles of single-layer lattice space structures. The second, and more important objective is to review the existing methods and to develop a geometrical method for their optimization, referred to as the “node orientation optimization” method throughout this article. Using the mentioned method, a series of optimizations are carried out in a number of free-form lattice space structures and the results are studied.

Influence of random pitting corrosion on moment capacity of thin-walled circular tubes subjected to compression force

Thin-walled circular tubes have been widely used in space lattice structures and other industrial areas. Steel tubes are prone to corrosion during their service life, significantly reducing their loading capacity and threatening the structural safety. This work aimed to investigate the residual moment capacity of corroded circular steel tubes (CSTs) subjected to compression force. The second-order effect of steel tubes was studied based on CSTs with outer diameter D = 100 mm. The effects of corrosion thickness, diameter of corrosion pit, and material strength on the residual moment capacity of CSTs were also investigated. The analytical formula with a second-order polynomial form was proposed for predicting the residual moment capacity of CSTs. The values of tc/t were assumed to be 0.1, 0.3, 0.5, and 0.7, and the values of F/Fu were set to 0, 0.5, and 0.7 to reveal the influence of corroded thickness with different axial compression ratios. The applicability of the proposed formula for CST with yield strength equal to 235, 345, and 460 MPa was also confirmed. According to the findings, the proposed analytical formula can accurately predict the residual moment capacity of CSTs with random pitting corrosion.

Influence of random pit corrosion on axial stiffness of thin-walled circular tubes

Thin-walled circular tubes have been widely used in space lattice structures and other industrial areas. Corrosion is inevitable for steel tubes in terms of service life, and it will considerably reduce the axial stiffness and change the mechanical behavior of the entire structure. The present work aims to investigate the axial stiffness of corroded circular steel tubes (CSTs) subjected to compression force. Initial and elastoplastic stiffness values were investigated, and an analytical formula was proposed. The influence of corrosion thickness tc and material strength fy on the residual moment capacity of CSTs was also investigated. The proposed analytical formula can accurately predict the axial stiffness of CSTs with random pitting corrosion.

Mechanical performance of welded hollow spherical joints with H-beams after elevated temperatures

Welded hollow spherical joints with H-beam (H-WHSJ), as a new connection pattern in space lattice structures, have been applied in practical engineering. This study aims to investigate the residual mechanical properties of H-WHSJ after loading in elevated-temperature environments and provide an important basis to evaluate the performance of space lattice structures after the occurrence of fire. The effects of temperature history, plastic residual deformation, sizes of WHSJ and H-beam, type of steel, and stiffening rib arrangement on the residual mechanical performance of H-WHSJs after exposure to elevated temperatures are determined via axial compression test by using 28 specimens and finite element (FE) parametric study. The major conclusions are as follows. (1) The residual characteristics of H-WHSJ after elevated temperature are rarely affected by temperature history, but mainly determined by the residual deformation at elevated temperature when the temperature is lower than 700 °C. (2) Plastic residual deformation can considerably reduce the residual bearing capacity (Nu,p) of the loaded H-WHSJ. In particular, Nu,p decreases by approximately 20% when the residual deformation is 6% of the hollow sphere diameter. (3) The formula to calculate the residual bearing capacity of H-WHSJ after loading in elevated-temperature environments has been proposed, and its prediction are in good agreement with the test and FE results.

Insights from electron backscatter diffraction into the origin of fibrous calcite veins in organic-rich shale from lower Es3 to upper Es4, Jiyang Depression, China

Abstract The origin of fibrous calcite veins developed in organic-rich shales, has attracted great attentions. However the growth direction, formation temperature and stress state are still controversial. The calcite veins in organic-rich shale from lower Es3 to upper Es4 in the Jiyang Depression has been analyzed with electron backscatter diffraction technology (EBSD), which can characterize the microstructures and orientation of mineral crystals in situ. On the basis of core observation and microscopic identification of petrological characteristics, the longitudinal and horizontal profiles of calcite veins were measured by EBSD. Crystallographic information on calcite veins, obtained by pattern quality mapping, phase diagrams, grain distribution maps, Euler graphs, grain misorientations and pole figures, clarifies the origins of these veins. The results show that calcite crystals in calcite veins belong to the sharp-rhombohedral space lattice structure of the trigonal system. Calcite crystals have a preferred orientation on the longitudinal profile, while there is no obvious preferred orientation on the horizontal profile. On the longitudinal profile of calcite veins, the misorientation of calcite crystals is the cause of the interference colour and extinction difference of calcite crystals under orthogonal light. The crystal interference and extinction characteristics on both sides of middle line in calcite veins are different, indicating that the growth direction of calcite veins is syntaxial. A shallow burial environment is suggested for calcite veins initial forming by the evidence that crystal morphology of calcite in calcite veins is most in the shape of sharp-rhombohedron, and some of which have hexagonal prism shape. The average orientation difference of calcite veins on longitudinal and horizontal profiles indicates that the average orientation of calcite grains is inhomogeneous. The stress concentration of small grains is higher than that of large grains, and cracks are developed in the interior or on the border of calcite grains on the longitudinal profile, which indicates that calcite veins are formed in the stress environment of three directional extrusion circumstances.

Flatbands and Perfect Metal in Trilayer Moiré Graphene.

We investigate the electronic structure of a twisted multilayer graphene system forming a moiré pattern. We consider small twist angles separating the graphene sheets and develop a low-energy theory to describe the coupling of Dirac Bloch states close to the K point in each individual plane. Extending beyond the bilayer case, we show that, when the ratio of the consecutive twist angles is rational, a periodicity emerges in quasimomentum space with moiré Bloch bands even when the system does not exhibit a crystalline lattice structure in real space. For a trilayer geometry, we find flatbands in the spectrum at certain rotation angles. Performing a symmetry analysis of the band model for the trilayer, we prove that the system is a perfect metal in the sense that it is gapless at all energies. This striking result originates from the three Dirac cones which can only gap in pairs and produce bands with an infinite connectivity. It also holds quite generally for multilayer graphene with an odd number of planes under the condition of C_{2z}T symmetry.

Load capacity of corroded welded hollow spherical joints subjected to bending moment and axial force

Welded hollow spherical joints (WHSJs) have been extensively used in space lattice structures. Corrosion is inevitable in the service life of WHSJs, and it can significantly reduce their load capacity and seriously threaten their structural safety. A series of nonlinear numerical analyses was conducted to investigate the moment and axial force interaction for corroded WHSJs. The moment-rotation surface of corroded WHSJs subjected to axial force was derived. The influence of the location, size, and thickness of corrosion of WHSJs on their compressive capacity were revealed in this study. Two types of corroded shapes were investigated. Results indicate that the geometrical parameters exert a significant influence on the moment and axial force interaction. An analytical equation has been proposed to quantify the influence of axial force on the bending stiffness and moment capacity of corroded WHSJs.

Seismic Isolation Research on a Double-Layer lattice Structure Using Shaking Table Tests

Typical failure patterns of members, supports, and joints were observed in double-layer lattice space structures during the 2013 M7.0 Lushan earthquake in the Sichuan province of China. Various isolation supports have been implemented in recent years to enhance the structural performance by reducing the dynamic responses. However, these isolation supports mostly focus on either horizontal isolation or vertical isolation, which is not applicable for synchronous isolation in both horizontal and vertical directions. Therefore, an innovative isolated support used for three-dimensional isolation was invented. In order to verify the feasibility of using the isolated support to reduce the earthquake response of double-layer lattice structures under small to strong earthquakes, a scale model was subjected to a shaking-table test before and after application of the isolated support. The dynamic characteristics, earthquake performance and failure pattern of the model with and without the isolated supports are discussed based on the earthquake responses, including acceleration, displacement, and strain. Results of the test indicate that the earthquake effect is underestimated without regard to the dynamic amplification effect of the lower supporting reinforced concrete structures, which led to the failure of the structure. The compared experimental results indicate that the isolated supports had remarkable earthquake isolation and reduction in both the horizontal and vertical directions.

Behavior of eccentrically loaded welded hollow spherical joints after elevated-temperature exposure

Welded hollow spherical joint is an extremely widely used connection pattern in space lattice structures. Understanding the behavior of the welded hollow spherical joint after elevated-temperature exposure is critical for the fire damage assessment of the entire space lattice structures. In this study, both experimental and numerical studies were conducted to reveal the mechanical behavior of eccentrically loaded welded hollow spherical joints subjected to eccentric loads after cooling from three elevated temperatures up to 1000°C, wherein two different methods were considered, namely, air and water cooling. Associate mechanical performance, such as load versus longitudinal displacement and load versus steel tube rotation responses, initial stiffness, load-bearing capacities, and strain development, were obtained and further analyzed. The results showed that the behavior of welded hollow spherical joints began to change when the exposure temperatures exceeded 600°C, with obvious reductions in both stiffness and strength. In addition, the influences of different cooling methods were significant. The joints cooled by water generally presented higher load-bearing capacities than those cooled by air. Furthermore, three-dimensional finite element analysis was conducted via ABAQUS software. After validating the finite element model against experimental results, parametric studies were performed and a practical formula was proposed to calculate the load-bearing capacity of welded hollow spherical joints subjected to eccentric load after elevated-temperature exposure.

Influence of pitting corrosion on the bending capacity of thin-walled circular tubes

Thin-walled circular tubes (TWCTs) have been extensively used in space lattice structures and other industrial areas. Corrosion is inevitable for steel structures with regard to its service life, and it will remarkably reduce the loading capacity and critically threaten the structural safety. The present work aims to investigate the influence of pitting corrosion on the bending capacity of TWCT. A series of nonlinear numerical analyses was conducted to investigate the influences of corrosion pit shape, specification, corrosion thickness, diameter, and thickness of TWCT on bending capacity. Corrosion was simulated by reducing the thickness of shell element. Random corrosion distribution was generated, and its influence on bending capacity was estimated. The method for generating a random corrosion would provide a reference for the analysis of other structures with corrosion.

Influence of welded hollow spherical joints on the mechanical behavior of single-layer reticulated shell structures

Welded hollow spherical joints (WHSJ) are widely used in space lattice structures. Beam models are widely adopted in analyzing integral structures for high computational efficiency. However, the influence of WHSJ cannot be estimated accurately, and few studies on the accuracy of beam models are available. Numerical models in different scales were established, and results derived from different models were compared to investigate their accuracy. Results indicated that the influence of WHSJ on the mechanical behavior of integral structures varies along with its scale. A large error may exist in the results obtained by the beam models, especially for the models with thick pipe and thin WHSJ. The largest error in ultimate strength is 250% when components were meshed into one beam element, and the minimum error of results derived from the beam model is approximately 10% when components were meshed by a sufficient number of elements. Results derived from multi-scaled models agree well with the results derived from the refined model.

Assessment of the bending capacity of welded hollow spherical joints with pit corrosion

Welded hollow spherical joints (WHSJs) are widely used in space lattice structures. Corrosion is inevitable for WHSJs during service, and this phenomenon will significantly reduce loading capacity and seriously threaten the structural safety. Pit corrosion is a typical corrosion type for steel structures. In this study, nonlinear numerical analyses were conducted to investigate the influence of several parameters on the bending capacity of a WHSJ. A numerical model of the WHSJ with random pit corrosion was proposed to investigate the mechanical behavior of the corroded WHSJ. Results indicated that the moment capacity of the WHSJ with random corrosion pits was normally distributed. A probabilistic distribution model of the corroded WHSJ was proposed. The failure probability could be deduced based on the formulae of the upper and lower bounds of the moment capacity.

Post-fire Behavior of Welded Hollow Spherical Joints Subjected to Eccentric Loads

Welded hollow spherical joints are widely used as a connection pattern in space lattice structures. Understanding the post-fire residual behavior of welded hollow spherical joints is crucial for fire damage assessment of the space lattice structures. However, the post-fire behavior of welded hollow spherical joints has not been explored in existing studies. In this paper, experimental and numerical studies were conducted to investigate the residual behavior of eccentrically loaded welded hollow spherical joints after fire exposure. Eccentric compressive tests were performed on five joint specimens after exposure to the ISO-834 standard fire (including both heating and cooling phases), and three highest fire temperatures, i.e., 600, 800, and 1000 °C, were considered. The temperature distributions in the specimens during the heating and cooling process and the related mechanical behavior of the specimens, such as load versus longitudinal displacement and rotation responses, load-bearing capacities, and strain distributions, were obtained and analyzed. Finite element analysis (FEA), including both heat transfer and mechanical analysis, were also developed using the ABAQUS software. Having validated the FE models against the experimental results, a design method was proposed on the basis of parametric studies to predict the residual load-bearing capacity of eccentrically loaded welded hollow spherical joints after fire exposure.

Growth, Crystal Structure, Theoretical Analysis and Properties of Te4+-Doped KTiOPO4

A single crystal of Te4+-doped KTiOPO4(Te:KTP) has been grown by the flux method. The electronic structure and density of states of KTiOPO4 (KTP) and Te:KTP were calculated from first principles. As the results reveal, there is no change in the space group or lattice structure of Te:KTP, but that some increase in lattice parameters occurred. The chemical composition of Te:KTP was analyzed using x-ray photoelectron spectroscopy (XPS). The possible existence of Ti3+ has been evaluated by measuring the electron paramagnetic resonance spectrum, and the results reveal that the ion is absent from this crystal. It was observed that Te4+ doping reduces the conductivity of the crystal from measurements of its conductivity at different temperatures and frequencies, indicating that Te:KTP has excellent electro-optical properties. The effect of Te4+ doping on the second harmonic generation in KTP was also studied. The thermal expansion, thermal diffusivity, thermal conductivity and specific heat capacity of KTP and Te:KTP were determined.

Bending capacity of corroded welded hollow spherical joints

Welded hollow spherical joints (WHSJ) have been widely used in space lattice structures. Corrosion is inevitable in the service life of WHSJ, which significantly reduces their bending capacity and seriously threatens their structural safety. This study aims to investigate the influence of corrosion that occurred at different places on the bending stiffness and bending capacity of WHSJ. The effects of corroded location and size, corroded thickness, and diameter and thickness of spherical body were investigated through a series of nonlinear numerical analyses. Two types of corroded shape were investigated. The equation used for predicting the residual bending stiffness of corroded WHSJ was established. Results indicated that corrosions in different places had distinct influence on the bending capacity of WHSJ. Loading capacity could be significantly reduced when corrosion occurred at other areas. The derived results would provide a foundation for estimating the residual bending stiffness and strength of structures connected by corroded WHSJ.

Behavior of welded hollow spherical joints after exposure to ISO-834 standard fire

Welded hollow spherical joints are extensively used as a connection pattern in space lattice structures. Provided that structural collapse does not occur after a fire, a reliable evaluation of the residual performances of the structures is necessary to decide whether the structures should be dismantled, repaired, or directly reused. Thus, understanding the post-fire residual behavior of welded hollow spherical joints, which act as key connection elements, is crucial for fire damage assessment of the space lattice structures. In this paper, experimental and numerical studies were conducted to reveal the residual structural behavior of welded hollow spherical joints after fire exposure. Axial compressive tests were performed on eight joint specimens after exposure to the ISO-834 standard fire (including both heating and cooling phases), and three highest fire temperatures, i.e., 600°C, 800°C, and 1000°C, were considered. The temperature distributions in the specimens during the heating and cooling process and the related mechanical behavior of the specimens, such as axial load–displacement curves, initial axial stiffness, yield loads, load-bearing capacities, ductility level, and strain distributions, were obtained and analyzed. Finite element analysis (FEA), including both heat transfer and stress analysis, were also developed using the ABAQUS software. Having validated the FE models against the experimental results, a design method was proposed on the basis of parametric studies to predict both the residual load-bearing capacity and initial axial stiffness of welded hollow spherical joints after fire exposure.

Residual behavior of welded hollow spherical joints after exposure to elevated temperatures

Welded hollow spherical joints are widely applied as main connection pattern in space lattice structures. During fire events, structures are inevitably exposed to elevated temperatures. Provided the general appearance of the structure remains satisfactory after a fire, the residual behavior of welded hollow spherical joints in these structures should be accurately estimated to ensure safety. However, the post-fire behavior of welded hollow spherical joints has not been explored in existing studies. Hence, experimental and numerical studies were conducted to reveal the post-fire residual mechanical behavior of welded hollow spherical joints. Seventeen specimens were initially heated to six various preselected temperatures up to 1000°C and were subsequently cooled down to ambient temperature via two different methods: air cooling and water cooling. Axial compressive tests were then performed, and related mechanical properties, such as axial load–displacement curves, initial axial stiffness, yield loads, load-bearing capacities, ductility level, and strain distribution, were obtained and analyzed. The mechanical behavior of welded hollow spherical joints significantly changed after exposure to temperatures exceeding 600°C, with phenomena of reductions in stiffness and strength but an increase in ductility level. Furthermore, the influences of different cooling methods were remarkable. A 3D finite element (FE) model was also developed using the ABAQUS software and validated against experimental results. Simplified design methods, based on parametric studies, were proposed to predict the post-fire residual load-bearing capacity and initial axial stiffness of welded hollow spherical joints.

Experimental studies of the seismic behavior of double-layer lattice space structures I: Experimental verification

Abstract Double-layer lattice space structures were found in a severe state of damage following the 2013 M7.0 Lushan earthquake in China. The failure of this kind of structure can result in huge damage and extensive repair costs. Therefore, the accurate definition of degrees of structural damage in double-layer lattice space structure is of high interest, in particular to give a better understanding of failure mechanisms and more accurately implement performance-based designs of these structures. In this paper, typical failure patterns of two gymnasiums are summarized, and possible reasons are broadly discussed. The seismic behavior of a double-layer lattice space structure with a lower supporting structure was then investigated using a shaking table test. To this end, a 1/10 scale model of a double-layer lattice space structure corresponding to the prototype structure with span of 40.8 m was designed. The dynamic characteristics including structure frequencies and damping ratio were obtained through the results under the input excitation of white noises with different amplitudes. Furthermore, two representative earthquake records were used to evaluate the performance and different damage degree by a 5 m × 5 m shaking table. The seismic responses including the acceleration and displacement placed at different height of the model as well as the strain gathered at the members were discussed. Results of the test indicate that the seismic effect is underestimated without considering the dynamic amplification effect of the lower supporting structure, which leads to the failure of structures. Therefore, the lower supporting structure should be considered as an integrated model with the upper structure when conducting seismic analysis and evaluation, rather than considering the lower supporting structure as rigid.