Spatial Grid Structures Research Articles

Grid Optimization of Free-Form Spatial Structures Considering the Mechanical Properties

In recent years, the application of free-form surface spatial grid structures in large public buildings has become increasingly common. The layouts of grids are important factors that affect both the mechanical performance and aesthetic appeal of such structures. To achieve a triangular grid with good mechanical performance and uniformity on free-form surfaces, this study proposes a new method called the “strain energy gradient optimization method”. The grid topology is optimized to maximize the overall stiffness, by analyzing the sensitivity of nodal coordinates to the overall strain energy. The results indicate that the overall strain energy of the optimized grid has decreased, indicating an improvement in the structural stiffness. Specifically, compared to the initial grid, the optimized grid has a 30% decrease in strain energy and a 43.3% decrease in maximum nodal displacement. To optimize the smoothness of the grid, the study further applies the Laplacian grid smoothing method. Compared to the mechanically adjusted grid, the structural mechanical performance does not significantly change after smoothing, while the geometric indicators are noticeably improved, with smoother lines and regular shapes. On the other hand, compared to the initial grid, the smoothed grid has a 21.4% decrease in strain energy and a 28.3% decrease in maximum nodal displacement.

Efficient analysis and evaluation method for overall lifting of large-span spatial grid structures

Large-span spatial grid structures are commonly employed on the roofs of various public buildings and are typically installed via an overall lifting method. However, the process of overall lifting cannot ensure complete synchronization, which may result in damage to the structure or the lifting equipment. It is imperative to ascertain the limit state of the structure under asynchronous conditions and to develop an accurate model for rapidly assessing the critical response during the lifting process. This paper introduces an efficient approach for evaluating and analyzing the overall lifting process of large-span spatial grid structures. The iterative limit boundary (ILB) method is proposed in this paper, which facilitates the rapid determination of the limit boundary and the limit state for a structure-equipment system with asynchronous lifting. Furthermore, the genetic algorithm is integrated into the ILB method to enhance its efficiency when dealing with numerous lifting points. An agent model capable of outputting key structural responses is developed for the rapid evaluation of those responses throughout the lifting process. Both a numerical example and an engineering example are provided to validate the proposed method. The computational results indicate that the method proposed achieves accurate results with a computational cost merely 3 % of that of the Monte Carlo simulation. Additionally, the agent model established within the limit boundary, operates at a speed 200 times faster than finite element analysis, thereby enabling precise and real-time critical response assessments.

An Efficient Progressive Grid Generation Method Considering Internal Quality and Boundary Grid Adjustment

Due to its elegant appearance and high structural efficiency, free-form grid structures are increasingly adopted in architectural design. However, it is a challenging task for engineers to generate a uniform and well-shaped grid on a free-form surface while considering the processing of both interior and boundary of grid, especially for composite surfaces. To generate well-shaped grids with uniform rods, regular cells and smooth visual effects over free-form surfaces, this paper develops an innovative triangular grid generation method capable of automatically managing grid boundary with extending initial surface. In the method, nodes of grid structure are considered to be zero mass particles and are progressively added to the extended surface from geometric center to the boundary of surface. A boundary-processing algorithm is then established to evenly distribute nodes on initial boundary curve, while ensuring that grid cells at the boundary do not exhibit elongation. A mechanical simulation system based on spring-mass model is improved to optimize spatial grid structure, rods of grid are regarded as linear springs, a surface attraction force and an anchoring force are performed on grid nodes. Moreover, the proposed method allows architects change grid direction and rods length easily, which can greatly improve the efficiency of design. Several case studies show that the method can effectively avoid distortion of grids and generate well-shaped grids that can meet aesthetic requirements.

Research on Arrangement of Measuring Points for Modal Identification of Spatial Grid Structures

In structural health monitoring, because the number of sensors used is far lower than the number of degrees of freedom of the structure being monitored, the optimization problem of the location and number of sensors in the structures is becoming more and more prominent. However, spatial grid structures are complex and diverse, and their dynamic characteristics are complex. It is difficult to accurately measure their vibration information. Therefore, an appropriate optimization method must be used to determine the optimal positioning of sensor placement. Aiming at the problem that spatial grid structures have many degrees of freedom and the fact that it is difficult to obtain complete vibration information, this paper analyzed the typical EI method, MKE method, and EI-MKE method in the arrangement of the measuring points, and it was verified that the EI method was more suitable for the vibration detection of spatial grid structures through the example of a plane truss and spatial grid structures. Measuring points under the assumption of structural damage were explored, and it was proposed that there might have been a stable number of measuring points that could cover the possible vibration mode changes in the structures. At the same time, combined with the three-level improved Guyan recursive technique, in order to obtain better complete modal parameters, the influence of the number of measuring points on the complete vibration mode information was studied. It was concluded that MACd was better than MACn as the quantitative target.

Numerical simulation and performance evaluation of compression members in long-span single-layer spatial grid structures constrained by steel bars

The collapse of long-span single-layer spatial grid structures can be triggered by the instability of compression members. To improve the stability of axially compressed members, this study proposes two novel compression members that are constrained using steel bars based on the design concept of existing constraint measures. A validated FE analysis is adopted to investigate the compressive mechanical behaviors, including parametric analysis. Members with different constraint measures are applied to single-layer latticed domes, and their feasibility in improving the progressive collapse resistance of the domes is evaluated. The results show that restraint measures using steel bars can significantly improve the stability of compression members, and when the ends of the restraint body are able to slide, the bearing capacity and ductility are greatly improved. The improvement can be maximized by reasonably designing various parameters of the constraint body. In addition, using different measures to constrain the compression members with higher key grades and thus improve the progressive collapse resistance of single-layer latticed domes is found to be feasible. However, the study finds that the failure mechanism of the constrained members sliding at the ends of the constraint body cannot be fully realized following dome collapse.

Crashworthiness of AAG joints with a foam aluminum layer gusset plate

The gusset joint is the most widely used joint system in an aluminum alloy single-layer reticulated shell structure; it plays a vital role in the spatial grid structure. In this paper, the effects of different thicknesses of aluminum alloy gusset plates on the dynamic response and failure modes of aluminum alloy gusset (AAG) joints were studied by impact tests of three specimens. The test results show that the failure modes of AAG joints are a slight depression of the gusset plate, the local buckling of members, the local distortional buckling of members, and tearing of the lower flange and a web of members. The AAG joint inclines along the direction of the failed member and collapses. The finite element model of the AAG joint was established using ANSYS software. The stress, displacement, and deformation modes in the test and numerical simulation results were compared and analyzed, and the rationality of the numerical simulation results was verified. Based on the failure mode of the specimens, a design method for improving the impact resistance of AAG joints with aluminum foam layer gusset plate (AFLGP) is proposed. The numerical simulation results show that an AAG joint with an AFLGP effectively reduces the maximum peak value of impact loads through the deformation of the aluminum foam. In the elastic and elastic-plastic stages, AAG joint with AFLGP had better impact resistance, and the energy absorbed by its rods was 25.44% ∼ 30.36% lower than that of AAG joints alone. Finally, the influence of the thickness of the AFLGP on the impact force and energy absorption of the AAG joint was studied. The aluminum foam gusset layer plate is approximately twice as thick as the aluminum alloy gusset plate had the best protection effect on the AAG joint.

Experimental investigation of aluminium alloy gusset joints’ dynamic response to lateral impact loads: Evaluating the influence of gusset plate bending stiffness

The traditional aluminium alloy gusset plate (AAG) joint is commonly regarded as a representative semi-rigid joint characterized by limited stiffness. This deficiency in stiffness significantly hampers its capacity for load transmission and resistance against progressive collapse in spatial grid structures. Notably, the dynamic response characteristics of semi-rigid joints, especially when subjected to short-term, highly intense loads such as impacts and explosions, deviate substantially from those of rigid joints. This research examines the dynamic failure behavior of six distinct traditional AAG joints with varying degrees of stiffness when subjected to impact loads. The first group comprises three specimens where the variance in AAG joint stiffness is achieved by altering the gusset plate’s diameter. The second group comprises three specimens aiming to manipulate the AAG joint’s stiffness by modifying the gusset plate’s thickness. The study yielded comprehensive data, including stress profiles, displacement patterns, acceleration time history curves, and failure modes of AAG joints. The experimental findings revealed that both groups of AAG joints under lateral impact loads exhibited brittle failure. The predominant failure modes included the rupture of the H-shaped aluminium alloy beam, distortional buckling of the beam, and warping of the thinner gusset plate. It is evident from the stress, displacement, and acceleration time history curves that the AAG joint adheres to the characteristics of a typical semi-rigid joint, and the diameter and thickness of the gusset plate exert significant influence on the AAG joint’s dynamic response. Subsequently, the six test conditions were simulated using ANSYS/LS-DYNA software. This simulation considered the stress distribution, impact force time history curves, and strain energy time history curves of AAG joints. It facilitated a detailed discussion of the failure mechanism underlying AAG joints when subjected to lateral impact loads.

Member separation and deformation recognition of spatial grid structures in-service

Bending deformation of members in spatial grid structures is a typical damage threatening structural safety. Conventional methods of deformation measurement have difficulty in detection member selection, high-altitude operation, or systematic error elimination. And reverse modeling technology for deformation detection is mostly utilized in entire structures or laboratory scenes. In this study, two kinds of member separation algorithms are developed based on point cloud registration and point cloud features respectively, both of which are suitable for engineering situations of insufficient point cloud density and multiple noise sources. The deformation recognition algorithm for members is improved accordingly with double judgment conditions. A field test has been carried out in a Sports Center Stadium in Guangzhou province. 7045 members are identified, and 29 crooked members are eventually recognized. The results demonstrate that the proposed algorithms can improve the efficiency of member separation and deformation recognition, and assist the monitoring and assessment of spatial grid structures in-service.

Loading capacity of welded hollow spherical joints strengthened by cone member

The Welded Hollow Sphere Joint (WHSJ) is frequently employed as a connection form in spatial grid structures. Structures don't retire immediately upon damage, necessitating reinforcement. However, effective solutions for reinforcing WHSJs still have shortcomings in practical engineering applications. Given this research context, a reinforcement scheme for WHSJs is proposed. Feasibility is confirmed through numerical simulation, showing that this reinforcement method is applicable to WHSJs with initial loads, enhancing their mechanical performance without being influenced by the initial loads. The study also initially uncovers the patterns of load-bearing capacity variation with geometric dimensions. Subsequently, an Artificial Neural Network (ANN) is used to predict compressive load-bearing capacity. It utilizes input variables such as sphere diameter (Ds), steel pipe diameter (Dp), reinforcement cone base diameter (Dt), sphere thickness (Ts), steel pipe thickness (Tp), cone thickness (Tt), and cone base angle (θ), with the output being the compressive load-bearing capacity of the welded hollow sphere joint post-reinforcement. Prediction errors are confined to within 10%. Using the Garson algorithm, the sensitivity analysis reveals that steel pipe thickness (Tp) and sphere thickness (Ts) play relatively significant roles in the prediction process.

A trajectory tracking method based on robust model predictive control for a bionic ankle–foot aided by a tensegrity mechanism

In this article, a robust model predictive control method is investigated for settling the trajectory tracking problem of a bionic ankle–foot aided by a tensegrity mechanism. In order to achieve adaptive movement of the ankle–foot mechanism, a three-degrees-of-freedom spatial ankle–foot mechanism is designed by tensegrity, which is a spatial grid structure composed of springs and struts. Dynamic analysis is the basis of control algorithm research, and the dynamic model of the mechanism can be established by a Lagrangian equation. Then, a controller is proposed for tracking the trajectory of the ankle–foot mechanism under external disturbances. Combining rolling optimization and feedback correction, the controller can be defined as an optimization problem, by solving which the ankle–foot mechanism can be controlled to track the desired trajectory quickly. Furthermore, stability analysis is an essential part of predictive controller design, which can help to understand the operational mechanism of the control strategy. Numerical results demonstrate that the proposed approach improves trajectory tracking accuracy and avoids mechanism movement problems caused by disturbances.

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.

Two-Step Identification Method and Experimental Verification of Weld Damage at Joints in Spatial Grid Structures

Welded joints in grid structures are susceptible to damage and destruction when exposed to random excitation. The complexity of the grid structure poses challenges for realizing the damage recognition of welded joints. In this study, a two-step method is proposed specifically for damage identification of welded joints in grid structures, combining wavelet analysis and fuzzy pattern recognition to accurately identify the location and extent of damage in welded joints. Firstly, the structure is divided based on the analysis of the influence range of joint damage. Key joints are selected within the sub-regions where sensors are installed, and the acceleration response of these key joints is measured. Wavelet analysis is then applied to identify the sub-regions where weld damage occurs. Secondly, an equivalent finite element model is established for joints with varying degrees of damage. The damage index, calculated as the ratio of the absolute value of the difference in the first-order element strain mode of the members, increases with the degree of damage during joint weld damage. By monitoring the changes in the damage index of sensitive members, which exhibit significant changes with varying weld damage degrees, a damage pattern database is constructed for each sub-region. The membership degree between joint damage and the patterns in the pattern database is then calculated to determine the location and degree of weld damage. To validate the effectiveness of the proposed method, an experiment was conducted using a grid structure model with replaceable members. Highly sensitive FBG sensors were designed to measure the acceleration response of the joints, resulting in accurate identification of damaged sub-regions solely through the measurement of key joint acceleration responses. Furthermore, within the damaged sub-regions, the fuzzy pattern recognition method precisely determined the location and degree of weld damage in the joints. The experimental results demonstrate that the proposed method effectively reduces the complexity of the structure by dividing the grid structure into sub-regions, and enables the two-step identification method to achieve successful damage identification for the joints in the grid structure with high efficiency and accuracy.

Investigating the failure behaviour of aluminium alloy gusset joints under impact loading: An experimental and numerical study

The AAG joint, also known as the Temcor joint, is a well-established method for constructing long-span spatial grid structures using aluminium alloys. This joint system has been widely used and tested is considered a mature technology in the field. This paper investigates the tensile properties of 15 stainless-steel bolt connections for aluminium alloy plates at room temperature. Through testing, the load–displacement curve was obtained and two failure modes of the connection were identified. Test results show that the increase in the number of bolts and the thickness of aluminium alloy plate increases the ultimate bearing capacity of the connection. The thickness of the aluminium alloy plate was found to have a significant impact on the slippage effect of the bolts and the warping deformation of the contact surface. Based on the test results of the connection, three specimens of AAG joints were designed to study their dynamic behaviour under different impact loads. Our findings detail the dynamic response behaviour of joints subjected to varying impact times, including stress, acceleration, and displacement, as well as the resultant joint failure phenomenon. The test results show that AAG joints have good impact resistance. The refined FE model of the AAG joint was established using ANSYS/LS-DYNA, and its effectiveness was verified by comparing the stress, displacement, and acceleration between the numerical model and the experimental model. By comparing and analysing the final deformation of AAG joints obtained through test and numerical simulation, three distinct failure modes of AAG joints under impact load were identified. Finally, based on the stress nephogram and impact force time-history curve obtained by numerical simulation, the stiffness degradation law of AAG joints is discussed. This paper also discuss the energy dissipation mechanism of AAG joints during impact load, based on the strain energy time-history curve of each component.

Programming application of contemporary jewelry design forms based on Grasshopper software

Abstract In recent years, by the influence of social progress and economic development, jewelry customers have continued to expand the demand gap. Today’s requirements for jewelry design are also more stringent than other design work. Excellent design should be a combination of natural beauty, spiritual beauty, and functional beauty. With the development of the computer industry and the advent of the information age, the design industry has undergone radical changes, and the way of design realization is gradually divided into hand-drawn design and computer-aided design. Although the hand-drawn design is beautiful and free, it is inaccurate and time-consuming. Computer-aided design is fast, accurate, and efficient, and the effect is real and fantasy, which is an important way to improve designers’ design efficiency. In order to address the problem of missing design results due to the weakness of details in the construction of 3D models in the original jewelry 3D design method. In this paper, the Grasshopper parametric design platform is used to prepare a program for the rapid modeling of spatial grid structures, and the details of how the program converts architectural models into SAP2000 structural analysis models are presented. Considering the large amount of work required to construct the surface cells for load application, a secondary masking program based on azimuth calculation is developed further to improve the modeling efficiency and universality of the program. Through an engineering example application, the effectiveness and practicality of the fast modeling program for spatial grid structures are verified, which provides a reference for structural engineers to develop similar programs to improve the modeling and analysis efficiency of complex structures and complete the programming application of contemporary jewelry design forms of Grasshopper software.

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.

Machine Learning and Deep Learning for the Built Heritage Analysis: Laser Scanning and UAV-Based Surveying Applications on a Complex Spatial Grid Structure

The reconstruction of 3D geometries starting from reality-based data is challenging and time-consuming due to the difficulties involved in modeling existing structures and the complex nature of built heritage. This paper presents a methodological approach for the automated segmentation and classification of surveying outputs to improve the interpretation and building information modeling from laser scanning and photogrammetric data. The research focused on the surveying of reticular, space grid structures of the late 19th–20th–21st centuries, as part of our architectural heritage, which might require monitoring maintenance activities, and relied on artificial intelligence (machine learning and deep learning) for: (i) the classification of 3D architectural components at multiple levels of detail and (ii) automated masking in standard photogrammetric processing. Focusing on the case study of the grid structure in steel named La Vela in Bologna, the work raises many critical issues in space grid structures in terms of data accuracy, geometric and spatial complexity, semantic classification, and component recognition.

Study of the Key Mechanical Properties of Welded Hollow Spherical Joints after Uniform Corrosion

The welded hollow spherical joint is the most common form of the spatial grid structure, but the corrosion treatment at the joint is difficult. There are many corrosion problems of the welded hollow spherical joint in the actual structure, which brings hidden problems to structural safety. To study the effects of uniform corrosion on the key mechanical properties of welded hollow spherical joints, the joint refinement FEM in one typical size is built considering the effect of uniform corrosion through the method of the element birth and death, and the tensile, compressive, and bending performance of the FEM has been analyzed. Based on the analysis results, the relation curves between the three bearing capacities of the welded hollow spherical joint and the uniform corrosion degree are given. The results show that the influence of early corrosion on the joint tensile and compressive performance is not obvious. After corrosion to a certain extent, the loss of tensile and compressive capacity has a significant linear relationship with the degree of corrosion, and the loss of bending capacity has a significant quadratic curve relationship with the degree of corrosion from the initial stage. This study can provide a theoretical reference for a better understanding of the mechanical properties of welded hollow spherical joints in one typical size after corrosion to evaluate structural safety.

Flexural performance of H-shaped aluminium alloy members with web openings

The application of aluminium alloy space structures is increasingly widespread. There is a new single-layer aluminium alloy spatial grid structure with H-shaped members web openings nowadays. In this paper, the flexural performance of H-shaped aluminium alloy members with web openings in this structure is studied through experiments, finite element analysis and theory. Parametric analysis is carried out to study the influence of initial imperfections, opening parameters and section properties on the flexural performance of the members. The conclusions are as follows: (1) The presence of initial imperfections can significantly reduce the ultimate load-carrying capacity of the component. The initial imperfection reduced the member capacity by 6.3% to 12.7%. (2)The web openings will affect the failure mode of flexural members with H-shaped web openings. When the opening ratio is 0.7, the bearing capacity of the test specimen decreases by 31.2%–47.1%. The local buckling of the flange and web occurs at the same time as the failure of the vierendeel mechanism. (3) The bearing capacity of narrow flange members can be reduced by 2.3 times as much as that of wide flange members. The greater the section width to height ratio, the greater the ultimate bearing capacity of the member. (4) The finite element method and theoretical formula proposed in this paper can better simulate the bearing capacity and failure mode of H-shaped aluminium alloy members with web openings under bending.

An Efficient Algorithm for Multi-dimensional and Multi-point Random Seismic Response Analysis of Spatial Grid Structure based on Computer

An Efficient Algorithm for Multi-dimensional and Multi-point Random Seismic Response Analysis of Spatial Grid Structure based on Computer

A Lidar-Inertial Navigation System for UAVs in GNSS-Denied Environment with Spatial Grid Structures

With its fast and accurate position and attitude estimation, the feature-based lidar-inertial odometer is widely used for UAV navigation in GNSS-denied environments. However, the existing algorithms cannot accurately extract the required feature points in the spatial grid structure, resulting in reduced positioning accuracy. To solve this problem, we propose a lidar-inertial navigation system based on grid and shell features in the environment. In this paper, an algorithm for extracting features of the grid and shell is proposed. The extracted features are used to complete the pose (position and orientation) calculation based on the assumption of local collinearity and coplanarity. Compared with the existing lidar navigation system in practical application scenarios, the proposed navigation system can achieve fast and accurate pose estimation of UAV in a GNSS-denied environment full of spatial grid structures.