Planar Truss Structure Research Articles

Assessing the Reliability of Truss Structures Based on the Bound Method and Collectively Exhaustive Events

Damage to long-span truss structures may cause structural deformation, load-capacity reduction, and even collapse. The design service life of truss structures is usually 50 years, so evaluating their reliability is of the utmost importance. Reliability considers the probability of failure as an analysis index. In calculating the probability of structural failure, important components are first selected to form a failure path, and then the failure probability corresponding to the failure path is calculated. A truss structure has many important components and failure paths, so calculating this probability requires extensive and thorough work. As a result, we propose selecting the important components via the approximation method to reduce the influence of the threshold of approximation. Collectively exhaustive events were established using the differential equivalent recursive algorithm to calculate the probability of structural failure. This process was considerably simplified, and validity was verified via a reliability analysis involving a three-bar truss structure, a plane truss structure, and a square pyramid truss structure. This method is suitable for selecting important components of regular flat truss structures.

Vibration-based methods for local damage identification of breathing cracks in truss-like structures

A vibration-based local damage identification method is proposed for truss-like structures with breathing cracks. Firstly, a bilinear model is established to represent the characteristics of breathing cracks, and the features of such cracks are detected through reciprocity and homogeneity tests on structural input-output signals. Since the crack is influenced by tensional and compressive forces on truss members, only one damage factor is required to quantify the stiffness reduction of each member. Subsequently, a dynamic equilibrium equation concerning the damage factor is constructed to identify the new load term. The integral equation method, which relies on the virtual work principle, is employed to obtain the displacement responses and loads under all tensile conditions. Finally, the mean value of cumulative damage coefficients for each truss member can be derived as their corresponding damage factor. Numerical examples involving a plane truss structure and a truss offshore platform are utilised to illustrate the effectiveness of this damage identification method. The results demonstrate exceptional precision and efficiency in accurately identifying various damages in truss structures under different excitations and signal-to-noise ratios. A actual space truss structure confirm that this damage identification method exhibits high-level precision in identifying single-member damages as well as multi-member damages with breathing cracks locally.

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.

Transmissibility-based operational modal analysis: A unified scheme and uncertainty quantification

The transmissibility-based Operational Modal Analysis (OMA) technique has attracted substantial research interest over the past two decades due to its capability to extract structural modal parameters in the presence of non-white excitation. The transmissibility function used in OMA can be categorized as Response Transmissibility (RT) and Power Spectral Density Transmissibility (PSDT). Modal parameters can be identified by combining RTs from multiple load cases or PSDTs from multiple transfer outputs. Nevertheless, the mathematical formulations and implementation procedures of the various RT-based and PSDT-based methods exhibit significant differences. Furthermore, the uncertainty associated with modal parameter estimates is rarely assessed in these methods. This work aims to propose a scheme that unifies various transmissibility-based OMA algorithms through a consistent parametric formulation. Within this scheme, a universal parametric model and a standardized implementation procedure are developed to accommodate two types of transmissibility in both time and frequency domains and six OMA algorithms; additionally, a generalized framework for quantifying the uncertainties associated with modal parameter estimates is provided. The proposed scheme is finally validated using a planar truss structure.

Constraint‐aware optimization model for plane truss structures via single‐agent gradient descent

AbstractThis study introduces the constraint‐aware optimization model (CAOM), a novel optimization framework designed to optimize the size, shape, and topology of plane truss structures simultaneously. Unlike traditional optimization models, which rely on gradient descent and frequently struggle with managing various constraints due to their dependence on a single optimization agent, CAOM effectively addresses this challenge. It does so by incorporating a variety of assistant modules along with the Adam optimizer, a variant of the gradient descent method. Uniquely, CAOM employs the leaky rectified linear unit (ReLU) activation function beyond its conventional use in neural networks, applying it as a mechanism to integrate constraints and losses seamlessly. The model's effectiveness was validated through two numerical examples and a practical application, demonstrating that CAOM can reduce structural weight by up to 84% compared to unoptimized designs while fully adhering to structural, dimensional, and moveable constraints. Furthermore, the study found that while shape optimization plays a key role for stiffness‐governed structures, size optimization is crucial for strength‐governed structures. Optimizing size, shape, and topology together consistently leads to the most weight‐efficient designs. This emphasizes the significance of a holistic approach in the optimization processes.

Automated planar truss design with reclaimed partially disassembled steel truss components

A promising solution to decarbonize steel construction is reusing steel structural components from existing disassembled structures as it avoids sourcing raw material and the heating associated with recycling, as well as reducing the amount of waste from construction and demolition. However, barriers associated with increasing the use of reused steel components in modern construction include concerns about an increased length of the demolition process and the dramatic changes it requires in the structural design task. To simultaneously alleviate these concerns, this work presents a new stock-constrained design and optimization framework for designing planar truss structures from a stock library of partially disassembled trusses. In contrast to existing design methods that rely on reuse at the element level, this work mitigates the demolition process requirements by avoiding the complete disassembly of all structural members. The new automated design framework eases the design process and aggregates partially disassembled triangular components while introducing new material members where necessary to ensure that the new design matches the exterior geometric requirements. The proposed approach is fast (on the order of 0.1 s to generate a trial truss), and a GA optimization module is added to select among generated trial designs. Three case studies with realistic stock libraries demonstrate the potential of partially disassembling and reusing truss components and illustrate how the user-defined design shape and the stock variability influence the resulting design.

A Case Study on the Static Behavior of a Pedestrian Bridge Built with a Steel Pratt Truss Deck Bridge Supported by an Inclined Roller Support

Construction of bridges commonly uses trusses due to their lightweight design, which can endure heavy loads and span large distances. However, there are instances when the supports of these trusses do not lie normally on a horizontal surface. For some, the supports lie on inclined foundations, which is the focus of this study. The main objective of this study is to present the basic theory of plane truss analysis with an inclined roller support using the Direct Stiffness Method (DSM) in comparison to the use of the Graphic Rapid Analysis Software Program (GRASP) to analyze the static behavior of the structure. Furthermore, a case study is conducted to check the effects of inclined supports on a plane truss structure. Based on the results, it was discovered that the introduction of inclined roller supports does have a negative effect on the stability of the structure.

Bio‐based laminated truss structures with bolted steel connections: Experiment, modeling, and model‐updating

AbstractBio‐based laminated structures offer a timely solution to meet the pressing demand for resource‐efficient and environmentally responsible construction practices in civil engineering. Bolted connections are commonly used in truss joints and significantly impact their global mechanical behaviors. However, existing studies on the complex behavior of joints for integrated bio‐based structures are lacking. Based on previous work by the authors about joint behavior, this study seeks to experimentally investigate the axial behavior of bolted steel to laminated timber and bamboo (glubam) connections with slotted‐in steel plates in planar truss structures. First, cyclic tests were conducted on Bio‐based laminated planar truss structures to evaluate their global and local hysteretic behavior. The test matrix encompasses eight distinct connection configurations, carefully selected to assess the connection behavior of Laminated Veneer Lumber (LVL) and Glued Laminated Bamboo (glubam). Subsequently, through the incorporation of the hysteretic model for truss joints, an advanced hybrid truss model was developed within the OpenSees framework and successfully validated using experimental data. Finally, this study proposes and demonstrates the effectiveness of an efficient model‐updating framework, which combines the power of the genetic algorithm (GA) and neural network, resulting in a significantly enhanced accuracy of the model.

The Effect of Preload Loss on the Mechanical Properties of Grid Structure Connected with Bolted-Ball Joints

Bolt-ball joints are widely adopted in grid structures due to their high installation accuracy and short construction period. Since the bolt is inside the joint, it is challenging to evaluate its health status from outside the structure. A finite-element plane-truss structure model, based on the actual grid structure, was constructed to investigate the influence of the rod’s preload on the overall stiffness and bearing capacity of the grid structure. Moreover, a model of the grid structure, with a bolt-ball joint connection, was constructed to analyze the influence of the preload loss in bolted-ball joints on the overall mechanical performance of the local members and structures. The results show that the release of preload on the outer web rod is less effective in terms of the overall stiffness and bearing capacity of the structure than on the inner web rod. The preload of the larger span direction rod plays an important role, and the preload of the upper chord has a greater impact, while the preload of the web rod and the upper chord in the smaller span direction has no significant effect on the normal stress in the surrounding rods.

A probabilistic method for dynamic force identification of uncertain structures

To address the dynamic force identification problem of uncertain structures with random parameters, this study proposes a novel approach to describe the probabilistic properties of the identified forces. First, the integral equation for the force probability density function (PDF) is derived from the mathematical mapping relationship between the identified force and random structural parameters. Next, the sample space of the random parameters is partitioned into non-overlapping subdomains using a point selection technique based on the generalized F-discrepancy. Meanwhile, the function fitting technique and Tikhonov regularization method are applied to identify the force samples under the corresponding partitioned subdomains. Thus, the integral equation of the force PDF is transformed into a summation of the force probabilities for all the subdomains. Subsequently, a smoothing technique is introduced to obtain the expression of the identified force PDF. Finally, the confidence interval over the entire time domain is constructed from the force cumulative distribution function, which effectively quantifies the influence of random structural parameters on the identified results. The efficiency and superiority of the proposed method are verified using an example of a plane truss structure with multiple random structural parameters, and force identification for a simplified launch vehicle model with connection uncertainties is discussed.

An improved weak-form quadrature element (IWQE) method for static and dynamic analysis of non-homogeneous plane trusses

Based on Chebyshev interpolation and Gauss-Lobatto quadrature together with the variational principle, an improved weak-form quadrature element (IWQE) method is developed and further customized for analyzing plane truss structures. Compared to existing WQE method which adopts Lagrange interpolation and Gauss quadrature, this developed IWQE method has demonstrated robustness for elements with a large number of quadrature points. Compared to finite element (FE) method whose stiffness matrix of an element is positive and semi-definite, the stiffness matrix of the IWQE method of an element is always positive and definite. Therefore, the displacements of an element's internal nodes can be uniquely expressed by using the values of its end nodes only. Accordingly, the sizes of the assembled matrices only depend on the number of end nodes and the orders of the assembled matrices for the whole structure can be greatly reduced. Such attributes can substantially increase the computational efficiency. To validate the developed IWQE method, the static and dynamic analysis of a plane truss structure with non-homogeneous properties are taken as an example for case study. Compared to the other numerical methods, such as differential quadrature element (DQE), WQE and FE, this IWQE method developed in present work demonstrates better convergence, accuracy and robustness, providing a more efficient and powerful numerical tool for analyzing structures with non-homogeneous attributes.

CGO and SNS Optimization Algorithm for the Structures with Discontinuous and Continuous Variables.

This study aims to find discontinuous and continuous approaches to reducing the size of planar truss structures with a specified shape and topology. The member's section area has assumed to be a decision variable, and the objective function is to minimize their weight. The member stresses and node displacements are the constraints that must maintain within the allowed limits for each condition. Chaos game optimization (CGO) and social network search (SNS) algorithms were used to optimize four well-known planar truss structures. In discontinuous-size cases, the results of the social network search (SNS) algorithm are the most cost-effective. However, the results of the chaos game optimization (CGO) algorithm are the most cost-effective in continuous-size cases.

A hybrid method for optimization of frame structures with good constructability

Frame structure optimization is a design problem posed to find an optimized structural member layout and the most suitable cross-sectional size according to the design requirements. This study proposes a hybrid optimization method, which integrates the continuum topology optimization, the transformation process, and size optimization to achieve this goal. Firstly, the continuum topology optimization is carried out to get the rough layout of structural members. Then using the method proposed in this paper, the result of continuum topology optimization is transformed into a frame structure which uses only non-curved and prismatic members to ensure ease of constructability. Finally, member sizes of the frame structure are optimized to obtain the optimal design of the structure. The high efficiency of the employed continuum topology methods significantly reduces the computational intensity of this three-step hybrid optimization method compared to that of the commonly-used discrete optimization method. This hybrid method builds a bridge between continuum topology optimization and size optimization of structure members, and has a lot of different application scenarios, such as the optimization of the bracing system of high-rise buildings, or the layout of plane truss structures.

Real-time Bayesian damage identification enabled by sparse PCE-Kriging meta-modelling for continuous SHM of large-scale civil engineering structures

This work presents a surrogate model-based Bayesian model updating (BMU) approach for automated damage identification of large-scale structures, which outperforms methods currently available in the literature by effectively solving the real-time damage identification challenge. The computational difficulties involved in Bayesian inference using intensive numerical models are circumvented by implementing a high-fidelity surrogate model and an adaptive Markov Chain Monte Carlo (MCMC) algorithm. The developed surrogate model combines adaptive sparse polynomial chaos expansion (PCE) and Kriging meta-modelling. The optimal order of the polynomials in the PCE is automatically identified by a model selection technique for sparse linear models, the least-angle regression (LAR) algorithm. Then, the optimal PCE is inserted into a Kriging predictor as the trend term, while the stochastic term is fitted through a global optimization algorithm. Afterwards, the surrogate model bypassing the original numerical model is used for BMU exploiting monitoring data extracted from continuous ambient vibration measurements. The computational demands of the MCMC algorithm are kept minimal by implementing an adaptive Metropolis sampling with delayed rejection (DRAM). The effectiveness of the proposed methodology is demonstrated through three case studies: an analytical benchmark; a planar truss structure; and a real case study of an instrumented historical tower, the Sciri Tower in Italy. The presented results demonstrate that the proposed BMU approach is compatible with real-time Structural Health Monitoring (SHM), providing promising evidence for the development of digital twins with superior probabilistic damage identification capabilities.

Algorithms for Large Scale Additive Manufacturing in a Free-Flying Environment

Large scale additive manufacturing (LSAM) refers to the fabrication of structures that exceed the build volume of conventional additive manufacturing setups. This can be used for in-space manufacturing (ISM), facilitating the production of large functional structures in space which cannot fit within the payload fairing of a launcher system. In this paper, a new approach for a continuous fabrication process of structural elements is presented, combining the reach of a free-flying satellite and a robotic arm, utilizing a fused filament fabrication (FFF) 3D-printing setup. A motion planning algorithm was developed which calculates energy-efficient movement trajectories based on a truss design input combined with the movement constraints of the satellite and robotic arm. Using this printing paradigm, a long support-free truss was manufactured. This approach was further elevated by extending the truss structure along the second planar axis, thus facilitating the manufacture of structures larger than generally possible through a layer-by-layer approach. Subsequently, combining the segmented and continuous printing approach, a planar truss structure was produced.

Pengembangan Aplikasi Analisis Struktur Rangka Batang Bidang Berbasis Antarmuka Pengguna Grafis

This research develops an analysis structure program for plane truss structure using stiffness matrix method and based on graphical user interface. The program is developed using GUIDE feature from MATLAB R2014 software. The features that were developed of this program is to analyze the reaction forces, internal forces and global displacement for plane truss structure. There are 3 (three) types of plane structures were considered. Reaction forces, internal forces and global displacement which obtained from the program were compared to commercial program which is ETABS 2016. Based on the result, there is not significantly different between the program which developed and ETABS 2016 for reaction forces, internal forces or global displacement. Therefore, the program can be an alternative software to analyze plane truss structure

Geometric and Material Nonlinear Analyses of Trusses Subjected to Thermomechanical Loads

In this article, geometric and material nonlinear analyses of planar and space trusses subjected to thermo-mechanical loads are performed using the Total Lagrangian formulation. The material properties are Thermally InDependent (TID). By obtaining the equilibrium path of these structures, their buckling and post-buckling behaviors are predicted under thermal and mechanical loads. To consider material nonlinearity, a mixed isotropic–kinematic hardening criterion is developed in this formulation. The behavior of material is assumed to be bilinear. To solve nonlinear equations iteratively, the Generalized Displacement Control Method (GDCM) is used. The authors’ scheme is general and can be employed for different types of planar and spatial truss structures having complicated geometries and behaviors. Several popular benchmarks are considered to show the accuracy and correctness of the proposed formulation. Corresponding equilibrium paths and stress–strain curves are reported for each problem.

A novel joint sparse regularization model to structural damage identification by the generalized fused lasso penalty

The sparse regularization (SReg) model is widely used for structural damage identification by employing the sparsity peculiarity of the structural damage. The conventional SReg model often separately conducts damage identification on each measurement, while ignores the utilization of the similarity information among different measurements. In this paper, we propose a novel joint sparse regularization model for structural damage identification. In detail, combined with the sparsity of the structural damage by the conventional SReg model, our model employs the similarity of different measurements to further improve the damage identification performance, which is realized by the generalized fused lasso penalty. Numerical simulations on the six-bay planar truss structure and experimental studies on the cantilever beam structure illustrate that the damage identification accuracy of our model is promoted 3.59% and 20.75% than the conventional SReg one, respectively.

Deformation Performance Analysis of a Truss Structure Based on the Deformation Decomposition Method

Trusses are among the basic components of large-span bridges and large-space structures. A method is proposed to conduct a comprehensive deformation analysis of a truss in terms of the basic rigid body displacements and the tension and compression deformation based on complete mathematical orthogonality and mechanical equilibrium. The correctness of the proposed method is verified by comparison with a traditional strain analysis. Furthermore, a relative deformation decomposition of the mode shape is proposed to analyse in detail its relative displacement and deformation. The correctness and superiority of the proposed method are verified by comparison with the modal mass participation coefficient method and the animation from observation method. Additionally, the relative deformation decomposition of a plane truss structure is realized under any load conditions based on the superposition of mode shapes. The quantitative analysis of the basic deformation performance of a plane truss structure can also be conducted by countable mode shapes, which do not involve load conditions. Finally, the number of mode shapes that must be considered differs when using the maximum displacement and the tension and compression deformation analysis indicators.

Calculation and Analysis of Truss Internal Force Based on Beam Element

For plane truss structure, starting from the analysis of ideal truss model, the influence of tangential deformation and angular deformation on the secondary internal force of the truss is fully considered through Python program. It is obtained through analysis that: in the ideal truss model, the Pδ second-order effect causes the member to produce tangential deformation and angular deformation, resulting in secondary internal forces. Numerical analysis shows that due to the influence of secondary internal force, the axial force error of ideal truss model can reach 19.731% and the secondary shear force is almost all the members of the truss, and the secondary moment only appears at the support. The research results have important reference value for the engineering design and high-precision internal force analysis of truss structures.