Truss Research Articles

Least failure energy density: A comprehensive strength index to evaluate and optimize heterogeneous periodic structures

Assessing the comprehensive strength of structures under multiple loading conditions is crucial for designing microstructures. This paper proposes the use of the least failure energy density (LFED) to measure the comprehensive strength of heterogeneous periodic structures, which corresponds to the minimum energy density required to destroy a structure. To enhance the comprehensive strength of a periodic structure, the LFED can be maximized. We constructed a two-layer optimization algorithm and found that the high time consumption renders topology optimization unfeasible. We subsequently developed an approach for solving inner-layer optimization analytically and quickly so that the problem becomes a single-layer optimization. We compared the LFED of several classical structures, including plate structures, lattice structures, and TPMSs. The calculations reveal that plate structures exhibit the best performance in terms of LFED, followed by TPMSs whereas truss structures have the poorest performance. Among the three types of classical structures, the octet plate, Schwartz-D minimal surface, and octet truss structures are the best-performing types, respectively. Additionally, the LFED is combined with the BESO topology optimization method to obtain the best 2D periodical structure, a 2D curved-edge kagome structure. For optimal 3D periodical structures, rarely discussed space kagome structures (plate or lattice) are obtained with an LFED superior to that of other counterpart classical structures.

Coupling model between building post structure and floors with the spectral element method

With the densification of urban area and public transport, the structure-borne noise disturbance due to railway traffic is a major issue. In order to mitigate it, ground-borne vibration propagation in building has to be investigated. The case of post-beam constructions necessitates 3D modeling with choices between complex, precise and computationally time-consuming approaches (3D finite element method for example), and fast but less accurate approaches like the statistical energy analysis (SEA) which need a strong modal density. For such post-beam constructions, the spectral element method (SEM) appears to be a good compromise. This method allows reducing the number of elements to represent the truss structure compared to the finite element method. However, the building walls and floor are difficult to consider with the SEM. In this paper, the challenge of coupling post-beam structures and floors is examined, a method is proposed and results are discussed. The aim is to develop a method applicable to different buildings while keeping advantage of SEM low discretization.

Truss sizing optimum design using a metaheuristic approach: Connected banking system

Several methods have been used to solve structural optimum design problems since the creation of a need for light weight design of structures and there is still no single method for solving the optimum design problems in structural engineering field that is capable of providing efficient solutions to all of the structural optimum design problems. Therefore, there are several proposed and utilized methods to deal with optimum design issues and problems, that sometimes give promising results and sometimes the solutions are quite unacceptable. This issue with metaheuristic algorithms, which are suitable approaches to solve these set of problems, is quite usual and is supported by the “No Free Lunch theorem”. Researchers try harder than the past to propose methods capable of presenting robust and optimal solutions in a wider range of structural optimum design problems, so that to find an algorithm that can cover a wider range of structural optimization problems and obtain a better optimum design. Truss structures are one of these problems which have extremely complex search spaces to conduct search procedures by metaheuristic algorithms. This paper proposes a method for optimum design of truss sizing problems. The presented method is used against 6 well-known benchmark truss structures (10 bar, 17 bar, 18 bar, 25 bar, 72 bar and 120 bar) and its results are compared with some of the available studies in the literature. The performance of the presented algorithm can be considered as very acceptable.

Research on the load transfer performance of large-span steel truss cable-stayed bridge structures

Since the wave is accompanied by the transfer of energy in the process of transmission, and the energy density at the node directly affects the bearing capacity and service performance of the steel truss cable-stayed bridge members and joints, this paper quantitatively studies the energy density at the key nodes of the long-span steel truss cable-stayed bridge from the perspective of the wave response of the structure. Firstly, according to the drawings of Xiangshan Bridge, a local finite element model of the steel truss cable-stayed bridge is established, and by changing the angle between the cable and the steel truss girder and the bending stiffness of the cable, the variation law of energy density at the connection node between the cable and the steel truss girder is obtained by changing the angle between the cable and the steel truss girder and the bending stiffness of the cableway. Due to the limitations of finite element wave analysis, from the perspective of theoretical analysis, this paper establishes the local scattering matrix at the node, proves the obtained law to a certain extent, and uses the return wave-light matrix method to analyze and solve the energy density at the connection node between the cable bar and the steel truss girder, and the final analytical solution is in good agreement with the numerical solution, which proves that the law obtained by numerical analysis is correct.

Robustness of a Steel Truss Bridge Subjected to Sudden Member Breakage during the Continuous-to-Simply-Supported Transition

Steel truss bridges are especially vulnerable in the event of a sudden loss of a load-carrying element, which can trigger a chain of failures. This paper describes a unique case study of a steel truss bridge under construction subjected to sudden member breakages with an extensive monitoring system. The failures occurred during the dismantlement of temporary members that had been used to transform a three-span simply supported steel truss bridge into a three-span continuous structure during incremental launching. These temporary members needed to be removed once the bridge reached its final position. The robustness of the bridge was assessed using computer simulations of various failure scenarios to evaluate its capacity to effectively activate alternative load paths (ALPs). The results demonstrated the structural redundancy of the steel truss bridge. However, the dynamic response resulting from the failure of the temporary upper chord, due to the initially high tension in the rods, should not be overlooked. To mitigate this issue, a structural retrofitting method was proposed, involving jacking the truss girder above the side pier to reduce the tension in the temporary upper chord above the middle pier. The effectiveness of this method was demonstrated through both simulated and formal experimental tests.

High speed vibration compensation using magnetic fiducials via NIMBLE

Additive manufacturing (AM) technology, specifically 3D printing, holds great promise for in-orbit manufacturing. In-space printing can significantly reduce the mass, cost, and risk of long-term space exploration by enabling replacement parts to be made as needed and reducing dependence on Earth. However, printing in a zero-gravity environment poses challenges due to the absence of a rigid ground for the print platform, which can result in vibrational and rotational forces that may impact printing integrity. To address this issue, this paper proposes a novel linear magnetic position tracking algorithm, named Navigation Integrating Magnets By Linear Estimation (NIMBLE), for dynamic vibration compensation during 3D printing of truss structures in space. Compared to the most commonly used nonlinear optimization method, the NIMBLE algorithm is more than two orders of magnitude faster. With only a single 3-axis magnet sensor and a small NdFeB magnet, the NIMBLE algorithm provides a simple and easily implemented tracking solution for in-orbit 3D printing.

An integrated optimization method for the damper placements, shape and size of truss structures

This work extends the application of the approximation concept in dynamic topology optimization for truss structures. The corresponding problem contains both continuous and discrete variables, encompassing damper placements, truss shape and cross-sectional area. First, the utilization of a branched multipoint approximation (BMA) function establishes sequential approximation problems that also involve such mixed variables, marking its innovative application in dynamic optimization. Then, a modified genetic algorithm (GA) is used to optimize discrete variables. To enhance convergence stationarity, the concept of ‘adjacent individuals’ is proposed to control the degree of difference in topology configuration between initial population members and the current optimal. Additionally, adjustments to the sequence-based crossover process ensure compliance with damper quantity constraints. Examples demonstrate that the introduction of adjacent individuals is beneficial to convergence stationarity, and the shape change of the truss increases the mode damping ratio by more than 20%. The created optimization platform can also tackle other mixed variables optimization problems.

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.

Designs and mechanical responses of 3D-printed Ti6Al4V porous structures based on triply periodic minimal surfaces with different iso-values

With the increasing applications of additive manufacturing in orthopaedic implants and numerous designs of porous structures available, there is a strong need and opportunity to optimize the structure designs for improved bone integration. Here we created a unique group of sheet structures based on triply periodic minimal surface (TPMS) by varying the iso-value and systematically examined how iso-value influences the mechanical performance of sheet diamond TPMS structures compared to the Octet truss structure. Four iso-values (C) 0, 0.25, 0.5, and 0.75 were designed for sheet Diamond (OSD) TPMS with varying porosity, and Ti6Al4V powder bed fusion was used to produce the porous structures. Compressive tests revealed that iso-value C significantly affected mechanical performance, and interestingly, the impact was porosity-dependent. At high relative density (>0.25), OSD0 (C = 0) displayed the highest elastic modulus and yield strength, whereas at low relative density (<0.25), OSD0.5 showed the highest among all OSD structures. Regarding failure mechanisms, OSD0, OSD0.25, and OSD0.75 showed a mixed domination of stretching and bending, while OSD0.5 was predominantly stretching-dominated. Finite Element Analysis (FEA) found that local yielding initiated at cell nodes upon loading, followed by surface bending and the formation of single or multiple shear bands near the cell nodes. This work demonstrated the feasibility of improving the mechanical performance of porous TPMS structures by simple adjustments in their governing trigonometric functions, serving as a starting point to customize porous structures for specific applications.

Bionic Robot with Multifunctional Leg-Arm Mechanism for In-Orbit Assembly of Space Trusses.

This article aims to address the in-orbit assembly needs of truss structures in space missions by designing a robot capable of moving on trusses and manipulating parts. To enhance the stability of the robot during movement and part manipulation, inspiration was drawn from the Dynastes Hercules beetle. Building upon detailed research on the Dynastes Hercules beetle, a biomimetic structure was designed for the robot system. Based on specific task requirements, the overall plan of the robot was developed, and its kinematic and dynamic models were derived. A prototype of the robot was created, which is capable of both movement and assembly functions, including handling spherical and rod-like objects. Through a series of experiments conducted with the robot, the research results demonstrated that the proposed design can effectively achieve the intended functions.

Flexural behavior of a UHPC slab - FRP truss hybrid beam implementing a novel FRP joint and tailored shear connector

A full-scale hybrid beam consisting of a UHPC slab and FRP truss girder was fabricated. The novel side plate FRP joint characterized with improved load-carrying capacity, stiffness, and preferred failure mode along with the tailored shear connector validated in the previous studies of the authors were adopted. Its flexural performance was characterized and compared with that of hybrid beams employing NC or UHPC slab but I-profile girder. The failure of the proposed hybrid beam subjected to bending was pseudo ductile whereas those of the other two hybrid beams were brittle. The load-carrying capacity and stiffness of the proposed hybrid beam outperformed the other two hybrid beams with comparable dimensions and material properties.

Kajian Struktur Rangka Batang Jembatan Wailola Besar Kabupaten Seram Bagian Timur

The Wailola Besar Bridge, which is located in Bula District, East Seram Regency, has a Warren truss type frame structure. However, unlike the truss used on other bridges, the truss on the Wailola Besar bridge has a larger size than the others. Because the span of the Wailola Besar bridge is 80 m, while the span of other bridges using the Warren truss type is a maximum of 60 m. The larger size than the other trusses makes the Wailola Besar bridge have a different truss from other trusses. The length of each horizontal bar is 6.65 m, while the maximum length for other bridges is 5 m. Then the purpose of this study is to determine whether the truss structure of the Wailola Besar bridge is capable of carrying the loads acting on the bridge, the method used is with the help of the SAP-2000 program to determine the truss forces then controlled with allowable voltage. In order to know whether the structure is able to withstand the forces acting. From the results of calculations with the help of SAP-2000 the rod forces acting on the largest truss structure are 11066.881 KN at constant loading and 12222.547 KN at temporary loading and the stress that occurs is 1742.82 Kg/〖cm〗^2. at constant loading and 1924.81 Kg/〖cm〗^2. The stress that occurs in the truss does not exceed the allowable stress.

Plane straight element with semi-rigid connections: formulation from an energetic approach

Discrete connectors, such as screws, nails, and others, are commonly used to fasten various structural elements. The established hypothesis regarding the behavior of joints conceived with discrete connectors directly impacts the distribution of forces. For example, in the design of truss structures, the resisting moments that arise due to the arrangement of the connectors are often disregarded, as considering the semi-rigid behavior of the joints introduces greater complexities in the modeling required to determine displacements and internal forces. This work presents the stiffness matrix of a plane straight element with semi-rigid connections and its support reactions for three loading cases from the application of the Principle of Virtual Work (PVW). Semi-rigid connections are represented by translational and rotational linear elastic springs at both ends of the element, giving it six degrees of freedom. One example shows the application of this formulation using the Classical Displacement Method and the results are also obtained numerically via the Finite Element Method (FEM)This work presents the stiffness matrix of a plane straight element with semi-rigid connections and its support reactions for three loading cases from the application of the Principle of Virtual Work (PVW). Semi-rigid connections are represented by translational and rotational linear elastic springs at both ends of the element, giving it six degrees of freedom. One example shows the application of this formulation using the Classical Displacement Method and the results are also obtained numerically via the Finite Element Method (FEM).

Numerical analysis of enhanced heat transfer and nanofluid flow mechanisms in fan groove and pyramid truss microchannels

A combined groove and truss structure is designed for rectangular microchannel heat sinks with 4 % Al2O3 nanofluid as the working fluid to address the heat dissipation requirements of high heat flux density electronic devices. The effects of fan shape, elliptical, waterdrop, rectangular, trapezoidal and triangular grooves on the heat transfer characteristics and mechanical properties of microchannels are investigated. The fan-shaped groove microchannels with the best overall heat transfer performance and excellent mechanical properties. The stress of the fan-shaped grooved truss microchannel is reduced by 76.41 % compared to the smooth microchannel. Three structural parameters were investigated, including the length of the truss in the spreading direction (Lx), the ratio of truss flow downstream length to upstream length (e) and truss rod diameter (d). The performance of the microchannels is reflected by the integrated heat transfer factor and the field coordination number. The individual structural parameters were analysed in a single-factor comparison. The microchannels exhibited the best hydrothermal performance in the Reynolds number range of 500 ∼ 1300 at Lx = 0.8 mm, e = 3, d = 0.2 mm. When the Reynolds number is 900, the microchannel with the optimal parameter combination exhibits a remarkable enhancement of 234 % in the Nusselt number and an 80 % increase in the integrated heat transfer factor compared to the rectangular microchannel.

A feasible smoothing accelerated projected gradient method for nonsmooth convex optimization

Smoothing accelerated gradient methods achieve faster convergence rates than that of the subgradient method for some nonsmooth convex optimization problems. However, Nesterov's extrapolation may require gradients at infeasible points, and thus they cannot be applied to some structural optimization problems. We introduce a variant of smoothing accelerated projected gradient methods where every variable is feasible. The O(k−1log⁡k) convergence rate is obtained using the Lyapunov function. We conduct a numerical experiment on the robust compliance optimization of a truss structure.

Generalization gap estimation for damage classification tasks when finite element simulated data is used for training: A numerical study and experimental validation on a steel truss

Labeled simulated structural responses by Finite Element (FE) methods may be used to construct training sets for monitoring the health state of structures. Such an approach appears to be an attractive way to avoid experimental costs. However, the main obstacle is the simulation error contained in such numerical responses. The error can contaminate the training data and lead to wrong conclusions when the learned features try to generalize on subsequent online experimental data. It is therefore very important to have an estimation of how good the available simulated data is for a given problem. The present work gives a novel methodology where classifiers trained by FE vibration response data are subjected to inputs of various perturbations, emulating in such way the generalization gap (classification errors) due to simulation errors. The response of the classifiers is gathered afterwards in a dataset which is used to construct a function that estimates the generalization gap based on the perturbed intact state response. Results are presented that show the behavior of the proposed gap estimation function for different binary damage classification scenarios. A numerical truss structure is used to test the concept. Convolutional Neural Networks (CNN) are applied for all data-driven related tasks, such as learning of health state features in vibration responses or evaluation of the gap function. The results show a promising methodology that can be used to estimate the reliability of numerically trained classifiers. In the final part of this study, the framework is tested on an experimental truss structure. The presented methodology contributes to the quantitative study of uncertainty when extrapolating from the numerical to the experimental domain in the presence of modeling errors.

Dynamic Characteristics of LIT Girder Railway Bridges

This study analyzed the dynamic characteristics of railway bridges with low-weight, innovative truss (LIT) girders and evaluated their dynamic behavior under general and high-speed railway operating conditions. A dynamic analysis was performed considering various variables, including the span length (30, 35, 40, or 45 m), track (single or double), main girder type (three or five girders), track type (concrete or ballast), and train type (KTX, HEMU, freight train, Mugunghwa, or express EMU). The train load was modeled as a moving concentrated load, and the damping ratio was applied according to railway design standards. The results of the dynamic analysis showed that in most cases, railway bridges with LIT girders met the allowable criteria for vertical deflection, vertical acceleration, and warping. However, in the case of a 30 m span bridge, the vertical acceleration exceeded the allowable limit at a specific speed of the HEMU-430X high-speed train. The results of this study can be used to evaluate the applicability of LIT girders in railway bridges and provide useful information for future design and construction.

Digital twin method for intelligent lifting of cable structures under multi-collaborative mode

In order to ensure the high efficiency and quality consistency of cable structure in each construction stage, this study proposes a digital twin method for intelligent lifting of cable structure under multi-collaborative mode. Firstly, a construction and operation methods of the digital twin logic model are formed. In the logical model, a relationship between the transmission and iteration of construction information in the collaborative process is defined. In order to realize the adaptability of working conditions, the coupling relationship between construction step and structural elevation is established. A cable structure lifting analysis model driven by an improved long short-term memory neural network is proposed, which effectively solves the problem of poor convergence of the traditional finite element method. An automatic time window selection method is formed for the neural network. An adaptive moment estimation method is used for neural network parameter optimization, which improves the efficiency and accuracy of the analysis. Taking the lifting process of a cable truss structure test model as an example, a digital twin collaborative construction platform is established to verify the effectiveness and feasibility of the research method. The results show that the digital twin logic model realizes the process collaboration, scene collaboration and data collaboration, and significantly improves the stability of construction quality and the linkage of construction process. Through the improved long short-term memory neural network, the coupling relationship between the construction step and the structural elevation is established, which accurately guides the whole construction process.

Glubam roof truss with riveted glubam connections adopting thin-walled steel tube: Experiment, modeling, and model-updating

Bio-based laminated structures offer a timely solution to meet the pressing demand for resource-efficient and environmentally responsible construction practices in civil engineering. Riveted connections are a kind of commonly used joint and significantly impact the mechanical behaviors of global structure. However, existing studies on the complex behavior of such joints for bamboo-based structures are insufficient. This study investigated the hysteretic behavior of riveted Glued Laminated Bamboo (glubam) connections using thin-walled steel tube and corresponding planar roof truss with thin-walled steel tube connections by experimental and numerical methods. Firstly, cyclic tests were conducted on the riveted glubam connections with thin-walled steel tube to investigate their hysteretic behavior. The test matrix encompasses four distinct connection configurations, carefully selected to assess the connection behavior of glubam. After the investigation of connection behavior, cyclic tests were further conducted on glubam planar roof truss structures to evaluate their global and local hysteretic behavior. Subsequently, the numerical hysteretic models for joints and hybrid roof trusses were developed within the OpenSeesPy framework. To accurately and efficiently calibrate the model parameters, a novel parallel genetic algorithm (PGA) was proposed to carry out an initial calibration on model parameters. Based on PGA, a more comprehensive model updating framework combining the neural network, prior knowledge and PGA was developed to obtain optimal parameters. Finally, the numerical models were successfully validated against the experimental data, demonstrating the effectiveness of the established numerical model and model-updating framework.

Sensitivity analysis of frequency response functions with imaginary parts decoupling based on multicomplex-step perturbation

Imaginary perturbation is used in the complex step differentiation method to compute first-order derivatives, widely known as an effective approach for sensitivity analysis in structural dynamics. However, coupling of imaginary parts occurs in the damped frequency response functions when employing this method. To mitigate this coupling, a novel approach for sensitivity analysis based on multicomplex-step perturbation is proposed in this paper, for sensitivity analysis of Frequency Response Functions in structural dynamics. The structural parameters are perturbed in multicomplex domain, the dimensions of structural matrices are expanded using the Cauchy Riemann matrix representation, the equation of motion for sensitivity analysis in frequency domain is transformed to matrix operation in field of real numbers, imaginary term will not exist in the equation of motion for sensitivity analysis, the imaginary part of the frequency response function and the imaginary part of the perturbation are decoupled, the structural frequency response functions and the corresponding sensitivities are obtained from the dimension-expanded equation of motion. A truss structure and a solar wing are adopted to verify the accuracy of the proposed method. Results show that the sensitivity of FRFs can be effectively calculated using the proposed method. Compare to the finite difference method, the proposed method is not depended on the step-size selection procedure. The multi-order and mixed-order sensitivity matrices, especially Hessian matrix can also be obtained using the proposed method.