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Curved shells are increasingly utilized in applied engineering due to their shared characteristics with other sandwich structures, flexibility, and attractive appearance. However, the inability of controlling and regulating vibrations and destroying them afterward is a challenge to scientists. In this paper, the curve shell equations and a linear quadratic regulator are adopted for the state feedback design to manage the structure vibrations in state space forms. A five-layer sandwich doubly curved micro-composite shell, comprising two piezoelectric layers for the sensor and actuator, is modeled by the fourth-order shear deformation theory. The core (honeycomb, truss, and corrugated) is analyzed for the bearing of transverse shear forces. The results show that the honeycomb core has a greater effect on the vibrations. When the parameters related to the core and the weight percentage of graphene increase, the frequency increases. The uniform distribution of graphene platelets results in the lowest natural frequency while the natural frequency increases. Furthermore, without taking into account the piezoelectric layers, the third-order shear deformation theory (TSDT) and fourth-order shear deformation theory (FOSDT) align closely. However, when the piezoelectric layers are incorporated, these two theories diverge significantly, with the frequencies in the FOSDT being lower than those in the TSDT. [ABSTRACT FROM AUTHOR]

Typical household recyclable bin in Australia contains around 60% of waste cardboard. Given the possibilities of developing a construction material, this study conducted a life cycle assessment (LCA) comparing the development of cardboard trusses with © timber trusses, encompassing production to construction. The results show that cardboard trusses offer significant environmental benefits, including a 73% reduction in climate change category, an 83% decrease in ozone-depleting potential, and almost complete avoidance of agricultural land occupation compared to timber trusses, showcasing their sustainability. In both material manufacturing and material transportation, cardboard trusses prioritize climate change mitigation, accounting for over half of the environmental impact. Timber trusses, in contrast, heavily impact land occupation and exhibit climate change dominance. A benefit analysis highlights advantages of cardboard trusses, particularly in reducing land occupation, sustainability, circular economy, and particulate matter formation. The life cycle cost analysis demonstrates an impressive 83% cost reduction for cardboard trusses compared to timber trusses, despite higher labor costs during manufacturing. [ABSTRACT FROM AUTHOR]

Introduction. Quantitative assessment of the structural reliability and safety level for structural solutions is an actual scientific and technical problem. The measure of reliability in this case can be the failure probability of a structural element. In practical problems of assessment and analysis of structural reliability, data on random variables can be obtained in the interval form (qualitative uncertainty), while the classic methods of reliability analysis do not allow to estimate reliability in the presence of such data. Lack of statistical data (quantitative uncertainty) is also present in practical tasks of reliability analysis.Materials and methods. The paper considers the use of the theory of evidence as an effective tool for reliability analysis of steel span structures in problems with interval uncertainty of statistical data.Results. The graphical interpretation of the reliability analysis algorithm is given. It allows to obtain clearly and operatively an estimate of the failure probability of the structural element, as well as to reduce the permissible load on the element to the required reliability level. Two-dimensional and three-dimensional models are considered for analyzing the reliability of a steel truss bar according to the buckling criterion.Conclusions. The theory of evidence allows effective modelling of various sources of uncertainties in practical engineering problems. Thus, with limited data, it is possible to get an idea of the quantitative expression of the reliability level by its lower bound, which can be increased by strengthening the element, more detailed probabilistic analysis or limiting the operational load on the structural element. By considering more non-deterministic quantities in the design, the engineer obtains a more cautious decision. When considering the cross-sectional area as a random variable, the reliability of the truss bar on the buckling was 23 % lower (lower reliability bound) than in a similar calculation with a deterministic value.

The next generation of large space infrastructure will require crucial advancements in current technology. Current methodologies focus on large deployable structures folded into cramped payload fairings or revolutionary assembly techniques requiring many moving components. Utilizing both in-space assembly and deployable concepts, a hybrid mixed assembly scheme was posed using smaller deployable units interspersed with rigid connecting elements to assemble these large architectures. The Built On-Orbit Robotically Assembled Gigatruss (BORG) structure allows for modularity in assembly and repair with the number of separate elements comprising the structure to be reduced, compared to strut-by-strut assembly. The following documents the process of constructing and running physical trials on a prototype BORG architecture. Additionally, a Semantic and Fiducial Aided Graph Simultaneous Localization and Mapping (SF-GraphSLAM) approach is taken to verify the relation of assembled and deployed truss elements to aid in error evaluation and state estimation. This technology demonstration stands as a proof of concept in verifying the viability of the BORG architecture as a method for large structure assembly. [ABSTRACT FROM AUTHOR]

An analysis of changing patterns of the values of member forces in a scissors truss, depending on the position of connections of its lower chords to the upper chords, is performed. Exploring effective truss structure designs in terms of balanced combination of maximum strength and minimum weight is a sustainable approach to a more rational use of building materials and the development of green construction. This determines the relevance of this area of research. The analysis of configurations of the truss under study was performed using the parameterized Maxwell - Cremona diagram. Such diagram is a visually informative tool in presenting the calculation results and it fully reflects the relationship between the member forces and the parameters of the structure. The research process was performed using the MS Excel spreadsheet editor. This eventually developed into a software tool for finding effective scissors truss designs, which has full potential for further improvement and development. Thus, the functionality of the tool can be easily expanded to designing scissors trusses made of various structural materials, as well as with various crosssectional shapes of its elements. The proposed approach to the calculation of such structures can serve as a basis for parameterization of trusses with other types of web.

Excessive time-consuming has been a great problem when applying metaheuristic algorithms to the optimization of structures using direct analyses, including steel truss structures. In this work, a robust optimization method was proposed to solve this issue. In the proposed method, an efficient variant of the differential evolution algorithm (DE), which was proved to be powerful in searching optimum designs and converged quickly, was employed as the optimizer. An effective framework based on LightGBM classification models was developed to save lots of time-consuming direct analyses required for evaluating constraints. To enhance the performance of LightGBM models, an adaptive parameter, which can reflect the convergence speed of the population, was proposed to prevent the imbalanced classification problem in the training data. Two truss optimizations with continuous design variables were studied, including a 47-bar power line and a 113-bar planar bridge. The results proved that the proposed method yielded better optimum designs than DE/best/1 and EpDE. It also saved more than 60% of time-computing compared to DE/best/1, EpDE, and 2EpDE. Besides that, the proposed framework for using LightGBM models was compatible with metaheuristics having different convergence rates, including DE/best/1, EpDE, and 2EpDE. [ABSTRACT FROM AUTHOR]

The paper is focused on the numerical analysis of the stability and load bearing capacity of a flat steel truss. The structure is supported by elastic lateral braces. The translational and rotational brace stiffness are taken into account. The linear buckling analysis is performed for the beam and shell model of the truss. The nonlinear static analysis is conducted for the structure initial geometric imperfections. As a result, the buckling and limit load depending on brace stiffness has been obtained. The reactions in elastic braces are compared to stabilizing forces calculated on the basis of actual code requirements. [ABSTRACT FROM AUTHOR]

Compared with natural wood, laminated veneer lumber has the characteristics of high strength, flexible specifications, excellent stability, and good economy. In order to study the bearing capacity of LVL trusses, the mechanical properties of LVL materials were tested. The static load test was carried out by using 3 pieces of LVL truss, and the load-deflection relationship, load-strain relationship, bearing capacity and failure mode of LVL trusses were studied. Based on the simplified joint analysis method, the metal plate connection and bolted truss were analyzed, and the bearing capacity calculation formula was developed. The results show that the upper chord instability is the main failure mode for large-span light LVL truss. A simplified formula for bearing capacity of LVL truss was proposed, and the predicted results were in good agreement with the experimental results. Finally, an application example of LVL truss engineering design and construction is briefly introduced. The research can provide technical support for the promotion and application of LVL truss of lightweight poplar wood.

Compared with natural wood, laminated veneer lumber has the characteristics of high strength, flexible specifications, excellent stability, and good economy. In order to study the bearing capacity of LVL trusses, the mechanical properties of LVL materials were tested. The static load test was carried out by using 3 pieces of LVL truss, and the load-deflection relationship, load-strain relationship, bearing capacity and failure mode of LVL trusses were studied. Based on the simplified joint analysis method, the metal plate connection and bolted truss were analyzed, and the bearing capacity calculation formula was developed. The results show that the upper chord instability is the main failure mode for large-span light LVL truss. A simplified formula for bearing capacity of LVL truss was proposed, and the predicted results were in good agreement with the experimental results. Finally, an application example of LVL truss engineering design and construction is briefly introduced. The research can provide technical support for the promotion and application of LVL truss of lightweight poplar wood. [ABSTRACT FROM AUTHOR]

This paper presents two hybrid optimization methods known as PSOHHO and DPSOHHO optimization algorithms. In the first method, using a number of formulae, the top populations are exchanged between the two algorithms and a new population is created and in the second method, we adopted the parallel optimization and optimized its performance. In this method, unlike other parallel methods, the population does not remain constant. With this ability, the strengths of an algorithm can be used to compensate for the weaknesses of the other algorithm. In these methods, no changes are made to the algorithms. The main goal is to use existing algorithms. These methods attain the optimal solution in the shortest time possible. Two algorithms of particle swarm optimization (PSO) and Harris Hawks's optimization (HHO) are used to present this method and two truss samples and CEC209 are considered to confirm the performance of this method. Based on the results, these methods have rapid convergence speed and acceptable results compared to other methods. [ABSTRACT FROM AUTHOR]

The present paper deals with the prediction of the fatigue life of a planar tubular truss, when geometrical parameters, material properties, and live loads are non-deterministic. A multi-level calculation uncertainty quantification framework code was designed to aggregate the finite element method and fatigue-induced sequential failures. Due to the incompleteness of the aleatory-type inputs, the maximum entropy principle was applied. Two sensitivity analyses were performed to report the most influencing factors. In terms of variance, the results suggest that the slope of the curve crack growth rate � stress intensity factor range is the most influencing factor related to fatigue life. Furthermore, due to the application of the entropy concept, the fatigue crack growth boundaries and fatigue crack semi-width boundaries obtained provide the most unbiased fatigue crack design mapping. These boundaries allow the designer to select the worst-case fatigue scenario, besides being able to predict the crack behavior at a required confidence level.

In this article, the object of research is spatial framed systems, one of the most commonly used types of spatial structures. The main feature of the research is the expansion of proven design solutions to the area of large-span frames with rectangular plan with an aspect ratio of less than 1:2, which is an urgent research and practical task. In this regard, the main purpose of the research study is to establish a connection between the main parameters of the projected object (geometric characteristics, structural loads) and their metal intensity. The study was based on a number of research methods. We used the finite element method in the numerical study of the coating stability of rods loaded in the axial direction. The method of physical modeling helped in experimental studies of models and coatings of their elements. Finally, the method of optimal design, specifically the Nelder–Mead method, was used to find the basic shape of a structure with a long-span rectangular plan. Main results. First, the data from theoretical and experimental studies confirmed a decrease in the estimated length of the compressed elements by 5...25 % due to their partial pinching in the ball nodes-connectors. Secondly, we developed an optimal design algorithm of spatial frames with long-span rectangular plans with an aspect ratio of less than 1:2. It differs from the previously developed ones due to a clarification of the load-carrying ability of axially loaded rods from the stability condition and the project designer's advanced capabilities in terms of their shaping. It provides an opportunity to use clear correspondences at the trial design stage and to clarify the specific metal consumption to set the optimal geometric parameters of the projected structure. We found patterns that make it possible to design optimal material consumption flat and spatial structural forms of spatial frames on rectangular large-span plans with an aspect ratio of less than 1:2, while taking into account the refined bearing capacity of rods loaded in the axial direction. The results obtained make it possible to use a proven limited range of structural elements in the form of round-section rods and connecting elements (ball-and-socket plug-connectors).

In the construction of modern bridges, tower cranes are used for vertical transportation and hoisting. In erecting and removing tower cranes, a high degree of risk occurs. Thus, we evaluated the risk of using tower cranes in construction and proposed preventive measures. [ABSTRACT FROM AUTHOR]

The present paper deals with the prediction of the fatigue life of a planar tubular truss, when geometrical parameters, material properties, and live loads are non-deterministic. A multi-level calculation uncertainty quantification framework code was designed to aggregate the finite element method and fatigue-induced sequential failures. Due to the incompleteness of the aleatory-type inputs, the maximum entropy principle was applied. Two sensitivity analyses were performed to report the most influencing factors. In terms of variance, the results suggest that the slope of the curve crack growth rate x stress intensity factor range is the most influencing factor related to fatigue life. Furthermore, due to the application of the entropy concept, the fatigue crack growth boundaries and fatigue crack semi-width boundaries obtained provide the most unbiased fatigue crack design mapping. These boundaries allow the designer to select the worst-case fatigue scenario, besides being able to predict the crack behavior at a required confidence level. [ABSTRACT FROM AUTHOR]

The next generation of large space infrastructure will require crucial advancements in current technology. Current methodologies focus on large deployable structures folded into cramped payload fairings or revolutionary assembly techniques requiring many moving components. Utilizing both in-space assembly and deployable concepts, a hybrid mixed assembly scheme was posed using smaller deployable units interspersed with rigid connecting elements to assemble these large architectures. The Built On-Orbit Robotically Assembled Gigatruss (BORG) structure allows for modularity in assembly and repair with the number of separate elements comprising the structure to be reduced, compared to strut-by-strut assembly. The following documents the process of constructing and running physical trials on a prototype BORG architecture. Additionally, a Semantic and Fiducial Aided Graph Simultaneous Localization and Mapping (SF-GraphSLAM) approach is taken to verify the relation of assembled and deployed truss elements to aid in error evaluation and state estimation. This technology demonstration stands as a proof of concept in verifying the viability of the BORG architecture as a method for large structure assembly.

This paper presents a multi-objective optimization of steel trusses using direct analysis. The total weight and the inter-story drift or displacements of the structure were two conflict objectives, while the constraints relating to strength and serviceability load combinations were evaluated using nonlinear inelastic and nonlinear elastic analyses, respectively. Six common metaheuristic algorithms such as nondominated sorting genetic algorithm-II (NSGA-II), NSGA-III, generalized differential evolution (GDE3), PSO-based MOO using crowding, mutation, and ε-dominance (OMOPSO), improving the strength Pareto evolutionary algorithm (SPEA2), and multi-objective evolutionary algorithm based on decomposition (MOEA/D) were applied to solve the developed MOO problem. Four truss structures were studied including a planar 10-bar truss, a spatial 72-bar truss, a planar 47-bar powerline truss, and a planar 113-bar truss bridge. The numerical results showed a nonlinear relationship and inverse proportion between the two objectives. Furthermore, all six algorithms were efficient at finding feasible optimal solutions. No algorithm outperformed the others, but NSGA-II and MOEA/D seemed to be better at both searching Pareto and anchor points. MOEA/D was also more stable and yields a better solution spread. OMOPSO was also good at solution spread, but its stability was worse than MOEA/D. NSGA-III was less efficient at finding anchor points, although it can effectively search for Pareto points. [ABSTRACT FROM AUTHOR]

In the construction of modern bridges, tower cranes are used for vertical transportation and hoisting. In erecting and removing tower cranes, a high degree of risk occurs. Thus, we evaluated the risk of using tower cranes in construction and proposed preventive measures.

Pipe bridges are structures that play an indispensable role in chemical and oil plants. They support cable trays or pipe-carrying material. This study aims to identify the ideal configuration of a pipe bridge through the comparative study of girders with drop hanger and truss arrangements for three different spans. The most efficient arrangement for each span was suitably identified. Through the analysis carried out, it was then identified that the Girder arrangement is suitable for smaller spans such as 15 meters; while the truss arrangement was preferable for longer spans. [ABSTRACT FROM AUTHOR]

Small-diameter round timber is a kind of by-product mainly from the thinning operation of the plantations. It is plentiful and inexpensive, and is generally destined for non-structural applications. The small-diameter round timber is rarely used as structural members. This study was aimed to provide an innovative but simple way to use the small-diameter round timber as structural members. Three kinds of composite members were developed to be used in light frame wood construction, i.e. the built-up studs, the wood-steel joists and the wood-steel roof trusses. The shearwalls and diaphragms made of the developed composite members were also examined. To facilitate the fabrication, the configurations of these members were described in details. Efforts were also made to investigate the structural performances of these members via full-scale tests. It was found that the developed composite members could be used as substitutes of dimension lumber in the framework of light frame construction. The developed members could be also pre-fabricated as standard components in a mill and assembled on site. As a result, application of small-diameter round timber as structural members developed would be an efficient way to increase use of forest resource from plantation and lower the construction cost of light frame buildings.

Metode elemen hingga adalah salah satu mata kuliah wajib pada hampir seluruh jurusan Teknik mesin di Indonesia. Pembelajaran mata kuliah ini biasanya dibantu menggunakan perangkat lunak komersial. Tetapi, penggunakan perangkat lunak komersial menyebabkan mahasiswa hanya memahami bagaimana menggunakan perangkat lunak tanpa memahami persamaan matematika dan bagaimana proses penyelesaiannya. Tujuan penelitian ini adalah mengembangkan perangkat lunak yang memungkinkan mahasiswa tetap memahami prosedur penyelesaian secara matematika dalam menyelesaikan sebuah masalah. Pengembangan perangkat lunak dilakukan dengan bahasa pemrograman MATLAB. Elemen truss dan aksisimetri digunakan sebagai contoh untuk implementasi pengembangan perangkat lunak. Hasil perhitungan perangkat lunak divalidasi dengan hasil perhitungan yang dilakukan dengan perangkat lunak LISA. Hasil validasi menunjukkan bahwa hasil perhitungan perangkat lunak yang dikembangkan memiliki tingkat kesalahan dibawah 1 % dibandingkan dengan hasil perhitungan perangkat lunak LISA. Dengan demikian maka perangkat lunak hasil pengembangan telah bekerja dengan benar.

In this paper deriving of dynamical model of the load-bearing structure in form of a Trusses of the excavator with rotor is elaborated. Finite Element Methods and real working conditions are used to derive the dynamical model and to perform the local linearization of the dynamic elastic line for the structure of the load-bearing of the excavator with rotor. As carriers with continuous masses were treated the upper bearing structure of the Dynamical model and the truss levels. Finally, in accordance with the requirements of the problem, the degrees of freedom and the reference nodes are selected. The second stage of reduction, represents the final formation of the dynamical model of the load-bearing infrastructure, which however must be more accurate during the dynamic behaviour of the excavator with the rotor. The exposed work with the formation of the dynamic model of the Truss bearing structure, enables the concrete solution of the oscillations of the excavator with rotor. In addition, the model is of a universal character, respectively, can also be used during the formation of the dynamical model of truss carriers in general.

Introduction. Truss structures are widespread in construction due to a number of advantages, such as economy, versatility, and scalability. Accordingly, their modeling and calculation are urgent tasks in the design of building structures. Automatic solution to these problems causes an increase in design efficiency, calculation accuracy, and lower costs. The objective of the study is to examine the functionality and operation algorithm of the software module developed by the authors that generates the geometry of two-dimensional truss structures for subsequent modeling.Materials and Methods. Following the research of the widespread truss configurations, the classification of chords available in the software under consideration is given. The method of parameterizing a truss structure is provided. This method includes base geometric parameters of the structure such as dimensions, model construction rules, and additional features, as well as a comprehensive algorithm. The software is developed in JavaScript.Results. The software module has been integrated into a web application for calculating two-dimensional rod structures. To illustrate the functionality of the software, the examples of user interface are given as well as an example problem. The example includes configuration and calculation of an inclined truss structure. The results, such as support reactions and internal forces with axial force diagram, are provided.Discussion and Conclusions. Using this software module within the framework of the tool for calculating rod structures allows for the simplified process of modeling and calculating complex truss structures, design time, and resource reduction. The software module provides tools for specifying various types of structures, applying loads and assigning properties of a rod system, which makes it a useful instrument for design engineers.

This paper explores a mixed assembly architecture trade study for a Built On-orbit Robotically assembled Gigatruss (BORG). Robotic in-space assembly (ISA) and servicing is a crucial field to expand endeavors in space. Currently, large structures in space are commonly only deployable and must be efficiently folded and packed into a launch vehicle (LV) and then deployed perfectly for operational status to be achieved. To actualize being able to build increasingly large structures in space, this scheme becomes less feasible, being constrained by LV volume and mass requirements. ISA allows the use of multiple launches to create even larger structures. The common ISA proposals consist of either strut-by-strut or multiple deployable module construction methodologies. In this paper, a mixed assembly scheme is explored and a trade study is conducted on its possible advantages with respect to many phases of a mission: 1) manufacturing, 2) stowage and transport, 3) ISA, and 4) servicing. Finally, a weighted decision matrix was created to help compare the various advantages and disadvantages of different architectural schemes.

The geometry of truss structure is expressed in terms of its nodal positions; that is, the nodal positions vector is the fundamental design variable for the optimal geometry design of a truss. In order to solve an optimal design problem, there are various approaches that uses differentiation of the objective function in terms of the design variable, such as the steepest descent method and the gradient projection method. Many of the objective functions of structural optimal design problems are formulated in terms of the stiffness matrix; the gradient or differentiation approach requires differentiation of the stiffness matrix in terms of the nodal positions vector. It is, however, not impossible but still impractical in many cases since we have to deal with the third-order differential coefficient tensor. In this paper, we deal with the differentiation of the product of the stiffness matrix and a vector in terms of the nodal positions vector. We develop a formulation in general form that can be applied to trusses of any configuration. Examples of optimal geometry designs of 2D and 3D trusses are demonstrated.

The main purpose of the reliability theory of structural systems is the optimal design based on the reliability concept. Trusses and space structures are widely used, and cost and safety both are important in these structures. Therefore the weight optimization of these structures based on the theory of reliability (probabilistic optimization) using Genetic Algorithms was studied in this paper. The objective function was weight of structure and the constraints were based on the failure probability of elements or nodes or the system. To increase the accuracy of structural safety calculations, the probabilistic form of buckling is presented in this research.The results of this study show that increasing the system allowable failure probability decreases the optimum weight of structure. The process of this weight loss occurred at first with a very fast slope and then with a gentle slope and finally tended to a constant value. Optimum weight was very sensitive to coefficient of variation comparison of allowable failure probability. In the probabilistic optimization, if the system allowable failure probability and coefficient of variation of load and yield stress are considered near zero, and if results are compared to the deterministic optimization, the difference in optimum weight is less than 9%. In this case, convergence for deterministic optimization was very fast and occurred in less than 20 generations but convergence in probabilistic optimization occurred slowly after 85 generations.

A topology formation method for frame and truss structures, which is relevant for use in computer-aided design, is proposed. A flat figure discretized into polygonal primitives is used as a basic structure. This structure is presented in the form of a finite element model and is assumed redundant. Its elements are excluded using the principle of maximizing the intensity of the force flow during the initial calculation and the shortest path of this force flow between the points that reflect force and kinematic connections. At the same time, the heuristic principle implemented in the ACO algorithms was used. Registration of geo-metrically variable systems is performed based on an estimate of the infinite norm of the stiffness matrix of the finite element model. For flat trusses and frames, examples of the formation of rational topolo-gies under given force and kinematic constraints are considered. Comparison with the method of redun-dant structure, which implements the exclusion based on the genetic algorithm, is performed. It has been shown that the proposed technique allows one to effectively select both one and several alternative vari-ants of the topology of bearing systems.

Being lightweight, strong, and tough, are qualities often sought-after in practical engineering materials. Herein, we present interpenetrating phase composites (IPC), based on the combination of additively manufactured alumina microlattices and infiltrated epoxy, that display an excellent combination of such characteristics. Experimental and simulation studies on the compressive behaviours of different truss-microlattices and their functionally-graded variants have been carried out. Lengthened stress plateau up to −0.6 strain and co-enhanced strength up to 65 % higher than the linear sum of their constituents have been observed. This constitutes a simultaneous high specific strength and specific energy absorption up to 113.5–142.6 MPa/(g/cm3) and 25.3–35.6 J/g, respectively, for the IPCs, at low densities of around 1.8 g/cm3. The mechanism of the co-enhanced strength attribute to the improved alumina fracture toughness whilst the lengthened plateau attributes to the progressive material failure and strain energy relaxation. Overall, this work demonstrates the potential of using a strong ceramic and epoxy to achieve simultaneously high specific strength and energy absorption.

• A robust and simple unsupervised neural network framework for large deformation analysis of truss structures. • Training data is small in size, independent of sampling procedures, without finite element analysis. • Reliability and stability of the proposed approach for nonlinear analysis without incremental-iterative techniques. In this study, a robust and simple unsupervised neural network (NN) framework is proposed to perform the geometrically nonlinear analysis of inelastic truss structures. The core idea is to employ the NN to directly estimate nonlinear structural responses without utilizing any time-consuming incremental-iterative algorithms as those done in standard finite element method (FEM). To achieve such an objective, the loss function built via the total potential energy principle under boundary conditions (BCs) is minimized in the suggested NN model whose weights and biases are considered as design variables. In our computational framework, spatial coordinates of truss nodes are treated as input data, whilst corresponding displacement degrees of freedom are taken account of output. At the beginning of each training step, feedforward is performed to get the predicted displacement field, and it is used to derive the loss function based on the physical law. Then, back-propagation is applied to update the parameters of the network. This adjustment, which is the so-called learning process, is repeated until the potential energy is minimized. Once the network is properly trained, the mechanical responses of inelastic structures can be easily obtained. The suggested methodology is also extremely simple to implement, while the unlabeled data is available, small in size, independent of sampling techniques, and without finite element analyses (FEAs). Several benchmark examples regarding geometrical and material nonlinear analysis of truss structures are tested to show the effectiveness and reliability of the proposed paradigm. Obtained outcomes indicate that the developed NN framework is robust and can be extended to apply for other structures. [ABSTRACT FROM AUTHOR]

This paper presents a multi-objective optimization of steel trusses using direct analysis. The total weight and the inter-story drift or displacements of the structure were two conflict objectives, while the constraints relating to strength and serviceability load combinations were evaluated using nonlinear inelastic and nonlinear elastic analyses, respectively. Six common metaheuristic algorithms such as nondominated sorting genetic algorithm-II (NSGA-II), NSGA-III, generalized differential evolution (GDE3), PSO-based MOO using crowding, mutation, and ε-dominance (OMOPSO), improving the strength Pareto evolutionary algorithm (SPEA2), and multi-objective evolutionary algorithm based on decomposition (MOEA/D) were applied to solve the developed MOO problem. Four truss structures were studied including a planar 10-bar truss, a spatial 72-bar truss, a planar 47-bar powerline truss, and a planar 113-bar truss bridge. The numerical results showed a nonlinear relationship and inverse proportion between the two objectives. Furthermore, all six algorithms were efficient at finding feasible optimal solutions. No algorithm outperformed the others, but NSGA-II and MOEA/D seemed to be better at both searching Pareto and anchor points. MOEA/D was also more stable and yields a better solution spread. OMOPSO was also good at solution spread, but its stability was worse than MOEA/D. NSGA-III was less efficient at finding anchor points, although it can effectively search for Pareto points.

The accurate understanding of the behavior and analysis of the structures is necessary to appropriate design of them. Over the past decades, various methods have been proposed for the analysis of structures that each of them include some deficiencies. The peridynamic is a new method for solving the problems. This method overcomes the deficiencies and limitations of conventional methods such as the finite element method due to its unique capabilities. Nowadays, it uses as a powerful method to solve problems. After the proposition of peridynamic theory in 2000, various problems have been solved. However, very limited work has been done in the solving longitudinal vibration of axial members and modeling of lattice structures. In this paper, the behavior of this type of members was examined by the peridynamics method and its capability to take into account the static and dynamic loading, as well as temperature variations, was shown using MATLAB software. The peridynamic results are in good agreement with analytical results. Also, for certain states of the problem, it is impossible or difficult to find an answer by analytical methods or other methods, while using the peridynamic method can easily be answered. Finally, the peridynamic model has been extended to truss modeling and the ability of this method to analyze any types of trusses were shown.

In order to effectively excite the local vibration mode of the structure,analyze response information and identify the damage,a structural damage detection method is constructed based on the excitation points optimization and energy of signals at different damage states. Firstly,the dynamic model of the structure is established and used to calculate the modal shapes,and then the minimum value of non-diagonal elements of MAC matrix is used as the fitness function. Modified particle swarm optimization（ MPSO） is used to optimize the number and position of excitation points,and evaluate of different excitation points arrangement schemes by MAC non-diagonal mean value and root mean square（ RMS） criterion. Then,the corresponding position of the truss test model is excited,and the time-domain signal energy at the measuring point before and after the damage is calculated,so as to identify the damage position and damage degree of the structure according to its relative change. In addition,the method can still identify the damage position and damage degree of the structure after Gaussian white noise with the signal-tonoise ratio of 10 dB is added to the signals at different working conditions. The experimental results verify the feasibility of the method.

The aim of the work - to propose a scheme and analytical calculation of a statically definable planar truss with a suspended lower belt. Methods. The formula for the dependence of the deflection of the truss under the action of a uniform load on the lower belt on its size and the number of panels is derived in the computer mathematics system Maple. The forces in the rods are found from the solution of the general system of equilibrium equations of all nodes in symbolic form. The deflection is calculated using the Maxwell - Mohr's formula. Generalization of a number of formulas for deflection obtained by increasing the number of panels sequentially to an arbitrary number is performed by double induction using two independent parameters. In this case, special operators of the Maple system are used, allowing for a sequence of coefficients in the desired formula to create and solve recurrent equations that satisfy the elements of the sequences. Results. The obtained solutions have a polynomial form for the number of panels. Curves of deflection dependence on the number of panels are constructed and analyzed. Asymptotic properties of solutions are found in the case of a fixed span length of the structure and a given total load. The proposed scheme is a statically determinate structure with two independent parameters of regularity allows for the finding of a fairly simple analytical solution. The resulting formula is most effective in calculating systems with a large number of elements, where numerical methods tend to accumulate rounding errors.

Relevance. Loads on structures are complex stochastic elements that include several types of uncertainties simultaneously. The article describes a probabilistic approach to the load modeling on structural covers taking into account limited statistical data, when the parameters of distribution functions are presented in an interval form. The aim of the work is development of an approach to modeling the probabilistic distribution of random load on the structural surface in conditions of limited (incomplete) statistical information about the design load. Methods. The probability distribution of a particular type of loading is represented as p-boxes (probability boxes). A numerical example shows an algorithm for determining a p-box consisting of a sum of p-boxes that characterize different loads with different boundary distribution functions. Results. Based on the proposed approach, it is possible to define the intervals of normative and design loads with a given confidence level, to estimate the failure probability of structural elements, to assess the risk of an accident and also to make selection for structural element cross-section at the target level of reliability.

A statically determinate truss of a beam type with a triple lattice with short descending and long ascending braces is considered. The mass of a truss is modeled by concentrated loads at its nodes. For the first natural frequency, the Dunkerley’s method derives a formula for the dependence of its lower boundary on the number of panels. The calculation of the efforts in the truss required to obtain the stiffness value according to the Maxwell-Mohr formula is performed in the Maple computer mathematics system by cutting out the nodes. It is shown that for a certain number of panels the proposed scheme of the truss has the property of kinematic variability. For admissible numbers of panels, by induction, the sequence of solutions for trusses with different numbers of panels is generalized to an arbitrary case. The coefficients of the required dependence are obtained as solutions of linear homogeneous recurrent equations. To obtain and solve recurrent equations, the operators of the Maple system are used. The found solution is compared with the minimum frequency of the spectrum obtained numerically. It is shown that the accuracy of the analytical assessment monotonically increases with the increase in the number of panels. Multiple frequencies and the independence of several higher frequencies from the number of panels were found in the frequency spectrum.

Direct design using nonlinear inelastic analysis has been recently enabled for structural design as this approach can directly predict the behaviour of a structure as a whole, which eliminates capacity checks for individual structural members. However, the use of direct design is often accompanied by excessive computational efforts, especially for complicated structural design problems such as optimization or reliability analysis. In this study, we introduce an efficient method for the sizing optimization of truss structures employing nonlinear inelastic analysis for the direct design of structures. The objective function is the total weight of the structure while the strength and serviceability constraints are evaluated with nonlinear inelastic analysis. To save computational cost, an improved differential evolution (DE) algorithm is employed. Compared to the conventional DE algorithm, the proposed method has two major improvements: (1) a self-adaptive mutation strategy based on the p-best method to enhance the balance between global and local searches and (2) use of the multi-comparison technique (MCT) to reduce redundant structural analyses. The numerical results of a 72-bar truss case study demonstrate that the performance of the proposed method has significant advantages over the traditional DE method.

Inspired by crystallography, the periodic assembly of trusses into architected materials has enjoyed popularity for more than a decade and produced countless cellular structures with beneficial mechanical properties. Despite the successful and steady enrichment of the truss design space, the inverse design has remained a challenge: While predicting effective truss properties is now commonplace, efficiently identifying architectures that have homogeneous or spatially varying target properties has remained a roadblock to applications from lightweight structures to biomimetic implants. To overcome this gap, we propose a deep-learning framework, which combines neural networks with enforced physical constraints, to predict truss architectures with fully tailored anisotropic stiffness. Trained onmillions of unit cells, it covers an enormous design space of topologically distinct truss lattices and accurately identifies architectures matching previously unseen stiffness responses. We demonstrate the application to patient-specific bone implants matching clinical stiffness data, and we discuss the extension to spatially graded cellular structures with locally optimal properties. [ABSTRACT FROM AUTHOR]

Background: Avascular necrosis (AVN) of the talus most commonly occurs secondary to trauma. Significant bone loss and collapse in severe talar AVN remains an operative challenge. Tibiotalocalcaneal arthrodesis (TTC) using femoral head allograft is at risk of collapse and subsidence. The use of a void-filling titanium truss can mitigate against this. This study describes the use of a novel keystone shaped 3D-printed titanium truss for treatment of severe talar AVN. Methods: Three patients with end-stage AVN of the talus were included. Each patient underwent a TTC arthrodesis with a custom-made, 3D-printed, keystone-shaped, truss implant in conjunction with a hindfoot intramedullary nail. Modified patient American Orthopaedic Foot & Ankle Society (AOFAS) scores were recorded at the preoperative, 6-month, 12-month, and annual postoperative timepoints. Results: All patients progressed to satisfactory radiological union by one year. Mean follow up time was 32 months (24-48 months). Mean preoperative modified AOFAS score was 5. There was progressive improvement in AOFAS scores from 6 months postoperatively. Mean modified AOFAS score improved from 28 at 6 months to 37 at 2 years postoperatively. Conclusion: Custom-made 3D-printed titanium trusses provide promising outcomes for treating severe AVN of the talus. The "keystone" design is advantageous as it allows for bone stock preservation and conforms to the shape of the native calcaneum. All patients showed progressive improvements in outcomes at sequential time intervals postoperatively. The implant provides a strong mechanical structure resisting collapse and subsidence during the arthrodesis process. Level of Evidence: Level IV, retrospective case series. [ABSTRACT FROM AUTHOR]

Pipe bridges are structures that play an indispensable role in chemical and oil plants. They support cable trays or pipe-carrying material. This study aims to identify the ideal configuration of a pipe bridge through the comparative study of girders with drop hanger and truss arrangements for three different spans. The most efficient arrangement for each span was suitably identified. Through the analysis carried out, it was then identified that the Girder arrangement is suitable for smaller spans such as 15 meters; while the truss arrangement was preferable for longer spans.

Introduction: Interbody fusion devices are customarily used in fusion of the anterior spinal column for treatment of degenerative disc disease. Their traditional role is to reestablish and maintain intervertebral disc height, contain bone graft and provide mechanical support for the spine while osseointegration takes place. Utilizing the principles of mechanobiology, a unique biokinetic interbody fusion device has been developed that employs an advanced structural design to facilitate and actively participate in the fusion consolidation process. Areas covered: This article profiles and characterizes 4WEB Medical's Truss Implant Technology™ which includes a range of 3D-printed titanium spinal interbody implants and non-spinal implants whose design is based on truss structures enabled by advances in additive manufacturing. Four main areas of the implant design and functionality are detailed: bio-architecture, mechanobiologic underpinnings, bioactive surface features, and subsidence resistance. Pre-clinical and clinical examples are provided to describe and specify the bioactive roles and contributions of each design feature. Expert opinion: The distinct and unique combination of features incorporated within the truss cage design results in a biokinetic implant that actively participates in the bone healing cascade and fusion process. [ABSTRACT FROM AUTHOR]

There is no direct evidence of woodwork of antique roofs, and, in many cases, the state of conservation of the blocks in the upper parts of the buildings is incomplete. In these conditions, how is it possible today to analyse the woodwoork of Greek monumental roofs ? The objective of this article is to suggest avenues to be explored on the study and restitution of Greek wooden roof structures, focusing more specifically on the benefits of taking into account the technical environment on the one hand, and on their structural dimension on the other hand. Beforehand, a brief inventory of the historiographical situation will make it possible to situate the origins of the interpretative framework of ancient wooden roof structures, which is still in force, and to indicate their limits.

In the protohistoric architecture with planted posts, it has always been considered that the farm could not exist before the Gallo-Roman period and that the axial post remains correspond to structures with high poles. However, taking into account historiography, the context in which these ideas emerged, and especially by comparing these theories to the realities of lifting, comparisons with existing frameworks, ethnoarchaeology, a new interpretation of the preserved layouts and the analysis of the mechanical functioning of the frameworks, it turns out that the chevron-forming-farm structures most likely existed during Protohistory, and even from the Neolithic, and that the central poles found in average or large buildings were not necessarily ridge poles but rather floor support elements.

So far, several methods have been utilized for truss optimization where metaheuristic thechniqes have been used as one of the most common methods for such purpose. These thechniqes have received much attention due to their independence from gradient information and efficient global search property. In some of the metaheuristic thechniqes, random generation of the preliminary population leads to creation of repetitive population, dependency of final optimum solution on preliminary population, increasing of the number of analyses and reduction of the algorithm efficiency. To overcome these disadvantages, the present study employs some intelligent thechniqes for the generation and the selection of the population. So, a new metaheuristic algorithm called SPR is proposed for discrete truss optimization problems. The SPR algorithm is based on the sensitivity of the elements, the partitioning of the search space and the rebirthing of the optimization procedure. The structural members which are more sensitive to changing the cross-sectional areas are recognized through the procedure. In order to find the best approximate solution for any design variable, the search space is discritized to some partitions. Rebirthing technique searches for better optimum solutions around the last local optimum point for any design variable to end the stagnation states. The performance of the proposed algorithm is investigated using several benchmark size optimization problems of truss structures from the literature. In comparison to the available results in the literature, the proposed SPR algorithm showed capable of obtaining the optimum design with much lesser computational attempt.

Purpose. Recently, the demand for reuse of industrial buildings that have not been in operation for some time has been increasing in Ukraine. Herewith, quite often the design of their roof requires the complete replacement and renovation by using modern roofing materials to meet the requirements of new government standards. Therefore, the choice and justification of the rational design of steel roof on the example of a short-span industrial building (18-24 m span), which is planned to be returned to exploitation after idle time, is the main goal of this publication. The object of the analysis is an unheated building equipped with bridge cranes of a small capacity (up to 10 tons). Me-thodology. To achieve this purpose, the comparison of structural variants of a roof steel collar tie was performed. Such variants include two types of collar tie cross-section –a lattice truss and a solid I-girder. The first type was analyzed for four possible types of section of elements – double angles, a roll-welded square profile, an electric-welded round tube and a rolled round tube. The second type was analyzed for two possible types of section – rolled I-section made of normal strength steel and fabricated sections of thin-gage high-strength steel. The design variants were compared on the basis of a numerical analysis of their work using the finite element method based on the software complex SCAD for Windows. Findings. According to the research results it should be stated that for the conditions of the city of Dnipro the most cost-effective variant of the steel collar tie cross section for the short-span industrial building is the truss made of electric-welded round tubes. Also the construction of collar tie made of roll-welded square profiles or fabricated section of thin-gage high-strength steel is considered quite effective. Originality. The research presented in the publication allows estimating the possibility and economic efficiency of usage for various types of cross-sections for the collar tie of a steel non-insulated roof of the industrial building for the reconstruction conditions in the Dnipro-city. Practical value. A practical estimation of mass and cost parameters for steel collar ties of various types has been carried out, and the methodology for conducting such estimation has been substantiated.

In 1875 a steel railway bridge was built in northern Warsaw. It had seven spans of 66.22 m and two spans of 15.24 m. In 1908 the second railway bridge was built downstream of the older one. The spacing of supports and spans were the same as in the older bridge. During World War I, both bridges were blown up and then rebuilt, first temporarily and then permanently. Again both were blown up in 1944. In 1945, a temporary crossing was built. In 1947 a permanent bridge was rebuilt, partially replacing rivets with welding. On the pillars of the older bridge, the Gdański Bridge was built (not in this study). In 1963 welded connections were strengthened, in 1980 the structure of the northern track was replaced. In 2016, the northern track was renovated. The replacement of the structure of the southern track is ongoing since 2018.

In this study, experimental tests were performed to evaluate the shear performance of encased steel truss (EST) composite girders that can resist loads at construction and composite stages. Four full-scale EST composite girders were fabricated, where the truss type (Pratt truss and Warren truss) and presence of stirrups were set as main test variables. The test results showed that in specimens applied with the Pratt truss, horizontal shear cracking occurring along the interface between concrete and steel was the dominant failure mode. Based on the crack pattern and failure plane observed from the test, the horizontal shear strengths of the Pratt truss specimens were calculated, which provided conservative results. On the other hand, in the specimens with the Warren truss inside, the strengths of the specimens were governed by the shear failure occurring in the screw rod connecting the truss elements prior to the yielding of the diagonal member. The shear strengths of the Warren truss specimens calculated based on the shear failure of the screw rod were similar to that obtained from the test. [ABSTRACT FROM AUTHOR]

The paper deals with the design approach of a subdefinite mechatronic system and focuses on the sizing stage of a gearbox of a wind turbine based on the interval computation method. Indeed, gearbox design variables are expressed by intervals to take into account the uncertainty in the estimation of these parameters. The application of the interval computation method allows minimizing the number of simulations and enables obtaining a set of solutions instead of a single one. The dynamic behavior of the gearbox is obtained using the finite element method. The challenge here is to get convergent results with intervals that reflect the efficiency of the applied method. Thus, several mathematical formulations have been tested in static study and evaluated in the case of a truss. Then the interval computation method was used to simulate the behavior of the wind turbine gearbox. [ABSTRACT FROM AUTHOR]

Thanks to scale-bridging fabrication techniques, truss-based metamaterials have gained both popularity and complexity, ultimately resulting in structural networks whose description based on classical discrete numerical calculations becomes intractable. We here present a framework for the efficient and accurate simulation of large periodic three-dimensional (3D) truss networks undergoing nonlinear deformation (accounting for linear elastic beams undergoing finite rotations). Although the focus is on elastic beams, the method is sufficiently general to extend to inelastic material behavior. Our approach is based on a continuum representation of the truss (and its numerical implementation via finite elements) whose constitutive behavior is obtained from on-the-fly periodic homogenization at the microstructural unit cell level. We pursue a semi-analytical strategy (previously reported only in two dimensions) which admits the analytical calculation of consistent tangents for convergent implicit solution schemes; the extension to 3D – through the addition of torsional deformation modes and the handling of 3D rotations – results in a powerful tool for the prediction of the complex mechanical response of large structural networks. We validate the small-strain response by comparison to analytical solutions, followed by finite-strain benchmarks that compare simulation results to those of fully-resolved discrete calculations. The homogenization of beam unit cells results in a regularized macroscale model with an intrinsic length scale, which manifests especially when modeling bifurcations or localization. We finally apply our approach to macroscopic boundary value problems involving complex-shaped truss metamaterials (with truss unit cells near the body's boundary mapped onto a conformal surface), which reveal only an insignificant effect of boundary layers on the overall mechanical response, again supporting the applicability of our homogenization approach. [ABSTRACT FROM AUTHOR]