Abstract

     Nonlinear dynamic of a flexible slender truss-structure mounted manipulator for on-orbit assembly, which can be simplified as a beam–rotating link interaction system, is theoretically investigated. The governing partial differential equations (PDEs) of beam with time-varying coefficients is established by using the D’Alembert principle incorporated with the moment balance method where the beam is of a Euler–Bernoulli type and the influence of slope is considered. Such system is a typical parametrically excited system. The multiple scales method is used to determine the approximate solution and the conditions of the primary resonance ( ω1≈ωref ) and sub-harmonic resonance ( ω1≈ 2ωref , ω1≈ 3ωref and ω1≈ 4ωref ) are obtained. In addition, the nonlinear response, stability and bifurcations for primary and sub-harmonic resonance conditions have also been investigated by varying system parameters. Moreover, the results of some specific conditions by the perturbation analysis are compared with the numerical solution and are found to be in good agreement. This work has certain guiding significance for autonomous on-orbit assembly task and the method can be extended to the more general three-dimensional case.

Introduction

     Future space exploration puts forward some new requirements of space structure, such as establishment of large space solar power plants to cope with energy depletion which is huge volume (from thousands of meters or even dozens of kilometers). To meet the requirements of such space missions, the space structures will be constructed too large to be launched and deployed as a whole [1]–[5]. It is identified as one of the most appealing solutions in which the manipulator is mounted on the long truss-structures to assemble or maintain the several adjacent blocks [6]. One problem of great concern is that of low-frequency structure may be easily excited by high-frequency robotic and hardly damped out in space environment due to the low-damping characteristics of the flexible structures [2], [7]. The vibration may cause inaccuracy of manipulator positioning, and more seriously, the premature fatigue failure of flexible structure [8] and it could be reduced by improving the dynamic model of the system. Therefore, it is significant to conduct studies to apprehend dynamic characteristics of such system and find some structural parameter design criterion to minimize the vibration amplitude.

     In this paper, a typical flexible slender truss-structure mounted manipulator (FSTMM) for on-orbit assembly, as shown in Fig. 1(a), is studied. During the robot is assembling the truss structure, the robot is mounted on the long truss to assemble the next module of the truss. To focus on the fundamental issues of the dynamic problem, the long truss structure can be simplified as a flexible beam [3], [9] and only the first link of manipulator is considered. Such system is a typical beam–rotating link interaction system. A very limited work of such system has been reported. For example, the speed exclusion zone of a wind turbine, which was regarded as a typical cantilever beam structure attached with a rotating unbalanced mass, was investigated to prevent tower resonance [10]. The nonlinear dynamic behavior of a non-ideal unbalanced motor in a simple cantilever beam system was investigated and the results indicate there appears the jump phenomenon, namely the Sommerfeld effect [11], [12]. A model using RLC circuits with variable capacitance based on the saturation phenomenon is used to control the vibration of a hinged-hinged beam supporting unbalanced machine [13]. A nonlinear dynamical model of a robot manipulator consisting of a flexible cantilever beam and rigid second link is derived using a Lagrange equation and a Lyapunov-based feedback control law is then introduced to suppressing bending vibrations in the flexible link [14].

Conclusion

     Nonlinear dynamic of a flexible slender truss-structure mounted manipulator for on-orbit assembly, which can be simplified as a beam–rotating link interaction system, is theoretically investigated for primary and sub-harmonic resonance. The PDEs of system is established by using the D’Alembert principle incorporated with the moment balance method in which the slope of beam is considered. Such system is a typical parametrically excited system. The multiple scales method is used to solve the second-order ODEs which is reduced by the Galerkin’s method with a single mode approach from obtained PDEs. Then, the non-linear response, stability and bifurcations for primary and all sub-harmonic resonance conditions have been investigated by varying system parameters. By inspecting the results of this analysis, the following conclusions could be made:

     When the excitation frequency of manipulator ω1 near equal to the linear natural frequency of flexible truss-structure ωref , there will exist simple resonance condition and only have nontrivial steady state solution. The system resonance could be classified into monostable and bistable region by saddle-node (SN) bifurcation point. The steady state responses of the system in bistable region are determined by the initial condition and a slight change of initial conditions may cause a significant change. On the other hand, increasing the level of damping, as well as decreasing the mass of rigid manipulator and installation position of manipulator close to fixed end will reduce steady state responses of beam.

Abstract

     Controlling the frequency response of an engineering component or structure is important in the aerospace and automotive sectors and is a key consideration when seeking a new and more efficient design for a given component. In this contribution, the standard truss layout optimization procedure is modified to incorporate semidefinite constraints to limit the minimum value of the first natural frequency. Since this increases the computational expense and reduces the scale of the problem that can be solved, a bespoke algorithm incorporating an adaptive ‘member adding’ procedure is proposed and applied to a number of benchmark example problems. It is demonstrated that this allows problems to be solved with relatively fine numerical discretization, allowing modified structures with an acceptable minimum first natural frequency response to be successfully identified.

Introduction

     In the design of modern engineering components, many considerations need to be taken into account including safety, cost, weight and manufacturability. The most prominent of these is safety, taking account of the regime of applied stresses to be sustained over the life of the component. Safety is influenced by the properties of the material employed, which may change as the design evolves. Additionally, when considering structures that include slender elements in compression, it is necessary to check for buckling instability to ensure safety is maintained. Another key parameter in the aerospace sector is the harmonic frequency of a structure. This should lie outside the frequency bands of surrounding components. Should a fundamental frequency of one component (e.g. a bracket) overlap with those of its attached neighbours, then resonance in the component may occur, also referred to as forced vibration. Forced vibration and resonance can then lead to High Cycle Fatigue (HCF) in the component, affecting its serviceable life and reducing its time to failure. It should be noted that a component may exhibit multiple resonant frequencies, each corresponding to a mode of vibration; repeated exposure to these frequencies may reduce the life of the component. However, this phenomenon is beyond the scope of the current contribution. Considering component manufacture, it is important to note that traditional manufacturing methods may limit the design freedom available; however, in the present contribution, it is assumed that Additive Layer Manufacturing (ALM) methods are available. The use of ALM means that complex truss forms can potentially be fabricated, beyond the scope of traditional subtractive manufacturing methods.

Conclusions

     Numerical layout optimization provides an efficient means of generating optimal truss structures for a given set of design requirements. However, traditional linear programming-based formulations are limited, and cannot for example accommodate frequency constraints. In this contribution, extended semi-definite programming-based formulations are considered that allow the minimum first natural frequency of a structure to be specified. The main conclusions are as follows.

     The use of a two phase approach, in which the traditional LP layout optimization formulation is used in the first phase and an SDP size optimization is used in the second phase, provides a computationally efficient means of generating solutions satisfying a specified frequency constraint. However, the solutions obtained are likely to be sub-optimal, with the resulting structures having higher than necessary volume.

     Alternatively, a constraint on frequency can be introduced in the optimization directly, furnishing layouts that satisfy both structural performance and first natural frequency requirements. However, when using a fully connected ground structure and a standard SDP solver, the computational cost and memory requirements have been found to be high, severely limiting the scale of problem that can be tackled.

Abstract

     Considering environmental factors such as temperature in structural health monitoring progress has been a consensus. However, the uncertainty of monitoring data usually makes it difficult. In this paper, the uncertainty factor has been introduced into the anomaly diagnosis process, a Markov chain-Monta Carlo (MCMC) anomaly diagnosis method based on temperature-induced response has been proposed. First, a novel diagnosis index has been developed based on the temperature data and static strain response data collected by the SHM system, the MCMC process is used to analyze the diagnosis index, and the posterior frequency distribution histogram of the actual diagnosis index is obtained. Finally, by analyzing the histogram of an unknown state and the initial state (baseline state) of the structure, the anomaly probability of the unknown condition is obtained, which can be used for anomaly probability diagnosis of components. The availability of the method is evaluated by a laboratory truss structure test under a series of working conditions and is verified by field monitoring data of a hanger roof structure. The results show that the method can make better use of the temperature effect of the structure for anomaly diagnosis, and the uncertainty is well considered.

Introduction

     Large building structures, including truss structures, are often used in airports, stations, factories, stadiums, and other important civil infrastructures [1], such structures often encounter sudden load changes (snow loads, high wind loads), changes in restraint conditions, member damage due to material degradation, and other structural anomalies during construction or service. Monitoring and diagnosing these structural anomalies using sensors placed on the surface of the structure is an efective means to ensure the safety of the structure throughout its life, and in recent years, with the development of sensor technology and intelligent algorithms, structural anomaly diagnosis (SAD) technique is becoming an increasingly important area.

     The vibration-based method is one of the most widely used SAD methods, which refects the abnormal state of the structure by monitoring the changes of vibration features [2–4]. However, the structural vibration features (e.g., natural frequencies) are not only related to the state of the structure itself, but also to environmental factors such as temperature, which will have an impact on the accuracy of SAD [5–7]. Although diferent solutions have been proposed for vibration-based SAD under environmental changes, these methods are still greatly limited by other defects in long-term practical monitoring, such as low sensitivity of vibration features to small local damage of the structure, the complicated method of sensor arrangement, and the large data transmission and storage caused by the high sampling frequency of the monitoring process, etc. [8].

Summary and conclusions

     In this paper, a temperature-based anomaly diagnosis of truss structure system using Markov chain-Monte Carlo method is proposed, which not only introduces the uncertainty method into a SAD method based on static response monitoring, but also actively uses the temperature efect of the structure for SAD. In this method, a novel diagnosis index based on T-stress-induced strain that takes uncertainties into account is proposed, which is obtained from the stress-induced strain and temperature measured by sensors arranged in the focus area of the structure. Then, the diagnosis index measurement data set is processed by MCMC to obtain the posterior relative frequency distribution histogram of the actual diagnosis index, and the histogram of the baseline state and an unknown state are analyzed to obtain the structural anomaly probability of the members under this unknown state. As two aspects of anomaly diagnosis, the structural damage diagnosis and state change diagnosis were verifed by a truss test and feld monitoring data of the BDIA hanger roof structure respectively, and the following conclusions were obtained:

Abstract

Purpose

     With the development of engineering structures towards the direction of large-scale, light-weight and multi-function, truss structures are utilized widely in the aerospace and civil sectors due to their outstanding advantages, e.g. light weight, large stiffness ratio and high packaging efficiency. Meanwhile, investigating the nonlinear dynamic mechanism and developing vibration control strategies for large space truss are of practical importance and give rise to interesting scientific issues.

Methods

     Finite element method is a popular approach but brings great challenges to the nonlinear dynamic analysis and vibration controller design of truss structures due to the high degree of freedom of the full-scale finite element model. Therefore, the equivalent continuum modeling methodology becomes one of the most important developing trends to address these difficulties and is of high-efficiency especially for the nonlinear dynamic analysis.

Results

     In the present paper, the research status about the equivalent continuum modeling of truss structures is sorted out including equivalent modeling methods (the energy equivalent method, the homogenization method, the displacement equivalent criterion, etc.) together with their advantages and drawbacks. Issues on static, dynamic, and buckling analyses of various structural styles (beamlike truss, platelike truss, hoop truss, etc.) with different connection joints are discussed.

Conclusions

     More specifically, the research progresses on equivalent nonlinear continuum modeling and the design of vibration control law of the large truss structures are investigated, respectively, and the gap on the nonlinear analysis and vibration control is summarized for the existing researches. Additionally, comment, perspective and opportunity are proposed which could be valuable for the future developments of equivalent continuum modeling and vibration control of the large truss structures.

Introduction

     Motivated by the ever-increasing demands for aerospace structures, the new opportunity to create large space deployable truss structures also call for advanced equivalent continuum modeling techniques, in particular when the number of the degrees of freedom (DOFs) increases dramatically for the large-scale truss structures [1–4]. Also, the truss structures are widely involved in civil engineering [5, 6] (e.g. buildings, bridges or transmission towers), material science [7, 8] (e.g. carbon nanotubes, graphitic materials), and other applications [9–11]. The fnite element method (FEM) is one of most popular methods to calculate dynamic behaviors of truss structures due to its convenience of intuitionist result. However, the FEM requires a signifcant amount of computing capacity for the large truss structures and the results cannot be applied efectively for the vibration controller design, especially, it is difcult to comprehend and grasp the essential nonlinear dynamic characteristics when the nonlinear analysis needs to be carried out. Therefore, the equivalent continuum modeling techniques are becoming increasingly promising in practical engineering felds [12, 13]. The equivalent continuum modeling approaches, their advantages, the development and future directions were summarized in Ref. [14]. The equivalent continuum modeling possesses three promising advantages, as follows:

Conclusions

     The spacecraft and civil engineering structures are developing towards to the directions of large-size, light-weight and fexibility, which motivates the studies about the equivalent dynamic modeling of the large space truss structures. In this survey, the status of the equivalent continuum modeling on the truss structures is frstly presented. Then, the equivalent continuum modeling work for linear truss systems is described, together with diferent modeling approaches, structural styles and connection joint. In addition, the solution methods and experimental studies are also discussed. Afterwards, the equivalent continuum modeling of nonlinear truss systems is investigated and classifed into geometrical, material and jointed nonlinearities. The vibration control researches involving the truss structures and their equivalent continuum models are performed, which are analyzed to have great potential and advantages of applications in large truss structures. Further research eforts, e.g. equivalent nonlinear modeling strategy for truss structures, solving approach of coupled three-dimensional nonlinear model, active vibration control of space trusses, as well as dynamic analysis and vibration control of fexible spacecraft with truss structures, are put forward for reference.

Abstract

     In order to obtain stable and realistic truss structures in practical applications, it is essential to include nodal and local buckling stability in truss topology optimization. There have been several approaches to address the challenges including nodal stability or local buckling stability. However, these approaches often lead to ill-conditioned optimization problems, such as convergence problems due to the concavity of the problem or high computational costs. In this study, two novel but conceptually simple methodologies, the nominal perturbing force (NPF) approach, and the allowable stress iteration (ASI) approach, are proposed to address nodal instability and local buckling instability problems in truss topology optimization, respectively. Initially, in the NPF approach, an infinite number of disturbing forces that a node may suffer are incorporated into the truss topology optimization problem in the form of nominal perturbing force conditions, whose magnitude and direction are discussed to capture the worst case. In the ASI approach, the allowable stress for each compressive bar is redefined in each iteration to ensure that the Euler critical buckling constraint is active. In this way, the concave local buckling instability problem is linearized in each iteration and can be solved efficiently by a linear programming solver. Finally, based on the finite element limit analysis (FELA) method, a truss topology optimization formulation incorporating the NPF and ASI approaches is proposed to solve the nodal stability and local buckling stability problems simultaneously. The proposed formulation is demonstrated through several numerical examples showing significant effects of including nodal stability and local buckling stability in the optimized designs, while at the same time demonstrating the validity and potential of the proposed approaches.

Introduction

     The pin-jointed truss topology (or “layout”) optimization problem is concerned with finding an optimal arrangement of structural bars subject to prescribed constraints. A typical truss topology optimization problem might comprise a design domain containing an array of fixed nodal points connected by potential members, called the ground structure [4,11,33,37,42]. The optimization objective might typically then be to minimize the total volume, mass [21,37], or compliance[28] of structure, with constraints ensuring that each node is in static equilibrium and that bar stresses are within predefined limits [22,47,48]. The optimal cross-sectional areas for all the bars in the ground structure are then determined as part of the optimization process; typically, many of these will be zero, leaving the optimal topology comprising only of bars with non-zero cross-sectional areas[20].

     Mathematically, the ground structure provides a feasible domain for the truss structure optimization problem. Typically, the truss topology optimization based on the ground structure method is mainly divided into four steps [19]. Firstly, as shown in Fig. 1a, the design domain with appropriate supports and loads is determined. Secondly, as shown in Fig. 1b, the nodes are arranged, usually evenly, to discrete the design domain. Thirdly, as shown in Fig. 1c, these nodes are connected with potential bars to generate the ground structure. Finally, as shown in Fig. 1d, some optimization algorithms are used to remove the redundant bars to generate the optimal structure.

Conclusions

     The main contribution of this study is the development of a truss topology optimization formulation including nodal and local buckling stability constraints. A brief review of literature has shown that a convenient approach to state the basic plastic problem of truss topology optimization relies on the FELA method.

     The novel nominal perturbing force (NPF) approach has been proposed to address the nodal instability in the truss topology optimization problem. In the NPF approach, nominal perturbing forces consistent with the directions of the Cartesian axes are used to model the possible perturbations of the unstable nodes. Compared with the conventional nominal lateral force (NLF) approach, (a) the NPF approach has higher computational efficiency because it contains fewer optimization variables; (b) the effect of tension bars connected to the nodes is considered in determining the unstable nodes, which can lead to a better optimization result.

     In addition, the novel nominal allowable stress iteration (ASI) approach is proposed to address the local buckling instability in the truss topology optimization problem. In this way, the concave local buckling instability problem is linearized in each iteration and can be solved efficiently by a linear programming solver. Numerical examples have shown the practical applicability of the proposed method for the preliminary design of truss structures.

Abstract

Introduction

     An engineering system consists of properly established activities and is put together to achieve a predefined goal. These activities include analysis, design, construction, research, and development. Designing and assembling structural systems, including buildings, bridges, highways, and other complex systems, have been developed over centuries. However, the evolution of these systems has been prolonged because the overall process is very costly and time-consuming, requiring primary human and material resources to be utilized. One of the options for overcoming these shortcomings is the use of metaheuristic algorithms as recently developed intelligent techniques. These algorithms can be utilized as upper-level search techniques for optimization procedures to achieve better results.

Objectives

     Shape and size optimization of truss structures are considered in this paper, utilizing the Chaos Game Optimization (CGO) as one of the recently developed metaheuristic algorithms. The principles of chaos theory and fractal configuration are considered inspirational concepts. For the numerical purpose, the 10-bar, 37-bar, 52-bar, 72-bar, and 120-bar truss structures as five of the benchmark problems in this field are considered as design examples in which the frequency constraints are considered as limits that have to be dealt with during the optimization procedure. Multiple optimization runs are also conducted for having a comprehensive statistical analysis, while a comparative investigation is also conducted with other algorithms in the literature.

Results

     Based on the results of the CGO and other approaches from the literature, the CGO can provide better and competitive results in dealing with the considered truss design problems.

Conclusion

     In summary, the CGO can provide better solutions in dealing with the considered real-size structural design problems with higher levels of complexity.

Introduction

     Over the past decades, human beings have put so much effort into maximizing the use of limited available resources. For example, one challenge is selecting design variables to consider design constraints in engineering designs and having the lowest constriction and material costs. In fact, the main goal is to properly meet the basic and advanced design standards by considering the project’s economic aspects. Recent advances in structural engineering reveal the need to consider greater accuracy, better performance, and higher construction speeds in the design of structural systems. Therefore, to address each of the above factors it is necessary to introduce new methods for design and optimization and implement them on complex and real-world systems. Optimization problems normally search for the minimum values ​​of a cost function to systematically select the values ​​for the variables that lead to the lowest cost. Metaheuristic algorithms are optimization methods that combine global and local search techniques to get the answers as close as possible to the optimal answer. Indeed, metaheuristic algorithms are types of approximate optimization algorithms capable of providing acceptable solutions and avoiding entrapment in local optimal points. Firefly Algorithm (FA) [1], Genetic Algorithm (GA) [2], Material Generation Algorithm (MGA) [3], Cuckoo Search Algorithm (CSA) [4], Chaos Game Optimization (CGO) [5], [6], Slime Mould Algorithm (SMA) [7], Atomic Orbital Search (AOS) [8], Particle Swarm Optimizer (PSO) [9], and Crystal Structure Algorithm (CSA) [10] are some of the recently developed metaheuristic algorithms. Nevertheless, the application of these algorithms alongside the improved or hybrid versions has been investigated in different fields. Investigation of Lévy flight distribution for engineering optimization [11], optimum design of engineering problems with dynamic differential annealed optimization [12], optimum design of reinforced concrete footings with metaheuristic algorithms [13], investigation of nature-inspired algorithms for getting of bridge scour information [14], performance assessments of an artificial bee colony in optimal design of steel skeletal structures [15], design optimization of reinforced concrete building structures with metaheuristics [16], and estimation of solar photovoltaic cell parameters with a new stochastic slime mould metaheuristic algorithm [17], are some of the recent researches in this field.

Conclusion

     Shape and size optimization of different large-scale truss structures are considered in this paper using the Chaos Game Optimization (CGO) as one of the recently proposed metaheuristic optimization algorithms. In this algorithm, the principles of chaos theory and the configuration of fractals are utilized as inspirational concepts. For the numerical purpose, the 10-bar, 37-bar, 52-bar, 72-bar and 120-bar truss structures as five of the benchmark problems in this field are considered design examples, in which the frequency constraints are considered as limits to be dealt with during the optimization procedure. Multiple optimization runs are also conducted for having a comprehensive statistical analysis, while a comparative investigation is also performed with other algorithms in the literature. Based on the results, the CGO can reach 524.4545 kg in dealing with the 10-bar truss problem, which is better than the previously calculated weights. The CGO can provide 524.5099 kg as the mean of 30 independent runs with 524.7488 kg as the worst run, which are the best statistical results among other approaches for this structure. The CGO provides a best optimum weight of 359.7893 kg for the 37-bar truss structure, while the other attempts in this case, such as IDE, calculate 359.8194 kg, which demonstrates the capability of the CGO. The CGO can provide 359.8842 kg as the mean of 30 independent runs with 360.0873 kg as the worst run, which are the best statistical results among other approaches. Based on the results of other algorithms from the literature for the 52-bar truss problem, CGO can reach 193.1876 kg which is the best among other approaches, while the IDE with 193.2085 kg is the next competitive result. The mean, worst and standard deviation of the conducted runs demonstrate that CGO provides very stable results with mean of 195.4586 kg and standard deviation of 3.8183. The CGO can reach 324.197 kg for the 72-bar truss structure, which is better than the results of other methods.

Abstract

     Modern and future high precision pointing space missions face increasingly high challenges related to the widespread use of large flexible structures. The development of new modeling tools which are able to account for the multidisciplinary nature of this problem becomes extremely relevant in order to meet both structure and control performance criteria. This paper proposes a novel methodology to analytically model large truss structures in a sub-structuring framework. A three dimensional unit cube element has been designed and validated with a Finite Element commercial software. This model is composed by multiple two-dimensional sub-mechanisms assembled using block-diagram models. This constitutes the building block for constructing complex truss structures by repetitions of the element. The accurate vibration description of the system and its minimal representation, as well as the possibility of accounting for parametric uncertainties in its mechanical parameters, make it an appropriate tool to perform robust Structure/Control co-design. In order to demonstrate the strengths of the proposed approach, a structure/control co-design study case is proposed and solved using structured robust -synthesis. The objective is to optimize the pointing performances of an antenna, minimizing the perturbations coming from the Solar Array Driving Mechanisms (SADM) of two solar panels, performing active control by means of multiple Proof Mass Actuators (PMA), and simultaneously reduce the mass of the truss-structure which connects the antenna to the main spacecraft body.

Introduction

     In order to systematically face the challenges associated with the next generation of satellites, the European Space Agency (ESA) and NASA have combined their past experiences to cope with the fine pointing requirements of high accuracy observation and Science missions [1]. This represent a domain which is extremely multi-disciplinary: structural, control and system engineering considerations must coalesce to limit the propagation and amplification of internally generated disturbances through the satellite’s flexible structures. For these reasons, the development of rigorous methodologies and design tools that can handle all these domains is crucial at early stages of design. The works of Preda et al. [2] and Sanfedino et al. [3,4] are example or this approach.

     In the past decades, structural and control co-design has attracted a lot of attention due to its ability of merging these multiple multidisciplinary requirements into a single design flow. Moreover, the increasing use of large structures and appendages for Space applications has rendered flexible modal analysis mandatory for the design of proper spacecraft control laws.

Conclusions

     This paper aimed at introducing new analytical tools to model large complex truss structures for space applications in the TITOP/NINOP framework with the specific objective of developing models for structure/control co-design and robust analysis and control. A series of 2D mechanisms block has been introduced to build a unitary 3D cubic element which serves as a building block for truss structures in a sub-structuring approach. The analysis displayed the potentialities of the approach, as large structures composed by a high number of beam elements can be easily assembled by using blocks of decreasing complexity. In addition, a full validation campaign by comparison with Nastran validated the representativeness of these models.

     A case study was then introduced to represent the strengths of the TITOP/NINOP approach in performing robust structure/control co-design in presence of parametric uncertainties. A complex 3D truss structure was built using the previously introduced cube elements and attached to a spacecraft to act as support for an high precision antenna. The objective of the co-design was to reduce the structural mass of the system while satisfying a fine pointing requirement. This study case highlighted the potential of these analytical blocks in performing complex multi disciplinary optimization problems. The direct co-design using structured ?∞ control synthesis allowed for computational cost reduction and brought to a mass saving of almost 76% of the original structural mass, while coping with stringent pointing performances and a large set of uncertainties in the mechanical design parameters. The main conclusion of this work is that it is possible to develop knowledge-based models for complex truss structures with an analytical dependence on the sizing, variable or uncertain parameters. These models can be directly used for robust design, robustness analysis or parametric optimization, thus simplifying model uncertainty quantification and model reduction in the overall control/structure integrated design process.

1- Introduction

2- Experimental program

3- Experimental results and discussion

4- Fatigue resistance evaluation

5- Conclusions

References

Abstract

While welded joints are extensively used in the connections of steel truss bridges, service life of the bridges is largely dependent on the fatigue resistance of the welded joints. Stress concentration and weld residual stress are two primary causes of fatigue damage in the welded joints. In this study, corner-fillet profile (CFP) and ultrasonic impact treatment (UIT) are used to improve the fatigue performance of the welded joints through relieving stress concentration and weld residual stresses, respectively. The fatigue resistance of welded joints is evaluated through experimentation. The results indicate that the use of CFP and/or UIT can alter the initiation location of fatigue crack. The fatigue resistance of welded joints was increased by 24% and 36% by using the CFP and UIT, respectively. The fatigue performance of welded joints was evaluated using three different methods, including the nominal stress method, effective notch stress method, and peak stress method. The peak stress method with a single fatigue resistance curve demonstrated the highest applicability and accuracy.

Introduction

Steel trusses have been extensively used in railway bridges and hybrid highway-railway bridges. Steel truss bridges are typically constructed by assembling prefabricated truss components on site. Fig. 1 (a) and (b) show a representative cross section of a main girder in a hybrid highway-railway bridge. The girder is assembled using different truss components, including the chords, vertical posts, diagonal elements, etc. The components are connected through welding and/or using high-strength bolts. Integrated welded joints (Fig. 1(b)) are usually prefabricated in factory to ensure high welding quality. The welded joints between the flange and gusset plates are subjected to varying tensile stresses and other adverse effects on fatigue resistance, and thus susceptible to fatigue damages. In general, the adverse effects include stress concentration, weld defects and residual stresses at welded joints [1–4]. Under cyclic loading, cracks tend to initiate at the welded joints (Fig. 1(b)) and compromise the long-term durability of the truss bridge. The effects of stress concentration, weld defect and residual stresses on fatigue resistance of welded joints have been investigated [1–9]. The stress concentration of steel truss joints has been studied through finite element analysis [1] and experimentation [2–9]. The geometry of weld joints was optimized, and a corner-filleted profile (CFP) at weld of cruciform joints was recommended to reduce stress concentration [5].

The economic, technical, and scientific developments in the construction industry have brought about a great number of structural systems. Among them, steel-concrete composite structures have proved to be efficient from the structural and constructive points of view. As for the structural aspect, one can emphasize the better usage of materials’ resistance properties, effectively exploring in a better way the potentials of concrete and steel [1]. The resulting combination of steel and concrete in composite beams, for example, provides lighter but more resistant structures. The use of composite structures with all its structural efficiency advantages [2] should be encouraged for bridge construction and even made more popular for medium and small construction too. As for the constructive aspect, steel-concrete beams can be built faster than reinforced concrete beams as the steel beam helps as support along the concrete slab curing process. Therefore, steelconcrete beams use less wood forms to cast the concrete slab. To accelerate even more the constructive process in making composite beams, precast concrete slabs can be associated with steel I-beam sections. Today, with increasing demand for infrastructures and dwelling, steel-concrete beam is a fast and cost effective system that may be well used for multi-story buildings and bridges. The efficiency of steel-concrete beams, as resisting structure, depends highly to the interaction between two key structural elements: (a) steel I-beam and (b) overlaid concrete slab. Effective links between concrete slab and steel profile are required because these two materials have to act as a unique structure. Steel connectors are used as shear connectors, and, generally, they are welded to the steel profile flange and merged into the concrete slab – even though other options are available today [3]. One important characteristic for a shear connector in composite beams is its ductility. Shear connector may be classified in two categories depending of its ductility: rigid or flexible. Rigid connectors do not deform much under service load. They can provide good connection without showing much relative slipping displacement between steel I-beam and concrete slab. However, the collapse of rigid connectors is brittle. In this case, concrete failures for shear or crushing, and brittle failure takes place.

Limit Analysis (LA) constitutes by today a well-established and consolidated discipline, for evaluating consistent bounds on the collapse (limit) loads acting on engineering structures characterized by a mechanical behavior that may be idealized as perfectly plastic, subjected to increasing live loads. LA may be considered as a milestone in the more recent history of structural mechanics and provides a rather powerful tool for structural design and assessment purposes in a wide variety of engineering situations. It has acquired its rational formulation thanks to the contribution by Drucker et al. [1], who formulated and demonstrated the fundamental theorems of LA for a continuum. More recent consolidated contributions, such as those by Massonet and Save [2], Kaliszky [3], Lubliner [4] and Jirasek and Bazant [5], have further made the theory and methods of LA rather fundamental in the applications of mechanics of solids and structures, becoming by now classical references on the topic (see also contributions in Spiliopoulos and Weichert [6] and Foreword by G. Maier in it). LA is a methodology characterized by intrinsic peculiarities that may be regarded as bringing considerable advantages in the engineering practice. These include the fact that it determines safety coefficients with respect to the ultimate limit state of a structure and the kinematics of a collapse mechanism, providing essential and very expressive results to structural designers. For this reason, it appears as particularly suitable for comparative evaluations among different design options, in order to easily guide engineers toward selecting the most efficient and feasible structural choices. LA provides theorems for the determination of the ultimate load of a perfectly plastic solid or a structure. The lower bound theorem, or equivalently the static (‘‘safe”) principle, states that if, for a given set of loads, an equilibrium stress field (satisfying also the stress boundary conditions) can be found, which nowhere violates the yield condition, the body will not collapse. The upper bound theorem, or equivalently the kinematic principle, states that, for a given collapse mechanism whose kinematics is compatible, the ratio between the internal and external rates of dissipation will be higher than or equal to that actually found at collapse, thus providing an upper bound on the ultimate load. It is a well-known fact that, in both cases, the plastic behavior intrinsically renders the problem to be non-linear. Essentially, two different approaches are usually adopted to deal with this issue: (i) the use of a polyhedral approximation to the yield surface; (ii) the implementation of direct non-linear programming algorithms.

Over the course of billions of years of evolutionary history, nature has heuristically (i.e. experimentally, especially by trial and error) developed a diverse and remarkably-ingenious set of dynamic and robust strategies that have endowed creatures and organisms with optimum yet sustainably-resilient adaptability to their in-flux environments. The last few decades saw significant research efforts that were devoted to understanding these strategies and exploring their applicability to solve complex engineering problems (e.g. see [1]). These efforts coupled with those driven by other inspirations (e.g. musical improvisation [2]) led to the development of several optimization techniques knows as optimization metaheuristics that in turn made previouslyunimaginable advances in structural optimization possible. The prefix meta-, meaning more developed/higher level, indicates that, in contrast to heuristic techniques, metaheuristics are problem-independent and versatile, making them suitable for various kinds of problems. In addition, compared to now-traditional gradient-based optimization techniques, the stochastic mechanism of metaheuristics allows them to effectively explore and exploit a vast search space enclosed by highly-nonlinear and discontinuous constraints without requiring gradient information and explicit formulations for the objective function and constraints [3]. It is not within the scope of the present study to detail the history of metaheuristics. However, a brief review of the most prominent metaheuristic optimization techniques is given below, and the interested reader is referred to, e.g., Sorensen et al. [4] for a portrait of the evolution of optimization metaheuristics. The phenomenal growth in the field of optimization metaheuristics has been taking place in a series of stages with divisions usually spaced out over several years. While the first use of heuristics by humans can be traced back to prehistoric times when they employed the strategies learned from determining the trajectory of a stone to hit a bear toward hitting a mammoth with a spear, the modern application of heuristics took place in the late 1950s and early 1960s when the advent of computer enabled researchers to develop and use algorithms to study the phenomenon of natural evolution. One of the first methods to receive recognition was the so-called evolution strategy, where the better of a solution and its mutated version is used as the parent for the next round of mutation [5]. Another method was evolutionary programming, where solutions are represented as finite-state machines that change from one state to another in response to a mutation operator [6].