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In this article, a Python-programmed advanced design paradigm is firstly introduced to topology and size optimization of the X-bracing system of nonlinear inelastic space steel frames. For that purpose, an advanced analysis method considering both geometric and material nonlinearities is utilized as an effective finite element analysis (FEA) solver. In which, X-bracing members are modeled by truss elements, while the beam and column members are simulated by beam-column ones. The bracing members’ cross-sectional area and their position are respectively treated as discrete size and topology design variables. The problem aims to minimize the weight of X-bracing system so that the constraints on the strength, inter-story drift and maximum displacement are satisfied. An adaptive hybrid evolutionary firefly algorithm (AHEFA) is employed as an optimizer. Numerical examples are exhibited to illustrate the powerful ability of the present methodology.

The moving element method (MEM) is applied in this paper to study the dynamic behavior of the Mindlin plate subjected to a moving mass-spring-damper system. Reissner–Mindlin plate theory is utilized to study the plate structure. The plate is modeled by the Isoparametric quadrilateral nine-node element. The governing equation of motion is built into a coordinate system which moves with the moving mass-spring-damper system and is based on the principle of virtual work. The MEM is proposed to solve the governing equation of motion of the plate resting on a Pasternak foundation under the moving mass-spring-damper system including roughness of plate surface which is a dynamic source. Numerical results are investigated and verified by comparing with the published results. The effects of different parameters, such as spring stiffness, damping coefficient and velocity of the moving load system, plate thickness, foundation parameters and roughness of the plate surface on the dynamic response of the Mindlin plate are investigated.

Responses of floating plates with the impact of moving excitations have been previously studied by several scholars. Generally, such structures were often assumed to be isotropic. Nonetheless, the directional-dependent bending stiffness should be considered for designing practical floating structures, especially for very large floating structures. Accordingly, this article aims to analyze hydroelastic responses of floating composite plates subjected to moving loads for the first time. For this, a novel numerical approach as a combination of boundary element method and moving element method which is named the BEM–MEM is proposed. In the this approach, governing equations of motion, moving element, and fluid matrices are formulated in a relative coordinate system traveling with moving loads. Consequently, the suggested paradigm can effectively eliminate difficulties in addressing the bound of computational domain and tracking the location of contact points which often encounter in the traditional finite element method owing to utilizing a fixed coordinate system. Several numerical examples are exhibited to demonstrate the performance and ability of the boundary element method-moving element method . Gained results are compared with those by the Fourier transform method and the asymptotic expression to verify the accuracy of the proposed methodology. The outcomes indicate that the speed of moving loads considerably affects the plate deflection. In addition, as the speed is larger than the minimum celerity of the free surface of hydroelastic system ( Cmin), the influence of anisotropy on the deflection becomes significant.

The paper used the moving element method (MEM) to analyze the dynamics of the functionally graded material (FGM) plate under the moving load considering the effect of temperature. To calculate the displacement of the plate, the study applied the Mindlin plate theory. A nine-node isoparametric element, each with five degrees of freedom, is used to model the plate element. According to the MEM, the equation of motion of the FGM plate is established based on the principle of virtual work and on a coordinate system that moves along with the moving load. The temperature field is assumed to be constant in the plane and varies across the plate thickness. By solving the governing equation of temperature transfer, it is possible to obtain a temperature distribution function. Both mechanical strain and temperature-induced strain are considered to determine plate strain. Numerical results were surveyed with different parameters and compared with published results to verify the reliability of the model. It is found that temperature significantly affects the dynamic response of the FGM plate. This study shows that the displacement of the plate increases when the temperature increase.

Nowadays, optimization problems have been one of the most challenges for solving real-work problems. Because of the importance of practical problems in other fields, more and more intelligent search algorithms have been proposed. Each algorithm has both advantages and disadvantages. It is difficult to find a suitable algorithm to solve real problems. In this article, the comparison of four robust algorithms including two classical algorithms such as particle swarm optimization (PSO) and artificial bee colony (ABC), and two algorithms which are presented recently, i.e., cuckoo search (CS) and gray wolf optimizer (GWO). To make a diversity in comparison, the first ten benchmark test functions were chosen to compare items such as convergence rate and accuracy of the algorithms. Moreover, the high dimensions (n = 30) in the search space are also examined to evaluate the effectiveness of the algorithms in the variable dimension problems. Through the results achieved, an algorithm which is achieved a balance between the convergence rate, and the accuracy level is submitted.

This paper is concerned with the reduction of hydroelastic responses of pontoon-type very large floating structures (VLFS) via the use of vertical elastic mooring lines connected at the fore and aft edges of VLFS to the seabed. These vertical mooring lines are used in addition to the mooring dolphin-rubber fender system that is used to restrict the horizontal movement of VLFS. The considered rectangular shaped VLFS is modeled as a Mindlin plate floating on an ideal fluid in which the linear potential theory is applicable. The hydroelastic analysis of VLFS with vertical mooring lines modeled as vertical elastic springs is performed in the frequency domain by using the hybrid finite element–boundary element (FE-BE) method. This study examines the effectiveness of vertical elastic mooring lines in reducing hydroelastic responses for various wavelengths, incident wave angles and aspect ratios. The stiffnesses of the mooring lines are optimized for maximum reduction in the hydroelastic response by using the Differential Evolution algorithm. It was found that hydroelastic responses of VLFS could be significantly reduced by using vertical elastic mooring lines with optimal stiffnesses.

In this paper, a computational scheme in conjunction with the moving element method has been proposed to investigate the dynamic response of a high-speed rail system in which the discrete sleepers on the subgrade support the railway track. The track foundation is modeled as a beam supported by uniformly spaced discrete spring-damper units. The high-speed train is modeled as a moving sprung-mass system that travels over the track. The effect of the stiffness of the discrete supports, train speed, and railhead roughness on the dynamic behavior of the train–track system has been investigated. As a comparison, the response of a continuously supported high-speed rail system that uses a foundation stiffness equivalent to that of a discretely supported track has been obtained. The difference in results between the “equivalent” continuously supported and the discretely supported high-speed rails has been compared and discussed. In general, the study found that a high-speed train that travels over a discretely supported track produces more severe vibrations than that travels over a continuously supported track of equivalent foundation stiffness.

This paper presents a new computational approach, namely Multi-layer Moving Plate Method (MMPM), for dynamic analysis of multi-layer connected plate resting on a Pasternak foundation under a moving load. The formulations of multi-layer moving plate element mass, damping and stiffness matrices are derived. To verify the accuracy of the proposed method, the static analysis of plates is investigated. Next, a parametric study is performed to examine the effects of various parameters on the dynamic responses of multi-layer connected plate structure.

The paper presents a damage identification methodology utilizing a model order reduction and a two-stage approach for truss structures. For that aim, a second-order Neumann series expansion is employed to condense structural physical characteristics owing to the limitation of a number of degrees of freedom (DOFs) measured by sensors. In the first step of the two-stage method, the location of potentially damaged candidates is determined via a modal strain energy based index (MSEBI), whilst the remaining one aims to accurately calculate the real damage extent via an inverse optimization problem. A recently developed adaptive hybrid evolutionary firefly algorithm (AHEFA) is utilized as an optimizer to resolve such optimization problems. A 31-bar truss is tested to verify the accuracy of the proposed paradigm.

In this paper, the moving element method (MEM) is developed to compute the hydroelastic response of a pontoon type very large floating structure (VLFS) in shallow water environment and subjected to a moving load. By using this method, the floating plate is modeled via the thin plate theory, while the linearized shallow-water equation is employed for the hydrodynamic modeling. Both computational domains of fluid and structure are concurrently discretized into “moving elements” whose coordinate system moves along with applied loads. The numerical results conducted by using the MEM are compared with the results obtained by alternative approaches. The paper also discusses the effect of water depth on the dynamic amplification factor of plate displacement and the loading’s critical speed.

Deflection patterns of a floating plate induced by a moving load have been mentioned in many studies. Generally, the structures have been assumed to be isotropic in those studies. In practical applications of floating structures, the directional-dependent bending stiffness should be considered. On the other hand, the direction of the moving load is not generally parallel to the strong material direction. Hence, the angle between these two directions should be also considered. Based on this issue, responses of a floating flexible orthotropic plate subjected to a moving load in consideration of the material angle are investigated. The plate is modeled as orthotropic Kirchhoff’s plate, while the linearized water wave theory is adopted for the hydrodynamic modeling. A mixed method of Boundary Element Method (BEM) and Moving Element Method (MEM) is introduced in this study in order to conduct the simulation. The dependence of deflection patterns on the material angle is considered according to numerical investigations.

This paper provides a further insight of galloping analysis of slender structures through a development of a transverse galloping analysis model. The well-known galloping theory of Glauert-Den Hartog is generalized. The role of mode shape, wind profile and structural parameters will be discussed. An application of the proposed theory for the famous sculptural structure “Endless column” shows drawbacks of the common galloping analysis. Critical aspects in engineering applications will be also highlighted.

A recently developed adaptive hybrid evolutionary firefly algorithm (AHEFA) as a cross-breed of differential evolution (DE) approach and firefly algorithm (FA) is utilized to address inverse optimization problems in two-stage damage detection of truss structures. In the first step, the most potentially damaged elements are recognized utilizing a modal strain energy-based index (MSEBI). In the remaining one, the AHEFA is employed as an optimizer to estimate the real damage severity relied on the afore-collected information in the first stage. The effectiveness and correctness of the present algorithm are demonstrated via three numerical examples. Results given by the current paradigm are validated with those solved by the DE and the FA. The outcomes indicate that the AHEFA can perform well in precisely recognizing the locations and extents of multidamage trusses with a lower computational attempt.

In this paper, the moving element method (MEM) is extended to cooperate with the boundary element method (BEM), namely, the BEM-MEM. This method is applied to compute hydroelastic responses of a pontoon type very large floating structure (VLFS) under wave action and also subjected to a moving load. By using this method, the structure is discretized into “moving elements” which are conceptual elements and “flow” with the moving load. Thus, the proposed method eliminates the need for keeping track of the location of the moving load with respect to the floating structure. The surrounding fluid is defined based on the potential flow theory and the motion of the floating plate is governed by the vibration equation of a thin plate. The governing equations of motion, as well as structural matrices of moving element and fluid matrices of boundary element are formulated in a relative coordinate system traveling at a constant speed. The numerical results conducted by using the BEM-MEM are compared with the results obtained by alternative approaches. The paper also discusses the effect of water depth on responses of the floating structure including displacements and drag force.

The dynamic response of high-speed train subject to braking is investigated using the moving element method. Possible sliding of wheels over the rails is accounted for. The train is modelled as a 15-DOF system comprising of a car body, two bogies and four wheels interconnected by spring-damping units. The rail is modelled as a Euler–Bernoulli beam resting on a two-parameter elastic damped foundation. The interaction between the moving train and track-foundation is accounted for through the normal and tangential wheel–rail contact forces. The effects of braking torque, wheel–rail contact condition, initial train speed and severity of railhead roughness on the dynamic response of the high-speed train are investigated. For a given initial train speed and track irregularity, the study revealed that there is an optimal braking torque that would result in the smallest braking distance with no occurrence of wheel sliding, representing a good compromise between train instability and safety.

The dynamic response of a high-speed rail experiencing heavy braking is investigated using the moving element method. Possible sliding of train wheels over the rails as the train decelerates is accounted for. The train is modelled as a 14-DOF system comprising a car body, bogies and wheel sets interconnected by spring-damping units. The railway track is modelled as an infinite Euler–Bernoulli beam resting on a two-parameter elastic-damped foundation. A convected coordinate system attached to the moving train is employed in the formulation of the governing equations. The effects of braking torque, coefficient of static friction between wheels and rail, initial train speed and the severity of railhead roughness (track irregularity) on the dynamic response of the high-speed rail, including the occurrence of the ‘jumping wheel’ phenomenon, are examined. The phenomenon describes the momentary loss of contact between the wheel and track. A combination of high braking torque, large static friction coefficient, high initial train speed and severe track condition promotes larger dynamic effects.

This article aims to firstly introduce a computational approach, named multi-layer moving plate method (MMPM), to dynamic analysis of viscoelastically connected infinitely long double-plate systems subjected to moving loads. The Reissner-Mindlin plate theory is utilized to describe the displacement field through the thickness of each plate, whilst quadratic serendipity shape functions are employed to represent unknown fields in finite element analyses (FEAs). The governing equations of motion of connected double-plate system are established in a moving coordinate system attached to the moving load. As a consequence, the paradigm can absolutely eradicate the update process of force vector since the applied load is taken into account as “stationary” in its coordinate system. First, several numerical examples for static, free vibration and dynamic analyses are exhibited to verify the accuracy of the proposed MMPM. Then, the influences of various parameters such as load’s velocity, damping coefficient, stiffness coefficient, and plate thickness on the dynamic responses of double-plate system are examined in great detail.

The article introduces a novel integrated moving element method (IMEM) to hydroelastic analysis of infinitely extended floating plates under moving loads in shallow water conditions. The floating plate is modeled via the Kirchhoff-Love theory, while the linearized shallow-water equation is adopted for the hydrodynamic modeling. Both computational domains of fluid and structure are concurrently discretized into “moving elements” whose coordinate system moves along with applied loads. Accordingly, the paradigm can absolutely eradicate the update procedure of force vector owing to the change of contact point with discretized elements not only for the plate but also for the fluid. Furthermore, the IMEM also requires fewer number of discrete elements than the standard finite element method (FEM) due to their independence with the distance of moving load. Results obtained in several numerical examples are compared with those of the Fourier Transform Method (FTM) to validate the accuracy and effectiveness of the proposed methodology. In addition, the influence of water depth, load speed, multiple contact points, as well as the distance between axles on the dynamic amplification factor of plate displacement and the loading's critical speed is also examined in great detail.

In this paper, hydroelastic behavior of a pontoon-type very large floating structure (VLFS) subjected to a moving single axle vehicle is computed using a novel numerical approach, in which the boundary element method (BEM) is firstly extended to cooperate with the moving element method (MEM), named the BEM–MEM. By utilizing this paradigm, the plate and fluid are discretized into “moving structural element” and “moving boundary element”, respectively, which are conceptual elements and “travel” with the moving vehicle. Thus, the proposed method can absolutely eliminate the need of keeping track the location of the moving load with respect to the floating structure. Particularly, the surrounding fluid is defined based on the potential flow theory and the motion of a floating plate is governed by the vibration equation of a thin plate. The governing equations of motion, moving element and fluid matrices of boundary element are formulated in a relative coordinate system traveling with the moving vehicle. Several examples are numerically conducted to illustrate the performance and ability of the BEM–MEM. Its obtained results are compared with those of the traditional finite element method for validation. The outcomes reveal that the proposed method is effective for the large-time behavior owing to the fact that it does not require a domain with the length greater than the horizontal displacement of the vehicle. The paper also discusses the effect of the liquid and structural parameters on responses of the vehicle and floating structure.

Proposed herein is a two-mode wave energy converter-type attachment to the fore edge of pontoon-type very large floating structures (VLFSs) for wave energy extraction and reduction of hydroelastic response. This attachment consists of floating horizontal and submerged vertical plates that are connected to the VLFS with hinges and linear power take-off systems. The use of both floating horizontal and submerged vertical plates combines the superior performances of floating plates in extracting wave energy from short waves (T 7 s). When deployed in sites where 5 s ≤ T ≤ 7 s, the two-mode attachment yields a larger power production than the sole usage of floating plates or the sole usage of submerged vertical plates. Interestingly, the two-mode attachment also combines the superior performance of submerged vertical plates in reducing hydroelastic response for relatively short waves (T

In this paper, a computational study using the moving element method (MEM) is carried out to investigate the dynamic response of a high-speed rail (HSR) traveling at non-uniform speeds. A new and exact formulation for calculating the generalized mass, damping and stiffness matrices of the moving element is proposed. Two wheel–rail contact models are examined. One is linear and the other nonlinear. A parametric study is carried out to understand the effects of various factors on the dynamic amplification factor (DAF) in contact force between the wheel and rail such as the amplitude of acceleration/deceleration of the train, the severity of railhead roughness and the wheel load. Resonance in the vibration response can possibly occur at various stages of the journey of the HSR when the speed of the train matches the resonance speed. As to be expected, the DAF in contact force peaks when resonance occurs. The effects of the severity of railhead roughness and the wheel load on the occurrence of the jumping wheel phenomenon, which occurs when there is a momentary loss of contact between the wheel and track, are investigated.

This paper presents the moving element method (MEM) for dynamic analyses of functionally graded (FG) plates resting on Pasternak foundation under moving harmonic load. The Mindlin plate theory is used to model the FG plates. Macroscopic material properties of FG plates are assumed to continuously vary across the thickness direction by a simple power-law distribution. The governing equation of the FG plate is formulated in a coordinate system which moves along with the applied load. In addition, the method simply treats the moving load as “stationary” at the discretized node of plate to completely eliminate the update procedure of force vector due to the change of contact point with elements. To verify the accuracy of the computational paradigm, static and free vibration analyses of FG plates are examined first. Dynamic analyses of FG plates subjected to a moving harmonic load are then conducted to investigate the effects of various parameters such as volume fraction exponent, Young’ modulus, load velocity, foundation damping coefficient and load acceleration/deceleration on dynamic responses of the plate.

The modeling and analysis for mechanical response of nano-scale beams undergoing large displacements and rotations are presented. The beam element is modeled as a composite consisting of the bulk material and the surface material layer. Both Eringen nonlocal elasticity theory and Gurtin–Murdoch surface elasticity theory are adopted to formulate the moment–curvature relationship of the beam. In the formulation, the pre-existing residual stress within the bulk material, induced by the residual surface tension in the material layer, is also taken into account. The resulting moment-curvature relationship is then utilized together with Euler–Bernoulli beam theory and the elliptic integral technique to establish a set of exact algebraic equations governing the displacements and rotations at the ends of the beam. The linearized version of those equations is also established and used in the derivation of a closed-form solution of the buckling load of nano-beams under various end conditions. A discretization-free solution procedure based mainly upon Newton iterative scheme and a selected numerical quadrature is developed to solve a system of fully coupled nonlinear equations. It is demonstrated that the proposed technique yields highly accurate results comparable to the benchmark analytical solutions. In addition, the nonlocal and surface energy effects play a significant role on the predicted buckling load, post-buckling and bending responses of the nano-beam. In particular, the presence of those effects remarkably alters the overall stiffness of the beam and predicted solutions exhibit strong size-dependence when the characteristic length of the beam is comparable to the intrinsic length scale of the material surface.

The paper proposes a computational approach to simulate the dynamic responses of composite plate resting on a Pasternak foundation subjected a moving load using the moving element method (MEM). The plate element stiffness matrix is formulated in a coordinate system which moves with the load. The main convenience is that the load is static in this coordinate system, which avoids the updating of the load locations due to the change of the contact points with the elements. The effects of the Pasternak foundation, energy dissipation mechanisms, load’s velocity, material properties on the dynamic responses of the composite plates are investigated.

Presented herein is a novel computational approach using the moving element method (MEM) for simulating the dynamic response of Mindlin plate resting on a viscoelastic foundation and subjected to moving loads. The governing equations and the element mass, damping and stiffness matrices are formulated in a convected coordinate system in which the origin is attached to the point of the moving applied load. Thus, the method simply treats moving loads as ‘stationary’ at the nodes of the plate to avoid updating the locations of moving loads due to the change of the contact points on the plate. To verify the accuracy of the proposed computational approach, static and free vibration analyses of plates are investigated first. Next, the dynamic response of plate resting on a viscoelastic foundation subjected to a moving load is examined. A parametric study is performed to determine the effects of the load’s velocity, foundation damping and foundation stiffness on the dynamic response of a plate. Finally, the comparisons of the dynamic response of plates resting on viscoelastic foundation and subjected to moving vehicles with three models of load (single-wheel, single-axle and tandem-axle) are discussed.

This paper presents a numerical study on the out-of-plane responses of a high-speed train running on a curved railway track segment using the moving element method. The accuracy and efficiency of the proposed computation model presented herein are compared with available analytical results from the literature and a finite element solver based on a simplified moving load model. Thereafter, a half-railcar moving sprung-mass model and a double-rail track-foundation model are presented to investigate the behavior of a high-speed train traversing a curved track, particularly when the train speed is greater than the design speed of the curved track segment. The results show that the train speed and severity of track irregularity significantly affect the contact forces on the rails. This paper also presents a case of a railcar overturning when the train speed is greater than 2.5 times the design speed of a curved track segment.

This paper is concerned with a numerical study on the dynamic response of a high-speed rail (HSR) system subjected to unsupported sleepers using the moving element method (MEM). A three-phase computational scheme in conjunction with the MEM is proposed to account for the motion of the unsupported sleepers in relation to the truncated rail segment in the moving coordinate system. The accuracy of the proposed computational scheme is examined by comparison with available analytical results in the literature and against the finite element method using commercial software. A parametric study is conducted using a computational model consisting of a 10-degree of freedom train model and a three-layer ballasted track model to investigate the effect of unsupported sleepers on the dynamic response of the HSR system. Various factors affecting the response of the HSR system, including the speed of the train, the number of unsupported sleepers and the distance between the unsupported sleepers, are examined and discussed.

The dynamic response of a high-speed multiple-railcar train experiencing deceleration under braking condition over a straight track is investigated using the moving element method. Possible sliding of train wheels over the rails is accounted for. The train is assumed to comprise a locomotive as the leading railcar and several passenger railcars connected to each other through train couplers. Each railcar is modeled as a 15-DOF system of interconnected car body, two bogies and four wheels. The rail is modeled as an Euler–Bernoulli beam resting on a two-parameter elastic damped foundation. The train and rails are coupled through normal and tangential wheel–rail contact forces. The effects of various parameters, such as braking torque, coupler stiffness, coupler gap, wheel load, wheel–rail contact condition, initial train speed and partial failure in braking mechanism on the dynamic response of the train subject to braking are investigated. It is found that there is significant interaction between neighboring railcars when the braking torque is applied between the optimal and critical torques. The former is the torque that would result in the smallest braking distance with no occurrence of wheel sliding and the latter is the smallest torque to cause wheel sliding in all four wheels.

In this paper, a computational study using the moving element method is carried out to investigate the dynamic response of a high-speed rail (HSR) experiencing sudden braking. The train is modeled as a 10-DOF system of interconnected spring-damping units. The Hertz contact theory is employed to account for the nonlinear contact force between the wheel and rail. The railway track is treated as an Euler–Bernoulli beam resting on a two-parameter elastic damped foundation. The effects of wheel sliding, initial train deceleration, initial train speed and the severity of railhead roughness on the dynamic response of the HSR are investigated.

In this paper, a computational study using the moving element method (MEM) was carried out to investigate the dynamic response of a high-speed train–track system. Results obtained using Hertz contact model and linearized Hertz contact model are compared and discussed. The dynamic responses of a train travelling across a uniform foundation and a transition region are also investigated. Parametric study is performed to understand the effect of various factors on the occurrence and patterns of the jumping wheel phenomenon such as the variation of foundation stiffness, travelling speed of the train and the severity of railhead roughness.