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The article discusses a new approach to modeling the behavior of structures under the influence of dynamic loads, including loads from ground and underground transport. The approach is to apply the direct integration method, as well as the SBFEM method to calculate the forces in load-bearing building structures under dynamic influences, taking into account a number of factors - the damping properties of the subgrade, physical nonlinearity of soils and the passage of waves in the soil space. The article presents the main theoretical premises, the results of a numerical experiment of a real monolithic building, built in the zone of influence of the subway.

Introduction: This paper reviews the analytical method of assessing the seismic and extreme load resistance of buildings with a complex macrostructure that includes elastic-plastic inserts operating in shear. Methods: We analyze a number of studies that rationalize the choice of models for simulating complex elastic-plastic deformation in a mechanical system with several degrees of freedom, as well as studies that review the durability and resilience of buildings with a complex macrostructure based on non-linear shear links when subjected to dynamic and extreme impact. We also consider the methods of structural analysis regarding buildings with elastic-plastic inserts, accounting for the plastic hinged joints of metal frames. Results: We apply the analytical method to linear and non-linear systems with n degrees of freedom. We propose a mathematical equation that describes the nature of shear link response to seismic and extreme loads. Our method makes it possible to obtain an analytical solution for structures with proportionate and disproportionate damping by using the direct integration algorithm. Discussion: Most structures with a broad range of construction material properties require a disproportionate damping model. In this study, we solve equations by using the direct integration algorithm based on disproportionate damping. Under high dynamic load, the reinforcement of shear inserts operates in a plastic state.

This paper proposes a time-dependent probability method to predict the time-variant pounding risk, owing to this reason that the required separation gap width fails to accommodate the relative movement between two adjacent decks, of bridge systems subjected to non-stationary stochastic seismic excitations. Firstly the pseudo excitation method in random theory is utilized to transform the motion equation of system under the non-stationary stochastic seismic excitations into the transient response equation under deterministic external loads. And then the high precision direct integration method (HPDIM) is also employed to reduce the large number of transient analysis into two times for overcoming the challenges of strenuous computing effort. The time-dependent pounding system probability of bridges is derived by the combination of extreme value distribution theory and matrix-based system probability theory. Finally based on the proposed time-dependent probability method the numerical analysis of a real two span simply-supported beam bridge subjected to spatial and non-stationary ground motions is conducted herein for the pounding risk assessment. The results of this study provides in-depth insight into the time-dependent pounding probability of bridge systems subjected to spatially varying and non-stationary ground motions.

Η παρούσα διδακτορική διατριβή αποτελεί συμβολή στην ανάπτυξη εξελιγμένων θεωριών δοκού για την ανάλυση ραβδωτών φορέων. Οι εξελιγμένες θεωρίες δοκού που αναπτύχθηκαν λαμβάνουν υπόψη φαινόμενα γενικευμένης στρέβλωσης (διατμητική υστέρηση λόγω κάμψης και στρέψης), διαστρέβλωσης (παραμόρφωση διατομής – distortion), ενώ πραγματοποιείται και γεωμετρικά μη γραμμική δυναμική ανάλυση δοκών σταθερής ή μεταβλητής διατομής, λαμβάνοντας υπόψη φαινόμενα ανώτερης τάξης όπως η περιστροφική και στρεβλωτική αδράνεια, η μη γραμμικότητα εξωτερικής φόρτισης, οι όροι Wagner και η βράχυνση λόγω στρέψης. Οι εν λόγω καινοτόμες θεωρίες συνδυάζουν την αυξημένη ακρίβεια με τα εγγενή πλεονεκτήματα των στοιχείων δοκού, οδηγώντας στην ανάπτυξη εξελιγμένων υπολογιστικών εργαλείων για την ανάλυση ραβδωτών φορέων.Η γενικευμένη στρέβλωση λαμβάνεται υπόψη, με την εισαγωγή ανεξάρτητων παραμέτρων, που εκφράζουν την «ένταση» της στρέβλωσης στο μήκος της δοκού. Οι παράμετροι αυτές πολλαπλασιάζουν αντίστοιχες συναρτήσεις στρέβλωσης, που προκύπτουν από ισάριθμα διδιάστατα προβλήματα συνοριακών τιμών στο χωρίο της διατομής. Στην παρούσα διατριβή αντιμετωπίζεται το πρόβλημα παραβίασης της συνοριακής συνθήκης μηδενισμού της διατμητικής τάσης στην παράπλευρη επιφάνεια της δοκού (ισορροπία σε επίπεδο υλικού σημείου) από τις τάσεις που προκύπτουν από το υιοθετούμενο πεδίο μετατοπίσεων. Προτείνεται διαδικασία «διόρθωσης» του τασικού πεδίου με χρήση της εξίσωσης διαμήκους τοπικής ισορροπίας. Μέσω της διόρθωσης αυτής βελτιώνεται η ακρίβεια των παραγόμενων αποτελεσμάτων χωρίς αύξηση των κινηματικών αγνώστων και διατηρείται κατά το μέγιστο δυνατό βαθμό η απλότητα της διατύπωσης.Όσον αφορά στη διαστρέβλωση (distortion), παράγεται κατάλληλη βάση συναρτήσεων διαστρέβλωσης/στρέβλωσης μέσω επαναληπτικού σχήματος ισορροπίας στο χωρίο της διατομής. Το σχήμα αυτό παράγεται χρησιμοποιώντας τις εξισώσεις τοπικής ισορροπίας της θεωρίας ελαστικότητας. Η προσέγγιση αυτή παρουσιάζει πλεονεκτήματα έναντι των αντίστοιχων προσεγγίσεων της διεθνούς βιβλιογραφίας που βασίζονται στην Ανάλυση Ιδιομορφών (ανεξάρτητος προσδιορισμός αξονικών, καμπτικών, στρεπτικών μορφών διαστρέβλωσης/στρέβλωσης). Συνεπώς, διατυπώνεται θεωρία δοκού με το μικρότερο δυνατό αγνώστων παραμέτρων διαστρέβλωσης που αντιπροσωπεύουν εξίσου όλους τους μηχανισμούς αντίστασης.Στη συνέχεια οι ως άνω θεωρίες ενσωματώνονται στη μητρωική ανάλυση ραβδωτών φορέων. Παράγονται καινοτόμα τρισδιάστατα στοιχεία δοκού τυχούσας διατομής που περιλαμβάνουν διατμητικές παραμορφώσεις, γενικευμένη στρέβλωση (μητρώο στιβαρότητας 20×20) και διαστρέβλωση (μητρώο στιβαρότητας 32×32) μαζί με τα αντίστοιχα διανύσματα ισοδύναμης επικόμβιας φόρτισης. Τα εν λόγω στοιχεία δοκού ενσωματώνονται σε υπολογιστικό εργαλείο που βασίζεται στoν αλγόριθμο της Μεθόδου Άμεσης Στιβαρότητας (ΜΑΣ, Direct Stiffness Method – DSM) διαμορφώνοντας εξελιγμένο υπολογιστικό εργαλείο για την ανάλυση πλαισιωτών φορέων. Προκειμένου να αρθεί η αδυναμία μετασχηματισμού των επικόμβιων Βαθμών Ελευθερίας (ΒΕ) ανώτερης τάξης σε μέλη συνδεδεμένα υπό γωνία, αναπτύσσεται μεθοδολογία μετασχηματισμού που λαμβάνει υπόψη τις συνθήκες μετάδοσης διαστρέβλωσης/στρέβλωσης στους κόμβους του πλαισίου.Παρουσιάζεται επίσης γενική μεθοδολογία για τη γεωμετρικά μη γραμμική δυναμική ανάλυση δοκών σταθερής και μεταβλητής διατομής. Όσον αφορά στις πρισματικές δοκούς, εξετάζεται η πλέον γενική περίπτωση διατομής, ενώ όσον αφορά στην περίπτωση μεταβλητής διατομής, εξετάζεται η συνήθης περίπτωση της διπλά συμμετρικής διατομής με ομαλό νόμο μεταβολής. Η δοκός υπόκειται σε τυχούσα εξωτερική χρονικά μεταβαλλόμενη φόρτιση, συνοριακές και αρχικές συνθήκες και αναπτύσσει μετρίως μεγάλες μετατοπίσεις και στρεπτικές στροφές. Το μη γραμμικό φαινόμενο της αλλαγής μοχλοβραχίονα του εξωτερικού φορτίου, η επιρροή της περιστροφικής και στρεβλωτικής αδράνειας, των συντελεστών Wagner, καθώς και του φαινομένου βράχυνσης λόγω στρέψης λαμβάνονται υπόψη.Στην παρούσα διατριβή, τα προβλήματα συνοριακών και αρχικών τιμών επιλύονται αριθμητικά χρησιμοποιώντας τη Μέθοδο Συνοριακών Στοιχείων (ΜΣΣ, Boundary Element Method – BEM) και τη Μέθοδο Αναλογικής Εξίσωσης (ΜΑΕ, Analog Equation Method – AEM), η οποία αποτελεί εξέλιξη της BEM. Η AEM αντιμετωπίζει τις εγγενείς αδυναμίες της BEM και προσφέρεται για την επίλυση μεγάλου εύρους προβλημάτων μηχανικής που ορίζονται από χρονικά εξαρτώμενες ή/και μη γραμμικές διαφορικές εξισώσεις ή εξισώσεις με μεταβλητούς συντελεστές.Βάσει των διαδικασιών που αναπτύσσονται, μελετώνται αντιπροσωπευτικά αριθμητικά παραδείγματα. Η ακρίβεια και αξιοπιστία των προτεινόμενων μεθόδων επιβεβαιώνονται με υπάρχουσες αναλυτικές και αριθμητικές λύσεις, πειραματικά αποτελέσματα καθώς και με προσομοιώματα στερεών πεπερασμένων στοιχείων και πεπερασμένων στοιχείων κελύφους.

Elastic response spectra that take into account the effects of soil-structure interaction on soft soils are developed. The response spectra are calculated utilizing a 3DOF system including deformations of the superstructure and foundation. The equations of motion of the system are solved using direct integration under normalized earthquake records. Statistical processing of the results is implemented resulting in response spectra for “short and dense buildings with low interaction”, “short and dense buildings with high interaction”, “tall and light buildings with low interaction” and “tall and light buildings with high interaction”. The resulting response spectra are smoothed and discussed.

Fracture mechanics parameters are used for numerical and analytical risk assessment of residual life of a cracked oil drilling rig welded pipe. Number of cycles to the critical crack length, obtained by direct integration of Paris law, verified by using extended Finite Element Method, are related to the number of cycles needed for 10 years of exploitation, to assess probability and risk due to fatigue crack growth.

This paper aims to define the non-linear response for concrete arch gravity dams, considering seismic actions as main external destabilizing actions. The plastic degradation theory has been used to define the reduction of the elasto-plastic modulus during the hysteretic cycles. The parameters to apply the model are obtained from the literature and numerical analysis. In this sense, working with a reduction of the elasto-plastic modulus is useful to define the displacement of the structure. The seismic input has been obtained from probabilistic and deterministic seismic hazard analyses. For that, a series of several earthquakes have been chosen to perform the time–history analysis. The response of the structure blocks under four earthquakes has been made using a step-by-step direct integration. An application to Rules Dam has been made to test the method. Results of the seismic analysis provide several specific accelerations for concrete arch gravity dams. Results of the structural show that in 2D analysis the maximum non-linear dam displacements reach value up to 27 cm, whereas for 3D analysis they reach up to 7 cm. Moreover, these cyclic displacements produce several accumulations of plastic deformations and cracks.

A finite element model for predicting the nonlinear aeroelastic behavior of composite panels undergoing intralaminar and translaminar progressive damage in supersonic flow is presented. The classical plate theory in conjunction with the von Karman nonlinear strains is used for structural modeling, and the linear piston theory is used to model the aerodynamic loads . Progressive damage is modeled by a smeared cracking formulation in which stress-based, continuum damage mechanics and fracture mechanics approaches are combined. No modal reduction is performed and an iterative form of the Newmark method is used for the numerical direct integration in time of the nonlinear equations. Simulations considering different lay-ups are conducted, in which the influence of progressive damage on the aeroelastic behavior of the panels is investigated, and damage extent and failure mechanisms are assessed. The results obtained in the analyses consist in important insights concerning the flutter-induced damage in composite panels.

High damping rubber bearings show highly nonlinear stress-strain behaviour. Deformation-history integral (DHI) model which can estimate small strain stiffness degradation and nonlinear plasticity via a relatively simple innovative formulation is implemented in this study to model HDRB as the rehabilitation method for a seismically vulnerable building. Considered structure in this study is a three-dimensional, four-story steel frame residential building with a concentrically braced system. Nonlinear direct integration time history analysis and plastic hinges approach were implemented to evaluate structural behaviour of considered structure. It was observed that structural responses enhanced significantly after rehabilitation. Absolute maximum base shear values decreased 61.8% and 92.2% in the worst and best cases, respectively. Most of structural elements remained elastic after rehabilitation and required performance level was satisfied. publishedVersion

Estimation of equivalent static wind loads for structures is one of the most important issues in wind engineering. So far, the well-known Davenport Chain has been commonly used and put in several international codes or regulations for structural engineers. However, due to its strict hypotheses, this method can be applied to limited structures and need certain modifications when conflicts with real designs. Other methodologies have been developed in the past thirty years, such as the load-response-correlation method [1], POD based universal equivalent static wind load [2], the consistent coupling method (Ke et al. 2012), the principal static wind load (Blaise and Denoel 2013), and so on. Recently, the load-response-correlation method has been added in ISO 4354 Appendix D10 as an option to estimate wind loads instead of applying gust loading factor method which is originally derived from the Davenport Chain. These developed methodologies can be categorized into two: (1) the one that needs the preliminary information from time-domain analysis results and (2) the one that needs specific hypotheses for calculations. The former usually takes more calculation time than the latter and is sometimes questioned for lack of practical meaning since the time domain analysis has been done in advance. None of these methodologies can hardly be responsible for precise calculations of all structures. This paper intends to introduce the advantages and shortcomings of the two main approaches in estimating wind loads via thirty-five different parametric cases of a two-dimensional large span roof structure. Time-domain analysis based on the direct integration method is also included for comparison. Finally, a general suggestion table is given for these methods for reasonable application ranges.

Hybrid simulation (HS) is an advanced simulation method that couples experimental testing and analytical modeling to better understand structural systems and individual components&rsquo, behavior under extreme events such as earthquakes. Conducting HS and real-time HS (RTHS) can be challenging with complex analytical substructures due to the nature of direct integration algorithms when the finite element method is employed. Thus, alternative methods such as machine learning (ML) models could help tackle these difficulties. This study aims to investigate the quality of the RTHS tests when a deep learning algorithm is used as a metamodel to represent the dynamic behavior of a nonlinear analytical substructure. The compact HS laboratory at the University of Nevada, Reno was utilized to conduct exclusive RTHS tests. Simulating a braced frame structure, the RTHS tests combined, for the first time, linear brace model specimens (physical substructure) along with nonlinear ML models for the frame (analytical substructure). Deep long short-term memory (Deep-LSTM) networks were employed and trained to develop the metamodels of the analytical substructure using the Python environment. The training dataset was obtained from pure analytical finite element simulations for the complete structure under earthquake excitation. The RTHS evaluations were first conducted for virtual RTHS tests, where substructuring was sought between the LSTM metamodel and virtual experimental substructure. To validate the proposed RTHS testing methodology and full system, several actual RTHS tests were conducted. The results from ML-based RTHS were evaluated for different ML models and compared against results from conventional RTHS with finite element models. The paper demonstrates the potential of conducting successful experimental RTHS using Deep-LSTM models, which could open the door for unparalleled new opportunities in structural systems design and assessment.

In this paper, the effect of green water impact on a flexible structure is studied based on three-step computational fluid dynamics (CFD)–boundary element method (BEM)–finite element method (FEM) approach. The impact due to shipping of water on the deck of the vessel is computed using commercial CFD software and used as an external force in coupled BEM-FEM solver. Other hydrodynamic forces such as radiation, diffraction, and Froude-Krylov forces acting on the structure are evaluated using 3D time domain panel method. To capture the structural responses such as bending moment and shear force, 1D finite element method is developed. Moreover, a direct integration scheme based on the Newmark–Beta method is employed to get the structural velocity, displacement, etc., at each time step. To check the effect of the green water impact on the structure, a rectangular barge without forward speed is taken for the analysis. The influence is studied in terms of bending moment, shear force, etc. Results show that the effect of green water impact on the bow region can be severe in extreme seas and lead to various structural damages. Similarly, it is also verified that vessel motion affects green water loading significantly and therefore one must consider its effect while designing a vessel.

The structural vibration of the main beam of a crane causes fatigue damage and discomfort to the driver. The swing of the payload has an effect on positioning precision, especially for a ladle crane, and this directly affects production safety. To study the influence of system parameters on the vibration of a crane’s main beam and the angle of the payload, a system consisting of the main beam, trolley, payload, and cabin was constructed. A rigid-flexible coupling dynamic model of a moving trolley with a hanging payload that moves on the flexible main beam with a concentrated cabin mass is established, and the direct integration method is used to solve the nonlinear differential equations of system vibration, which are obtained through Lagrange’s equation. Then, the time domain responses of the flexible main beam, payload angle, and cabin vibration are obtained. The influences of the trolley running speed, quality of the payload, and quality and position of the cabin on the vibration of the main beam and payload angle are analyzed. The results indicate that the amplitude of the main beam is directly proportional to the quality of the trolley, payload, and cab; the position of the cabin is closer to the mid-span; the amplitude of the main beam is larger; the structural damping has some influence on the vibration of the main beam; and the swing angle of the payload is related to the maximum running speed of the trolley, acceleration time, and length of the wire rope. In order to reduce the vibration of the main beam and cabin, the connection stiffness of the cabin should be ensured during installation.

Due to the low costs of distributed optical fibre sensors (DFOS) and the possibility of their direct integration within layered composite members, DFOS technology has considerable potential in structural health monitoring of linear underground infrastructures. Often, it is challenging to truly simulate the actual ground conditions at all construction stages. Thus, reliable measurements are required to adjust the model and verify theoretical calculations. The article presents a new approach to monitor displacements and strains in Glass Fiber Reinforced Polymer (GFRP) collectors and pipelines using DFOS. The research verifies the effectiveness of the proposed monitoring solution for health monitoring of composite pipelines. Optical fibres were installed over the circumference of a composite tubular pipe, both on the internal and external surfaces, while loaded externally. Analysis of strain profiles allowed for calculating the actual displacements (shape) of the pipe within its cross-section plane using the Trapezoidal method. The accuracy of proposed approach was positively verified both with reference spot displacement transducer as well as numerical simulations using finite element method (FEM). DFOS could obtain a comprehensive view of structural deformations, including both strains and displacements under externally applied load. The knowledge gained during research will be ultimately used for renovating existing collectors.

This work presents an efficient explicit finite element model for predicting the nonlinear aeroelastic behavior of composite panels in the supersonic regime. The first-order shear deformation plate theory in conjunction with the von Karman nonlinear strains is used for structural modeling and the linear piston theory is used to model the aerodynamic loads. In order to reduce the computational cost of the simulations, a lumping procedure is employed in the mass and aerodynamic damping matrices of the finite element model. No modal reduction is performed and the central difference method is used for the numerical direct integration in time of the nonlinear equations. The model is verified using results from the literature and it is demonstrated that the lumping procedure drastically reduces the computational cost of the simulations.

The application of the sampling surfaces (SaS) method to the three-dimensional (3D) stress analysis of laminated composite plates is presented in a companion paper (Kulikov GM, Plotnikova SV. Strong sampling surfaces formulation for laminated composite plates. Compos Struct 2017;172:73–82). In this paper, we extend the strong SaS formulation to the 3D vibration analysis of laminated plates. The SaS formulation is based on choosing the arbitrary number of SaS parallel to the middle surface in order to introduce the displacements of these surfaces as basic plate unknowns. Such choice of unknowns with the use of the Lagrange polynomials in spatial approximations of displacements through the layer thicknesses leads to a robust laminated plate formulation. The feature of the proposed approach is that all SaS are located inside the layers at Chebyshev polynomial nodes. The use of outer surfaces and interfaces is avoided that makes it possible to minimize uniformly the error due to the Lagrange interpolation. Therefore, the strong SaS formulation based on direct integration of equations of motion of the elastic body can be applied efficiently for the 3D free and forced vibration analyses of laminated composite plates.

Local fatigue approaches, such as, the stress-life, strain-life or energetic approaches defines a framework to estimate the fatigue crack initiation from notches of structural details. Various engineering structures, such as, bridges, wind towers, among others, are subjected to cyclic dynamic loadings which may substantially reduce the strength of these structures. Nowadays, the structural systems tend to be more complex being necessary to find computationally efficient solutions to perform their fatigue analysis, accounting for dynamic actions corresponding to long complex loading events (e.g. diversity of trains crossing a bridge), mainly if local approaches are envisaged. Thus, this paper aims at presenting and validating a generalization of a methodology based on modal superposition technique, for fatigue damage parameters evaluation, which can be applied in fatigue analysis using local approaches. This technique was applied recently in the context of fatigue crack propagation based on fracture mechanics, although it can be extended to compute the history of local notch stresses and strains at notches. A very important conclusion is that the technique can be explored for the case of local confined plasticity at notches whenever the global elastic behaviour of the component prevails. Local submodelling can be explored with this technique to avoid the necessity of large computational models. Local models are only needed to be run under linear elastic conditions for the selected modal shapes of the structure, being the local time history of fatigue damage variable computed by modal superposition for each loading event. That time history may be further post-processed for elastoplastic conditions using Neuber or Glinka’s analyses. Comparisons with direct integration elastoplastic dynamic analysis confirmed the feasibility of the proposed approach.

This investigation is aimed to develop a model of experimental-computation determination of a support moment of a cantilever beam loaded with concentrated force at its end including the optimal choice of coordinates of deflection data points and parameters of transformation of deflection data in case of insufficient accuracy of the assignment of initial parameters (support settlement, angle of rotation of the bearing section) and cantilever beam length. The influence of distribution and characteristics of sensors on the cantilever beam on the accuracy of determining the support moment which improves in the course of transition from the uniform distribution of sensors to optimal non-uniform distribution is shown. On the basis of the theory of inverse problems the method of transformation reduction at numerical differentiation of deflection functions has been studied. For engineering evaluation formulae of uncertainty estimate to determine a support moment of a cantilever beam at predetermined uncertainty of measurements using sensors have been obtained.

Present investigation is concerned with the free vibration property of a beam with periodically variable cross-sections. For the special geometry characteristic, the beam was modelled as the combination of long equal-length uniform Euler-Bernoulli beam segments and short equal-length uniform Timoshenko beam segments alternately. By using continuity conditions, the hybrid beam unit (ETE-B) consisting of Euler-Bernoulli beam, Timoshenko beam and Euler-Bernoulli beam in sequence was developed. Classical boundary conditions of pinned-pinned, clamped-clamped and clamped-free were considered to obtain the natural frequencies. Numerical examples of the equal-length composite beam with 1, 2 and 3 ETE-B units were presented and compared with the equal-length and equal-cross-section Euler-Bernoulli beam, respectively. The work demonstrates that natural frequencies of the composite beam are larger than those of the Euler-Bernoulli beam, which in practice, is the interpretation that the inner-welded plate can strengthen a hollow beam. In this work, comparisons with the finite element calculation were presented to validate the ETE-B model.

To determine the influence of temperature on the mechanical properties of crane metal structures, three Q355 alloy steel samples were processed and their elastic moduli were tested at different temperatures using a metal tension test bed. The constitutive equation for the elastic modulus of Q355 alloy steel at different temperatures was predicted using test data and a neural network algorithm. Based on crane structural characteristics and the principle of system dynamics, a coupling vibration model was established that included the crane flexible girder, cabin, trolley, crane, and temperature. System motion equations were established according to the Lagrange equation, and the approximate solution of nonlinear system vibration was solved by the direct integration method (the Newmark method). The dynamic characteristics of the main beam and cabin were analyzed at different temperatures, as well as safety during service. The results show that, with increasing temperature, the maximum midspan displacement of the main beam increases gradually, by 14.3%, 21.4%, and 57.1% at temperatures of 300°C, 400°C, and 600°C, respectively. The cabin vibration displacement increases with temperature, by up to 32.5% at 600°C, but the influence of temperature on cabin vibration acceleration is not obvious. It was concluded that the influence of temperature on the dynamic characteristics of the main beam must be considered during the design stage of cranes. The proposed model and analysis method provide a theoretical basis for the design of casting cranes according to temperature.

Based on Mindlin plate theory and finite element method (FEM), dynamic response analysis of sandwich composite plates with auxetic honeycomb core resting on the elastic foundation (EF) under moving oscillator load is investigated in this work. Moving oscillator load includes spring-elastickand damperc. The EF with two coefficients was modelled by Winkler and Pasternak. The system of equations of motion of the sandwich composite plate can be solved by Newmark’s direct integration method. The reliability of the present method is verified through comparison with the results other methods available in the literature. In addition, the effects of structural parameters, material properties, and moving oscillator loads to the dynamic response of the auxetic honeycomb plate are studied.

This paper presents a numerical dynamic analysis of a self-supporting transmission line (TL) latticed steel tower, for the purpose of compare the results with those obtained in an experimental dynamic analysis of a full-scale tower. The main objective of this work is to calibrate the structural damping ( c ) in the numerical model until the damping ratio ( ζ ) results the same that in the experimental analysis, since the damping is a fundamental parameter in numerical analysis, which can change significantly the response of the structure, especially in terms of dynamic amplification. It should be noted that in this type of structure is crucial perform a structural analysis most accurate possible, given the fact that in a TL are built hundreds of identical towers and the collapse of one can lead to a cascading failure. The dynamic characteristics, such as the frequencies and normal modes were evaluated in a modal analysis, using the ANSYS © program v. 15.0, and also through the direct numerical integration method, using an explicit approach (central finite differences). The experimental tower was tested using impulsive loads, which were reproduced in the numerical model to allow comparison with the experimental results. In the modal analysis were employed models commonly used in actual designs, that is, with space truss and space frame members. For the direct integration method, was used a program developed in FORTRAN, in which only space truss elements are allowed, necessitating the adoption of the fictitious bars to eliminate internal instabilities. The consideration of the damping in the direct integration method was taken in a simplest form, that is, proportional to the mass. Finally, the numerical values found were very close to the experimental response, setting the value of structural damping for use in such projects of this type of tower.

A sensitivity-based finite element model updating approach is presented to identify the local damages in axially functionally graded (AFG) beams. The local damage is simulated by a reduction in the elemental Young's modulus of the beam. In the forward analysis, free vibration analysis is conducted to obtain the natural frequency of the beam. Then forced vibration responses of the beam under external force are obtained from Newmark direct integration. In the inverse analysis, an objective function is established and a sensitivity-based finite element model updating approach is used to identify the local damages in the beam. Two numerical examples are investigated to illustrate the correctness and efficiency of the proposed method. Damage identification results from measured natural frequencies and the dynamic responses from different excitation forces are compared. The effects of measurement noise on the identification results are investigated. Studies in this paper indicate that the proposed method is efficient and robust for identifying damages in the axially functionally graded beams. Good identified results can be obtained from the short time histories of a few number of measurement points and the first several natural frequencies.

The effect of soil-structure interaction (SSI) on the dynamic responses of seismically isolated three-span continuous reinforced concrete (RC) bridge is investigated. Also, tuned mass damper(s) (TMD/s) is/are installed to control undesirable bearing displacement, even under the SSI effect. The TMDs are placed at the mid-span of the bridge and each tuned with a modal frequency, while controlling up to first few modes as desirable. The soil surrounding the foundation of pier is modeled by frequency independent coefficients. Dynamic analysis is carried out in time domain using direct integration method. In order to specify the effects of the SSI, the responses of the non-isolated, isolated, and controlled isolated bridge are compared. It is observed that the soil surrounding the pier has significant effects on the bearing displacement of the isolated RC bridges. In addition, it is observed that the seismic responses of isolated RC bridge reduced significantly with installation of the TMDs.

Based on the concept of isoparametric mapping, a generic approach for investigating the bending and shear deformation in a non-prismatic elastic beam with corrugated steel webs (CSWs) was presented in this study. The strain field of an actual element (namely, the non-prismatic beam segments) is expressed as a function of the local coordinates in the parent element. Continually, the solution of the bending and shear deformation of the non-prismatic beam segment can be transformed into the integration of strain in the parent element under local coordinates. Since it is usually laborious to solve the displacement field by direct integration of strain in a non-prismatic beam segment using global coordinates. In addition, this study found that shear deformation cannot be ignored in the actual design of this type of structure because the thin-walled section has a small shear stiffness. In contrast, for a composite beam with CSWs, shear deformation occurs beyond bending deformation and becomes a major contributor of total deformation in some critical sections. Finally, experimental study of the mechanical properties of a non-prismatic beam with CSWs is conducted for the first time. The experimental results further demonstrate the validity of the proposed theoretical analysis methods.

This paper deals with the problems investigating of parameters that influence the dynamic behaviour of the carrying structure of type H portal cranes with high carrying capacities excited by the motion of the crane and the load swing. The introduction of the paper presents the importance of the problem of the dynamics of structures. In accordance with the given problem, dynamic spatial models of the boom and portal of the crane were formed and solved. The main part of the paper presents a modal analysis and determines dynamic responses of the space structure with the application of the finite element method and direct integration. The influence of changes in speed and acceleration on the dynamic response of the structure was analysed. The influence of the change of boom rotation angle on the dynamic response of the structure was also analysed. The investigation results provide significant bases and conclusions for designing portal cranes and continuation of research in this field.

A combined analysis method is developed in the present paper for studying the dynamic properties of a type of geometrically nonlinear vibration isolator, which is composed of push–pull configuration rings. This method combines the geometrically nonlinear theory of curved beams and the Harmonic Balance Method to overcome the difficulty in calculating the vibration and vibration transmissibility under large deformations of the ring structure. Using the proposed method, nonlinear dynamic behaviors of this isolator, such as the lock situation due to the coulomb damping and the usual jump resulting from the nonlinear stiffness, can be investigated. Numerical solutions based on the primary harmonic balance are first verified by direct integration results. Then, the whole procedure of this combined analysis method is demonstrated and validated by slowly sinusoidal sweeping experiments with different amplitudes of the base excitation. Both numerical and experimental results indicate that this type of isolator behaves as a hardening spring with increasing amplitude of the base excitation, which makes it suitable for isolating both steady-state vibrations and transient shocks.

The vibration analysis of bar element systems with continuous variable parameters using the direct integration method is proposed. The method is based on analytical solutions of the appropriate differential equations. By using this method, the problem of free flexural vibrations of a straight bar with arbitrary, continuously varying transverse stiffness and mass per unit length is solved. Formulas in analytical form are derived for dynamic parameters of bar structures, and the procedure for their numerical implementation is presented. Free vibrations of a truncated cone and chimney with a variable wall thickness are studied.

Functionally graded materials (FGM) are newly developed materials described by variation in the characteristics gradually over volume. These materials find applications in very high temperature environments namely aerospace industry, nuclear reactors, gas turbines, and electronics cooling. These materials are used in high temperature environments with dynamic load conditions, so their transient thermoelastic analysis under these conditions is necessary. In this paper, transient thermoelastic investigation of FGM is carried out using finite element method (FEM). The effect of temperature dependence is considered in the thermophysical properties of a FGM plate in the direction of its thickness. FEM is applied to solve the thermo mechanical equations and Newmark direct integration scheme is used for obtaining the solution for transient loading. This method improves the accuracy for three dimensional cases and produces solutions directly in time domain. A comparative study is made with some existing methods, and it is found that temperature and thermal stresses remain within safe limits at higher temperatures while preserving the deformation in the structure. The results show that the grading parameter has a dominating effect on transient thermoelastic behavior on FGM plate.

Extended finite element method (XFEM) and time integration by α-method are coupled in the direct integration scheme to study the 2D dynamic fracture of concrete gravity dam-foundation-reservoir interaction. The advantages of XFEM for the strong displacement discontinuity description of a crack and α-method for the time integration in dynamic analysis to dissipate the shockwaves after crack growth are combined together. The proposed method can improve the computation efficiency and can avoid numerical instability to judge the crack propagation orientation of XFEM. Obtained results show by increasing the value of α in time integration, the shock waves after crack growth are decreased and the stability of numerical solution is increased. In addition the accuracy of the dynamic fracture simulation using the proposed method is investigated in comparison with other reported in the literature. To apply the interaction in finite element model, zero thickness six-nodal contact elements are used in which the dam, foundation and reservoir are formulated with Lagrangian approach. Also, to predict dynamic fracture behavior of a cracked dam, dynamic stress intensity factors (DSIFs) are used. The interaction integral (conservation integral) originally proposed to evaluate SIFs to incorporate dynamic effects is utilized to evaluate DSIFs. Effective parameters in problem-solving such as the contribution of each distinct term in the interaction integral, crack tip element, length of crack growth, integration radius, location of initial crack, angle of initial crack, internal damping ratio of the dam, and fracture energy based on proposed method are discussed.

Summary Fibre optic sensing technologies, and in particular Fibre Bragg Gratings (FBGs), are enabling high precision and detailed mapping of strain in various structures by direct integration into the material layers. Here, embedding fibre optic sensor lines in asphalt has been demonstrated to detect miniscule changes in lateral strain due to vertical deformations of road construction layers, in response to the loads in real-time traffic conditions. The spatial and temporal resolution of the system allows for very detailed mapping of the deformations due to vehicle loads, including the extraction of the viscoelastic properties of the pavement and the rigidity characteristics of the underlayers. By continuous and/or periodic monitoring of the dynamic asphalt behaviour in response to controlled loads, the long-term changes in the near-surface properties due to material aging because of weather conditions or traffic loads can be extracted. Such detailed analysis can enable monitoring of large-scale assets, literally paving the way for a new approach to asset management of roads.

We propose a simplified numerical technique to quantify the effects of non-linear stiffness in MEMS resonators and we validate our approach on a clamped–clamped beam, a softening Disk Ring Gyroscope (DRG) and a shallow arch showing internal resonance. We generate a Reduced Order Model (ROM) which is integrated with either a direct integration approach or a continuation technique with arc length control. Finally we compare and validate the results with a full FEM model.

In this study, a set of analytical methods was proposed to evaluate the reliability of composite wind turbine blades after material aging, and to improve the blade structure strength to enhance its reliability. Because, the material aging will occur when the blade is affected by the external environment for a long time, consequently, time is an extremely important factor in reliability. Therefore, it is necessary to simulate the effect of environment on materials by aging experiments, so as to obtain the relationship between time, material strength and material constant. The reliability evaluation method used in this study is the direct integration method, which can quickly evaluate the reliability of blades degraded by materials. Because the reliability of the unmodified blade impossible be more than 98% after 20 years, it is necessary to improve the blade and then evaluate the reliability. The weight of the improved blade increased by only 8.57%, but the wind speed of buckling could be delayed by 32.47%, and the reliability could be more than 99% after 20 years, so the improved method meets the demand.

Most of current vulnerability related researches have focused on the regular bridges with equal height piers, whereas the practical bridge engineering rarely have piers of absolutely equal. This study develops both the component and system fragility of a typical irregular multi-span continuous reinforced concrete girder (MSCRCG) bridge with unequal height piers, which is commonly equipped with the plate-type elastomeric bearings in China. Unlike the conventional deterministic analysis, the seismic fragility function provides a probabilistic approach to quantify the seismic performance of the bridge by accounting for various sources of uncertainty. Moreover, this study applies the direct integration method and Monte-Carlo method to generate the system level fragility function of the bridge engineering. Both the component level and system level fragility functions are used to examine the isolation effect of the common used plate-type elastomeric bearings (PTEB) on the MSCRCG bridges with unequal height piers. Analyses show that it is an efficient and practical method to balance the component fragilities of unequal height piers and decrease the system fragility of the bridge by adjusting the geometric sizes of the PTEBs. In addition, the present study suggests that the stiffness radio between the higher pier-bearing system and the adjacent lower pier-bearing system should also no smaller than 0.75 that is recommended for multi-frame bridge by the Caltrans SDC.

This paper focuses on the methods of calculating load-bearing systems in the case of a failure of a structural element. This kind of failure makes it necessary to assess further behavior of the structure with a possibility of the progressive collapse development. The stress-strain state analysis of a load-bearing system in the case of a failure of a structure is carried out by two main methods – static and dynamic calculation. It is shown that the static calculation (quasi-static analysis using the dynamic amplification factor) is not a universal method. This paper justifies the application of the direct dynamic calculation in the mode of direct integration of motion for the design analysis of load-bearing systems with high rigidity stories (protection structures for a load-bearing system). It also gives recommendations for selecting parameters of the direct dynamic calculation in the case of a failure analysis of a bearing structure.

In the works published earlier were obtained dependence which allows to obtain the value of the maximum force (the second group of limiting States) depending on the geometric characteristics of eccentrically compressed columns. This article will be a comparison of the proposed method the calculation method of the State construction norms of Ukraine. As the sample was adopted square steel cold formed electrically welded pipe section 50х50х2 mm length l = 3000 mm l = 6000 mm . The calculation was performed for the three design schemes: a hinged column, loaded at one end eccentrically applied force F; the column is rigidly fixed at the bottom, hinged at the top and abbert loaded eccentrically applied force on the upper end; a column rigidly fixed at the bottom, loaded at the free end of the eccentric applied force. In the proposed equations the value of the maximum power to obtain analytically, we can not, but knowing the geometrical characteristics of columns and using the method of direct integration it is possible to obtain the values of the ultimate strengths. The calculation process is organized as follows: set the step load in each approximation calculated deflection. The calculation continues until the load at which the obtained value of the deflection derevovolos limiting value thus. Calculated load is taken for the maximum force F which characterizes the bearing capacity of the columns. After analyzing the results of the calculations, and received the error that does not exceed 19 %, we can talk about the possibility of using the proposed formulas for calculation of the maximum posacenere because they can afford to automate the process and reduce the computation time. The proposed formulas allow to obtain the maximum power depending on the preset value of deflection.

The transient behaviour of laminated composite spherical shell cap is investigated using the finite element method . An eight node degenerated isoparametric shell element is considered with five degrees of freedom at each node. The governing equations of forced vibration are solved using the Newmark’s direct integration method. Results are presented for dynamic response of deflection and stresses of orthotropic and laminated spherical shell caps subjected to suddenly applied uniform normal pressure.

Summary Study of collapse-resisting properties of structures has attracted widespread attention because of frequently occurring earthquakes and extreme events (e.g. blast) around the world. The developments in computational methods have enabled researchers to numerically simulate the collapse of structures under different kinds of loadings and provide reliable assessments of the collapse performance of structures. The dynamic nature of structural collapse requires a direct integration algorithm to solve the equations of motion of the numerical simulation model. A major concern in such simulations is the computational efficiency, which stems from the need to use a small time step size in both implicit algorithm and explicit algorithm. In this paper, modeling techniques to simulate typical failure mechanisms in reinforced concrete frame structures combined with the application of the recently developed explicit, unconditionally stable, parametrically dissipative KR-α integration method to investigate collapse simulation are presented. A fiber beam-column element is used to model the frame members, where the material nonlinearities, especially material softening, are simulated by a plastic damage model combined with a failure criterion. Numerical examples are presented to illustrate the proposed collapse simulation technique. The results indicate that the proposed technique provides an accurate result and has exceptional computational efficiency. Copyright © 2015 John Wiley & Sons, Ltd.

Summary Traditional self-centering coupling beams display a beam elongation effect under large shear deformation. The beam elongation effect conflicts with the rigid slab assumption and may induce harmful compressive stress between the coupling beam and the walls. This paper proposes a novel self-centering coupling beam, aimed at eliminating the beam elongation effect. The proposed self-centering coupling beam consists of two connecting parts and one central rocking part. The main feature of the self-centering coupling beam is the gap between the central rocking part and the one connecting part. This gap provides sufficient space for the beam elongation effect. Friction dampers are installed at the corners of the coupling beam to provide energy dissipation capacity. An experimental study, including three specimens, was carried out. The test results demonstrate the satisfactory self-centering and energy dissipation capacities of the novel coupling beam. Based on these test results, we quantitatively discuss the pretension force in the pretensioning strands, the friction force of the damper and the gap width in the coupling beam. A finite element analysis is performed, showing that the coupling beam gap protects the coupling beam and adjacent shear wall from damage caused by the beam elongation effect. Copyright © 2015 John Wiley & Sons, Ltd.

Dynamic modeling of beveloid gears is less developed than that of conventional involute gears with parallel axis because of their complicated mesh mechanism and 3-dimensional dynamic coupling. For evaluating the dynamic characteristics of a marine gearbox with crossed beveloid gears more realistically, a systematic dynamic modeling approach was proposed based on the lumped parameter and the finite element method. Considering the time-varying mesh stiffness excitation, time-varying loaded translational transmission error excitation, sliding friction excitation and backlash nonlinearity, a coupled gear–shaft–bearing–housing dynamic model for a marine gearbox with crossed beveloid gears was developed based on the proposed modeling method. Then, numerical integrations applying the explicit Runge–Kutta formula and the implicit direct integration were used to solve the nonlinear dynamic model. The dynamic transmission error, dynamic mesh force, and dynamic equivalent shaft-bearing supporting force were obtained as well as the dynamic response of the housing. Finally, a test rig was established for the marine gearbox with crossed beveloid gears and vibration tests were performed to investigate the dynamic responses. Through analyzing the responses in time domain and frequency domain, the experimental results compared well with the theoretical dynamic results.

This paper introduces Romberg-Richardson\'s method as one of the numerical integration tools for computation of stress intensity factor in a pre-cracked specimen subjected to a complex stress field across the crack faces. Also, the computation of stress intensity factor for various stress fields using existing three methods: average stress over interval method, piecewise linear stress method, piecewise quadratic method are modified by using Richardson extrapolation method. The direct integration method is used as reference for constant and linear stress distribution across the crack faces while Gauss-Chebyshev method is used as reference for nonlinear distribution of stress across the crack faces in order to obtain the stress intensity factor. It is found that modified methods (average stress over intervals-Richardson method, piecewise linear stress-Richardson method, piecewise quadratic-Richardson method) yield more accurate results after a few numbers of iterations than those obtained using these methods in their original form. Romberg-Richardson\'s method is proven to be more efficient and accurate than Gauss-Chebyshev method for complex stress field.

The paper studies the efficiency of seismic isolation system in the form of rubber-metal bearings with different height buildings at multicomponent seismic impact. As an example, seismically insulated monolithic reinforced concrete 5-, 9-and 16-storey buildings are considered. The solution of the problem is obtained by a direct integration of the motion equations for an explicit scheme in the software package LS-DYNA. The calculation is performed considering nonlinear nature of rubber bearings. The analysis of the effectiveness of buildings with seismic insulation and without it is performed.

Reactor Coolant Pumps (RCPs) are very important to the safe operation of Nuclear Power Plants (NPPs), especially during the earthquake, which needs detailed seismic analysis of individual RCPs and the boundary conditions, for example, at the nozzles. In this paper, three-dimensional finite element model of Reactor Coolant System (RCS) is constructed from a systematic perspective to perform dynamic evaluation, in which the boundary conditions could be given. The seismic spectrum analysis with three orthotropic directions is performed to obtain the stress and displacement response, which shows that the maximum Tresca stress locates in the connection part of SG with RCP and the maximum displacement occurs at the surge line. Sensitivity analysis of spectrum input angle and stiffness of supports is performed, which may be useful to further design and analysis. Furthermore, direct integration method is used to perform time-history analysis, and the boundary conditions of RCP, the loads, acceleration and displacement at nozzles are obtained, which could support the detailed analysis of RCP components. Besides, the lumped mass model of RCS is also constructed to compare with three-dimensional finite element model, which means that for the complicated geometry the 3-D model is better than the lumped mass model.

In this chapter, two typical dynamic analyses, namely the modal and transient dynamic analyses, are introduced. First, the element mass matrix, not needed in static analyses, is presented. This is followed by finding the natural frequencies and mode shapes in modal analysis and adding damping to mitigate the effect of resonance. Next, two direct integration methods are derived and examples are given to illustrate how these methods work in a step-by-step manner. Finally, brief rationales are given regarding the selection of implicit and explicit integration schemes for various types of FEA.

Aim of the paper is the evaluation of the bearing capacity of fiber reinforced concrete (FRC) sections, without any traditional steel reinforcement, subjected to different values of the fire duration. At this purpose, bending moment (M)–axial force (N) interaction envelopes are defined, through an analytical model based on the direct integration of the hot or residual mechanical properties of the material, throughout the member cross section. Finally, a parametric survey, specifically related to tunnel segments, with different geometries and FRC materials allows highlighting the worst (or better) scenarios.

The paper presents an approach to evaluation of the dynamic wind action on scaffolding structures. FEM model of the scaffolding was created on the basis of geodetic measurements and verified by in-situ dynamic measurements of vibrations. Wind field, random in space and time, was simulated using Weighted Amplitude Wave Superposition (WAWS) method. Wind forces were applied to the nodes of the FEM model in every connection between stands and decks in outer plane of the scaffolding. Direct integration was used as the solution method. The time-dependent response of the structures was determined. Maximum response of the scaffolding was compared with results calculated according to the code recommendations.

The article deals with a multi-storey monolithic concrete building calculation on the earthquake. The problem is solved in the time domain by a direct dynamic method. Direct integration of motion equations is carried out on an explicit scheme. This technique allows us to solve the problem in a nonlinear dynamic formulation considering geometric and physical nonlinearities. The paper presents and analyzes the main results of the calculation.

The use of high-performance materials in bridges is leading to structures that are more susceptible to wind- and traffic-induced vibrations due to the reduction in the weight and the increment of the slenderness in the deck. Bridges can experience considerable vibration due to both moving vehicles and wind actions that affect the comfort of the bridge users and the driving safety. This work explored the driving safety and comfort in a very slender arch bridge under turbulent wind and vehicle actions, as well as the comfort of pedestrians. A fully coupled wind–vehicle–bridge interaction model based on the direct integration of the system of dynamics was developed. In this model, the turbulent crosswind is represented by means of aerodynamic forces acting on the vehicle and the bridge. The vehicle is modeled as a multibody system that interacts with the bridge by means of moving contacts that also simulate road-surface irregularities. A user element is presented with generality and implemented using a general-purpose finite-element software package to incorporate the aeroelastic components of the wind forces, which allows modeling and solving of the wind–vehicle–bridge interaction in the time domain without the need for using the modal superposition technique. An extensive computational analysis program is performed on the basis of a wide range of turbulent crosswind speeds. The results show that bridge vibration is significantly affected by the crosswind in terms of peak acceleration and frequency content when the crosswind intensity is significant. The crosswind has more effect on the ride comfort of the vehicle in the lateral direction and, consequently, on its safety in terms of overturning accidents.

This paper presents design procedures for 1-D and 2-D strain hardening cement composites (SHCC) members based on analytical models. Closed-form solutions of moment-curvature responses of SHCC are derived based on elastic perfectly plastic compressive model and trilinear strain hardening tension model. Tension stiffening behavior of SHCC due to fiber toughening and distributed cracking are considered and incorporated in the cross-sectional analysis. Load-deflection responses for beam and panel members are obtained using several different methods including moment-area, direct integration and Yield Line Theory. The proposed models provide insights in the design of SHCC to utilize the hardening properties after cracking. Using proper parameters, generalized materials model are applicable to both SHCC and strain softening cement composites such as steel fiber reinforced concrete (SFRC), textile reinforced concrete (TRC) and ultra-high performance concrete (UHPC).

Reinforced concrete staircases are structurally designed as cantilevered, slab type or beam-slab type. Within this study an irregular cantilevered staircase is studied and its structural dynamic characteristics are explored. An eigen-value modal analysis is performed to determine the mode shapes, their corresponding modal participation factors and natural periods of vibration. The highest modes of interest are identified. Following on that, a scaled record of a previous historical earthquake was applied within a direct integration time-history analysis in order to assess the performance of that irregular stair case under earthquake loading. That load was applied within two perpendicular load cases representing the different possible directions of earthquake vibrations in which the effect of the structure irregularity was assessed per direction. The structure was found to have large drifts creating a need to change the structural system.