Nonlinear Transient Dynamic Analysis Research Articles

A new approach for nonlinear transient dynamic analysis of micro SMA beam considering size effect and instantaneous phase transformation

Shape Memory Alloys (SMAs) have attracted lots of attraction in the recent years due to their unique characteristics. However, studies in the field of behavior of SMAs at micro scale is not enough and more research is required. The present paper presents a nonlinear dynamic solution for a micro made of NiFeGa SMA, located on a viscoelastic foundation. The recommended approach takes into account instantaneous variations of martensite volume fraction and size effect which are the main novelties of the present study. In this regard, the formulation proposed by Hernandez and Lagoudas is used to capture and model the size effect of the SMAs. The governing differential equations obtained for Euler-Bernoulli micro beam using the Hamilton’s principle, considering the Von-Karman nonlinear strain. The nonlinear equation of motion is solved applying the semi-exact method. In this study, the return mapping convex cutting plane is used, in order to overcome the material nonlinearity of the problem. The obtained results are compared with the reference papers which shows the accuracy of the present model. Results show that with considering the size effect, the loss factor of vibration will increase by increasing the thickness of the micro SMA beam. While regardless of the size effect, this factor remains almost constant. The reason for this phenomenon is that when size effect is taken into account, the thermodynamic properties and critical stresses of phase transformation will change with resizing the SMA. Outputs also show that by increasing the damping coefficient and decreasing the stiffness of foundation, more energy is wasted in the vibration of the micro SMA beam. In addition, it was observed that micro beams with lower thicknesses are more sensitive to foundation characteristics meanwhile the loss factor of vibration with lesser thicknesses changes more by changing the foundation stiffness and damping coefficients.

Assessment of the Blasting Efficiency of a Long and Large-Diameter Uncharged Hole Boring Method in Tunnel Blasting Using 3D Numerical Analysis

Cut blasting is one of the most essential processes to reduce blast-induced vibration in tunnel blasting. The long and large-diameter uncharged hole boring (LLB) method is an example of one of the cut blasting methods, which utilizes large-diameter uncharged holes drilled in the tunnel face. In this study, blasting simulations were performed to analyze its blasting mechanism, and the LLB method and the traditional burn-cut method were simulated to compare their blasting efficiency. A 3D numerical analysis using LS-DYNA code, a highly non-linear transient dynamic finite element analysis using explicit time integration, was used to simulate the blasting process, and a Johnson–Holmquist constitutive material model, which is optimal for simulating brittle materials under dynamic conditions, was used to simulate the rock behavior under blasting. The modified LLB method showed a 3.75-fold increase in the advance per round compared to the burn-cut method, due to the increased formation of long and large-diameter uncharged holes compared to blast holes. This modified LLB method used 30% less explosives, so its failure range was approximately 1.25 times less than that of the burn-cut method, but its advance was approximately 4 times larger than the burn-cut method, which was similar to the original LLB method. This confirmed that the modified LLB method is significantly more efficient in terms of increased blasting efficiency (particularly the advance per round) as well as reduced blast-induced vibration, compared to the traditional cut blasting method.

Nonlinear and linearised analyses of a generic rotor on single-pad foil-air bearings using Galerkin Reduction with different applied air film conditions

The compressible Reynolds Equation is typically integrated within a fully-coupled dynamical foil-air bearings (FAB)-rotor system via spatial discretisation transformation e.g. Finite Difference (FD), Finite Element (FE). This paper presents a novel application of an arbitrary-order Galerkin Reduction (GR) method, which does not involve spatial discretisation, to both nonlinear and linearised analyses of rotor systems supported by single-pad FABs. The novel aspects are: application to generic flexible rotors; Jacobian-based linearisation of the GR-transformed system for the extraction of the full mode set and linear stability map; the facility to apply a pressure constraint at a circumferential location and/or the Gümbel condition. These developments are comprehensively verified on two previously considered systems by comparing alternative (GR, FD-based) simulations. The overall features of the experimental nonlinear phenomena are predicted satisfactorily. Transient nonlinear dynamic analysis (TNDA) with GR is found to be less prone to numerical divergence than with FD. For static equilibrium, stability and modal analysis (SESMA), GR is found to be over twice as fast, requiring 70-90 times less memory for saving the results.

Thermo-mechanical nonlinear transient dynamic and Dynamic-Buckling analysis of functionally graded material shell structures using an implicit conservative/decaying time integration scheme

In this paper, the nonlinear time history response and dynamic-buckling of functionally graded material (FGM) shell structures in thermal environments with temperature-dependent material properties is studied. An implicit conservative/decaying time integration scheme and a curved 8-node degenerated shell element are used for time and spatial discretization respectively. Numerical results show that the developed shell element formulation with the implicit time integration scheme is capable of solving nonlinear dynamic-buckling and large displacement dynamic problems of FGM shells in severe thermal environments. Th influence of material constituents, power-law indexes and thermo-mechanical loadings on the transient dynamic response and dynamic-buckling phenomena are considered.

Computational simulation of pacifier deformation and interaction with the palate.

ObjectivesThe objective of this study is to demonstrate that computational finite element models can be used to reliably simulate dynamic interaction between a pacifier, the palate, and the tongue during nonnutritive sucking (NNS). The interactions can be quantified by the results of finite element analyses which include deformation, strain, stress, contact force, and contact area.Materials and MethodsA finite element model was created based upon CAD solid models of an infant pacifier and palate. The silicone pacifier bulb is represented by a hyperelastic constitutive law. Contact surfaces are defined between the pacifier and palate. A time and spatially varying pressure load is applied to the bulb representing peristaltic interaction with the tongue. A second time‐varying, periodic pressure representing NNS is applied to the model simultaneously. A large displacement, nonlinear transient dynamic analysis is run over two NNS cycles.ResultsResults from the finite element analysis show the deformed shape of the bulb with maximum principal elastic strain of 0.23 and a range of maximum principal stress on the palate from 0.60 MPa (tensile) to −0.27 MPa (compressive) over the NNS cycles. The areas of contact between the pacifier and the palate are shown in surface contour plots.ConclusionsA nonlinear transient dynamic finite element model can simulate the mechanical behavior of a pacifier and its interaction with the tongue and contact with the palate subject to NNS. Quantitative results predicting deformation, strain, stress, contact force, and contact area can be used in comparative studies to provide insight on how pacifiers cause changes in dental, orthognathic, and facial development.

Multi-Hazard Assessment of Bridges in Case of Hazard Chain: State of Play and Application to Vehicle-Pier Collision Followed by Fire

This study focuses on multi-hazard analysis for bridges, following a two-tier approach. First, it identifies relevant open issues and recent literature developments in the field, presenting data in a meaningful manner, with specific focus on the issues related with the analysis of hazard chain scenario treated as low probability-high consequence events. Second, it describes a practically useful and sufficiently generic approach for efficient computational investigation of hazard-chain scenarios in highway bridges. Following that, the applicability of the approach is exemplified in an appealing and commonly encountered in real-life hazard-chain scenario, in which a multilevel modeling strategy is adopted to assess the structural response under hazard chain scenarios of a highway viaduct. Among the considered scenarios is the impact of a heavy vehicle (tank truck) on the bridge pier, and the fire spread following the collision due to the presence of inflammable material. The bridge structure is a typical 189m long multi-span composite highway viaduct. The impact is modelled with a non-linear transient dynamic analysis that accounts the inertial effect of the global structure, while the fire modelling is performed with non-linear quasi static dynamic analysis focusing on local behavior with a sub-structured model. Then different impact and fire scenarios are considered, including different impact velocities of the truck.

The effects of air film pressure constraints and top foil detachment on the static equilibrium, stability and modal characteristics of a foil-air bearing rotor model

The linear force coefficients method (LFCM) has been a mainstay in the computation of the onset of instability speed (OIS) and Campbell diagrams of foil-air bearing (FAB) rotor systems, despite reported inconsistencies with low amplitude dynamic analysis of the nonlinear system. The author recently established a linearisation method that eliminates such errors since it is based on the Jacobian of the nonlinear system. Unlike LFCM, this static equilibrium, stability and modal analysis (SESMA) procedure is not restricted to a spring-damper foil model. This paper investigates for the first time the effects of air film constraints and top foil detachment using SESMA, backed by transient nonlinear dynamic analysis (TNDA). The novel FAB model comprises an air film acting on a modal beam top foil that can detach from discretely distributed bumps according to a smoothed bilinear model. Application to a symmetric rigid rotor on single-pad FABs reveals abrupt shifts in modal frequencies and damping as the contact state of a bump with the top foil changes with speed. The applicability of the Gümbel correction for simpler models is illustrated. The SESMA procedure operates efficiently and accurately. The TNDA results present the first independent verification of previously presented top foil detachment simulations.

Numerical Analysis of Shock Initiation on Highly Energetic Material LX-04

The paper presents investigation of shock initiation effects on highly energetic material LX-04, an HMX based one, by a blunt brass projectile using numerical modelling methods implemented in LS-Dyna software. Multi – Material Arbitrary Lagrangian Eulerian (MM-ALE) formulation has been used to provide the possibility of fulfilment of the elements with multiple materials accordingly to multiple phases of the composition detonated. The work is focused on LS-Dyna’s equation of the state keyword *EOS_IGNITON_AND_GROWTH_IN_HE. Proper comparison with experimental data is presented. The introduction into the subject of highly nonlinear transient dynamic finite element analysis, possibilities, and superiority of this kind of modelling are being discussed. Reasons of sustaining the need of data by numerical solutions rather than experimental handling in military applications are given. Some of typical technical issues, occurring during such a fast-performing phenomenon, and the need of experimental validation of the models are typed together with detonation-state determination’s observation capabilities.

An efficient technique for extraction of nonlinear dynamic features in a model-based feature extraction scheme for machine learning–based structural health monitoring

Super-harmonic components in response to the harmonic excitation are sensitive indicators of damages such as breathing cracks in beams or kissing bonds in adhesive joints. In a model-based damage identification process using pattern recognition, these damage indicators can be extracted from the finite element model for all probable damage cases using stepped-sine simulation that necessitates nonlinear transient dynamic analysis with high computational costs. In this study, a procedure based on nonlinear autoregressive with exogenous input model is introduced as an alternative shortcut method for extraction of the damage indicators. As a case study, the finite element model of a beam connected to a rigid support via a flexible adhesive layer was used to investigate the efficiency of the proposed method. Kissing bond was introduced to the model as the source of nonlinearity via contact elements. The results prove that the super-harmonic components of orders up to 3, extracted from the nonlinear autoregressive with exogenous input model, agreed well with those extracted directly from the finite element model, whereas the computational time is reduced by a factor of 1/5. Consequently, the proposed method is very advantageous in the stage of damage pattern database creation in a real-world model-based damage identification process based on pattern recognition.

Investigations on the ship-ice impact: Part 1. Experimental methodologies

In the structural design of the Polar Class ships, glancing impact with ice has been considered as the governing load scenario for dimensioning the bow structure. At present, non-linear transient dynamic analysis has been reckoned as a fundamental requirement in the assessment of the structural strength of ships with higher ice classes. Under such requirement, understanding of the dynamic characteristics of the ship-ice impact load appears significant importance. The present study aims to investigate the spatial and temporal variations of the impact loads by simulating the glancing impact events between a polar research vessel and giant ice floes in ice tank. The ship-ice impact loads were recorded by a grid-based tactile sensor attached on the bow area of the model ship. To achieve a reasonable simulation on the design scenario described by the IACS Unified Requirements for Polar Class Ships (UR I), a series of methodological calibration tests were preliminarily carried out to determine the key parameters that should be carefully monitored and controlled, accompanying with thorough discussions on the ship-ice impact process. This paper provides detailed information on the preliminary methodological calibrations and the tactile data processing techniques, including the identification of the ship-ice contact area, the depiction of the ice loading trail and the outline of the spatial distributions of local ice pressures. A companion paper provides detailed analyses and discussions regarding the spatial and temporal variation of the ice impact loads from the formal tests based on the proposed testing procedures obtained by the methodological calibrations.

Fragility analysis of an ageing monopile offshore wind turbine subjected to simultaneous wind and seismic load

The loads induced as a result of seismic activities may jeopardize the serviceability of offshore wind turbines or may even lead the structure to reach the ultimate strength. The maximum load-carrying capacity of a support structure can be estimated by performing a structural assessment which accounts for the nonlinear effects arising from the material and geometry. The present work aims to analyze the fragility of a 5 MW monopile offshore wind turbine structure subjected to seismic activities accounting for soil interactions and time-variant structural degradation. The offshore wind turbine structure is subjected to different ground motions with different intensity. The nonlinear full transient dynamic structural analysis is carried out based on the finite element method, and the nonlinear monopile structural response during the different seismic activities is discussed. Finally, the fragility curves associated with the serviceability limit state design and the ultimate strength limit state are developed.

Nonlinear transient dynamic analysis of laminated composite parabolic panels of revolution with variable thickness resting on elastic foundation

In this article, nonlinear transient behavior of laminated composite Parabolic Panels of Revolution Structure(s) (PPRS) with variable thickness resting on elastic foundation is investigated using Generalized Differential Quadrature (GDQ) method. Winkler-Pasternak model is used to represent elastic foundation. Linear, arch, sine and cosine thickness functions are used to express variable thickness. In transient analyses, First Order Shear Deformation Theory (FSDT) is used to consider the transverse shear effects. Nonlinearity is taken into account using Green-Lagrange nonlinear strain-displacement relations considering deepness effect. Virtual work principle is used to derive the equations of motion. Partial derivatives in the equation of motion are expressed with GDQ method and time integration is carried out using Newmark average acceleration method. Several problems are solved and compared with finite element results in order to validate the proposed method. After validation, effects of thickness functions, thickness variation parameter, geometric characteristic parameter of PPRS, boundary conditions, elastic foundation parameters as well as composite lamination scheme on nonlinear transient dynamic behaviour of PPRS are investigated.

Semi-exact solution for nonlinear dynamic analysis of nanobeams reinforced with functionally graded carbon nanotube located on a viscoelastic foundation

In this investigation, a transient nonlinear dynamic analysis of nanobeams reinforced with carbon nanotubes, which is located on a nonlinear viscoelastic foundation under the impulse loading, is investigated. The boundary conditions of the nanobeam are considered as clamped-clamped, and the carbon nanotube is distributed in different distribution along the thickness of nanobeam. First, using the Hamiltonian method and taking advantage of the couple stress theory and considering the Von Karman relationship between strain and displacement, the differential equation governing for Euler–Bernoulli nanobeam is obtained. Then, by using the semi-exact method and the Galerkin's method, the displacement derivatives are separated from the time derivatives and the equation derived is solved using Runge–Kutta's numerical method. In order to confirm the equation and its solution, a comparative study is performed that shows an appropriate fitting between the results. Finally, the influence of parameters such as nonlinear coefficient of foundation, applied force, size effect, and type of nanotube distribution on the nonlinear frequency to linear frequency ratio and transient nanobeam dynamic response is investigated. A study is also conducted on the effect of foundation damping coefficient and the inclusion of nonlinear effects on the transient dynamic response when the nanobeam is under impulse load and resonance conditions. The results show that the nonlinear vibrational frequency of the nanobeam with the FG-X carbon nanotube distribution is the highest, and the FG-O carbon nanotubes distribution is the least.

The extraction of Campbell diagrams from the dynamical system representation of a foil-air bearing rotor model

Abstract Campbell diagrams describe the variation with speed of the modes of low amplitude (linear) free vibration of a rotordynamic system about its static equilibrium condition, and are an important tool that aids the interpretation of the nonlinear response. However, Campbell diagrams for foil-air bearing (FAB) rotor systems are currently derived using the linear force coefficients (FC) method and individual modes have not been verified by transient nonlinear dynamic analysis (TNDA) at low amplitudes. In fact, significant discrepancies between FC and TNDA predictions for the stability of the leading (i.e. least damped) mode have been reported. This paper establishes for the first time a method for deriving Campbell diagrams of a generic FAB-rotor model that avoids the FC method. It is based on an eigenvalue analysis of the Jacobian matrix of the dynamical system. Through suitable scaling and the application of appropriate criteria, the multitude of eigenvectors of the Jacobian can be filtered to extract the relevant modes. Each mode is verified using TNDA with mode-specific initial conditions derived from the Campbell diagram analysis. The methodology is successfully tested on three cases in the literature, which respectively illustrate its applicability to complex bearing types (3-pad), complex foil models, and flexible rotors.

Transient analysis of nonlinear locally resonant metamaterials via computational homogenization

In this paper, the transient computational homogenization scheme is extended to allow for nonlinear elastodynamic phenomena. The framework is used to analyze wave propagation in a locally resonant metamaterial containing hyperelastic rubber-coated inclusions. The ability to properly simulate realistic nonlinearities in elasto-acoustic metamaterials constitutes a step forward in metamaterial design as, so far, the literature has focused only on academic nonlinear material models and simple lattice structures. The accuracy and efficiency of the framework are assessed by comparing the results with direct numerical simulations for transient dynamic analysis. It is found that the band gap features are adequately captured. The ability of the framework to perform accurate nonlinear transient dynamic analyses of finite-size structures is also demonstrated, along with the significant computational time savings achieved.

Influence of repairable bolted dissipative beam splices (structural fuses) on reducing the seismic vulnerability of steel-concrete composite frames

After a strong earthquake, repair work of conventional steel-concrete composite buildings can be very expensive, and very often, impossible due to practical problems. Within the EU-funded research project FUSEIS, a new steel-concrete composite frame type has been developed, as a cost-effective and robust alternative to conventional earthquake resistant structures. In this new frame type, damage concentrates mainly in the bolted dissipative beam splices acting as “structural fuses”, which can be easily and inexpensively replaced after strong seismic events. After the replacement, the building can be restored to its original form. This paper studies a benchmark building frame with and without bolted dissipative beam splices. The performance of both innovative and conventional structures has been quantified in terms of energy dissipation, floor displacements and inter-story drifts, as a result of nonlinear transient dynamic analysis. Different than similar studies in the literature, the numerical models explicitly consider the presence of reinforced concrete slab by means of fiber-based distributed plasticity approach. They have been calibrated according to the experiments, both provided in the literature and performed in the FUSEIS research project. The models allowed the quantification of the energy dissipated by each component of a steel-concrete composite frame (structural fuses, steel elements, concrete slab and steel reinforcement), which gave an insight on redistribution of dissipated energy in the case of adopting the structural fuses with respect to the traditional steel-concrete composite buildings. Based on the results of the numerical analysis, the reparability aspect has been discussed.

An explicit algorithm for geometrically nonlinear transient analysis of spatial beams using a corotational total Lagrangian finite element formulation

An explicit method for nonlinear transient dynamic analysis of spatial beams with finite rotations using a corotational total Lagrangian finite element formulation is presented. The kinematics of the beam element is described in the current element coordinate system constructed in the current configuration of the beam element. The element deformation and inertia nodal forces are derived by the virtual work principle, the d'Alembert principle, and the consistent linearization of the geometrically nonlinear beam theory. A nodal rotation vector is used to represent the finite rotation of a base coordinate system rigidly attached to each node of the discretized structure. A numerical procedure of explicit method is proposed for the solution of the nonlinear equations of motion. The standard central difference method is applied to the incremental displacement vector and the incremental rotation vector, and the time derivatives of displacement vector and rotation vector. The nodal orientations are updated by the incremental nodal rotation vectors. The values of nodal rotation vectors are reset to zero in the current configuration.In order to assess the efficiency and the accuracy of the proposed method, numerical examples are studied and compared with the results obtained using the implicit method based on the Newmark method.

Numerical and experimental investigations of the low velocity impact in GFRP plates

Abstract The paper deals with experimental and numerical investigations of the composite plate subjected to low velocity impact (LVI). The discussed plates were made of eight-layer Glass Fiber Reinforced Polymer (GFRP) laminate with quasi-isotropic ply system and are predefined to conduct the impact and the Compression After Impact (CAI) tests. The numerical analyses were performed in Ansys® environment. Three numerical models were prepared. The implicit analyses were conducted with and without the implementation of the progressive failure algorithm and the application of the bilinear traction-separation law. The analyzed problem demonstrated the influence of the element-level time-incrementation, damping and time integration method (Newmark and Hilber-Hughes-Taylor) on agreement with the experimental results. The advantages of using impact constraints for modeling contact in a nonlinear transient dynamic analysis were shown. High consistency of numerical and experimental results was achieved. Application of the Hashin's criterion lead to a valid prediction of the fiber failure areas and to overestimation of the matrix failure areas.

Structural response analysis of slamming impact on free fall lifeboats

The evaluation of impact induced slamming loads experienced by ships and offshore structures using advanced fluid structure interaction methods may be a challenging task involving complex and time consuming engineering solutions. This is the reason why to date the application of well understood and validated quasi-response approaches remains the most rational alternative used by experts for preliminary design assessment. Based on a benchmark study carried out by the International Ship and Offshore Structures Congress Technical Committee II.1 on Quasi-Static Response this paper demonstrates the practical use of “quasi-response” prediction methods for the assessment of impact loads on modern free fall lifeboats. The case study presented is considered relevant in terms of technical background and ship design for safety. Following a brief review rationalising the practical relevance of the engineering solutions examined, the influence of high speed impact is evaluated using linear-elastic and nonlinear beam models, as well as a nonlinear transient dynamic finite element analysis idealisation. Comparisons of the methods presented against experimental results led to the conclusion that the nonlinear quasi-dynamic beam approach accounts for the influence of the dynamic effects of strain by suitably idealising the effects of nonlinear geometric stiffness. It may therefore be more appropriate to employ this approach at preliminary stage, especially when conducting comparisons against simplistic linear methods used for rigid structures (e.g. stiffened steel and aluminium panels), or advanced nonlinear finite element analysis and other multi-physics methods that may be computationally complex and time consuming.

Material Modeling of Concrete for the Numerical Simulation of Steel Plate Reinforced Concrete Panels Subjected to Impacting Loading

The steel plate reinforced concrete (SC) walls and roofs are effective protective structures in nuclear power plants against aircraft attacks. The mechanical behavior of the concrete in SC panels is very complicated when SC panels are under the action of impacting loading. This paper presents a dynamic material model for concrete subjected to high-velocity impact, in which pressure hardening, strain rate effect, plastic damage, and tensile failure are taken into account. The loading surface of the concrete undergoing plastic deformation is defined based on the extended Drucker–Prager strength criterion and the Johnson–Cook material model. The associated plastic flow rule is utilized to evaluate plastic strains. Two damage parameters are introduced to characterize, respectively, the plastic damage and tensile failure of concrete. The proposed concrete model is implemented into the transient nonlinear dynamic analysis code ls-dyna. The reliability and accuracy of the present concrete material model are verified by the numerical simulations of standard compression and tension tests with different confining pressures and strain rates. The numerical simulation of the impact test of a 1/7.5-scale model of an aircraft penetrating into a half steel plate reinforced concrete (HSC) panel is carried out by using ls-dyna with the present concrete model. The resulting damage pattern of concrete slab and the predicted deformation of steel plate in the HSC panel are in good agreement with the experimental results. The numerical results illustrate that the proposed concrete model is capable of properly charactering the tensile damage and failure of concrete.