Nonlinear Impact Response Research Articles

Nonlinear low-velocity impact response of magneto-electro-elastic beams with initial geometric imperfection

Nonlinear low-velocity impact response of magneto-electro-elastic beams with initial geometric imperfection

Nonlinear similarity characterisation and validation of dynamic response of ship stiffened plate structure under explosion load impacts

The similarity test of ship stiffened plate structures under underwater explosions is a cost-effective and efficient method to evaluate the vitality of ships and guide the design of their shock resistance. This study focuses on the nonlinear impact response model tests of ship stiffened plate structures and their similarity laws with actual ships. The vertical motion of the ship stiffened plate structure is characterized by the Hurst index, and an equivalent relationship between the Hurst index of the model and the prototype is derived from classical similarity law. Based on the Hurst index, a similarity transformation relationship between the strain signals of the model and prototype is established. To verify the conclusions, similarity experiments of underwater explosions were conducted on both the model and the prototype. The original signals were grouped by the natural vibration period to determine the variation of the Hurst index over time. The model experiment strain signals for each natural vibration period were converted and compared with the prototype experiment results to verify the method's effectiveness. Simultaneously, the Hurst index of the stiffened plate structure under explosive shock load and its similarity transformation relationship with the prototype were simulated and analyzed. This provides theoretical and technical support for conducting analogous nonlinear response experiments for ship underwater explosions.

Impact response analysis and prediction of FRP-RC beams with varying flexural stiffness: Numerical simulation and modified two-DOF calculation

The damage behavior and simplified calculation of fiber-reinforced polymer reinforced concrete (FRP-RC) beams subjected to impact loading have attracted substantial attention. In this study, a finite element model incorporating strain rate was employed. Based on the model, the progressive damage behavior and nonlinear impact response of FRP-RC beams with varying stiffness under hammer-to-beam mass ratios were examined. The results indicate that in the investigated conditions, the damage mode of FRP-RC beams does not vary with the changes in the tension reinforcement ratio, but is affected by the hammer-to-beam mass ratio. Due to the absence of a yielding stage for FRP bars, a nonlinear alteration occurred in the rebound of the FRP bars’ strain and the beam’s displacement with a redistribution of stress. When the reinforcement ratio varies from 0.32% to 3.37%, the peak displacements, reaction and impact forces vary by 25%-49%, 53%-78%, and 0.1%-1% under different mass ratios, respectively. The reinforcement ratio does not change the relationship between the mass ratio and the curve shape of the impact force time history. Additionally, an improved two-degree-of-freedom model considering the FRP’s elastic brittleness effect and modified contact stiffness scaling factor was developed, their accuracy was verified. However, there are still many inconveniences to applying the two-DOF model in engineering. Consequently, based on the above two-DOF model, explicit formulas considering contact stiffness, bending stiffness, impactor velocity and mass for displacement and impact force response of impacted FRP reinforcement concrete beams were proposed, which greatly facilitates engineering calculations.

Nonlinear low-velocity impact response of sandwich beams with FG porous aluminum core reinforced by GPLs

Sandwich beam structures facing low-velocity impact frequently throughout their life cycle, making it necessary to investigate the impact response of these structures to enhance their design and reliability in service. In this paper, sandwich beam structures subjected to nonlinear low-velocity impacts are investigated, comprising a functionally graded (FG) porous aluminum core reinforced by graphene platelets (GPLs) and two aluminum alloy face sheets. The mechanical properties of FG-GPLRC core are predicted by a generalized Halpin-Tsai model, which takes porosity into account, where the material properties of the closed-cell aluminum alloy foam are established on experimental data. The numerical investigations are conducted using the finite element method and apply the Hertz contact law. The simulation results indicate that the FG-X pattern, where the porosity coefficients are designed to have the maximum values at the top and bottom layers, while to have the minimum values at the mid-plane layers, exhibits the best impact resistance, and that the incorporation of GPLs enhances the impact response. Furthermore, the findings suggest that the thickness of the core has no impact on the duration of the initial impact. Moreover, an increase in impactor velocity, density and radius results in an increase in both deflection and contact force.

A Nonlinear Repeated Impact Model of Auxetic Honeycomb Structures Considering Geometric Nonlinearity and Tensile/Compressive Deformation

Abstract This study aims to improve the impact protection performance of composite structures by combining a honeycomb core with negative Poisson’s ratio and graphene platelets reinforced (GPR) face sheets. The paper investigates the nonlinear repeated low-velocity impact responses of auxetic honeycomb composite plates, taking into account loading-unloading-reloading processes. Effective material properties of the auxetic honeycomb core and GPR face sheets are obtained by using the proposed modified Gibson function and Halpin–Tsai model. Then, taking into account geometric nonlinearity, the nonlinear equations of motion for the system were derived by Hamilton's principle. Afterward, the time-varying contact force between the composite plate and a spherical impactor is defined by the modified nonlinear Hertz contact theory. The Galerkin method and variable-step Runge–Kutta algorithm are selected to obtain nonlinear impact responses. The proposed methods are verified by finite element simulation and experiment. Finally, the study evaluates the effects of key parameters on the nonlinear repeated low-velocity impact responses.

Nonlinear low-velocity impact response of graphene platelet-reinforced metal foam cylindrical shells under axial motion with geometrical imperfection

Nonlinear low-velocity impact response of graphene platelet-reinforced metal foam cylindrical shells under axial motion with geometrical imperfection

Nonlinear low-velocity impact response of GRC beam with geometric imperfection under thermo-electro-mechanical loads

This paper presents an investigation on thermo-electro-mechanical nonlinear low-velocity impact behaviors of the geometrically imperfect functionally graded (FG) graphene-reinforced composite (GRC) beam with surface-bonded piezoelectric layers. Both uniformly distributed and FG patterns of graphene nanoplatelets (GPLs) are considered along the thickness of the GRC host beam. The effective Young’s modulus is calculated by the Halpin–Tsai model. The Poisson ratio and mass density are calculated by the rule of mixture. The modified nonlinear Hertz contact law is employed to predict the impact force between the spherical impactor and the geometrically imperfect GRC piezoelectric beam during impacting. By considering the first-order shear deformation theory and von Kármán nonlinear displacement–strain relationship, the nonlinear governing equations are obtained by Hamilton principle and dispersed by differential quadrature (DQ) method. The Newmark-β method associated with Newton–Raphson iterative process is adopted to parametrically identify the impact force and the dynamic response of the system. The effects of geometric imperfection, weight fraction and distribution pattern of GPLs, temperature variation, thickness of piezoelectric layer and impactor’s initial velocity on nonlinear low-velocity impact behaviors of geometrically imperfect GRC beams are discussed in detail. Our results illustrate that the coupling effect of geometric imperfection and thermo-electro-mechanical load has a significant effect on the nonlinear low-velocity impact behavior of GRC beam, and GPLs distributing into the piezoelectric layers is better for reducing the impact response of geometrically imperfect GRC piezoelectric beam.

An accurate hyperelasticity‐based plate theory and nonlinear energy‐based micromechanics for impact and shock analyses of compliant particle‐reinforced FG hyperelastic plates

AbstractThe current article is devoted to the nonlinear dynamic and impact response analyses of rectangular incompressible neo‐Hookean hyperelastic plates with uniform/nonuniform transverse distributions of stiff elastic reinforcing particles. The nonlinear finite element governing equations are derived by using the principle of minimum total potential energy and solved by an updating scheme that uses the Runge‐Kutta time integration and penalty methods. The impact energy expressions are written for the integrated plate‐indenter system. The novelties of the article are: (i) realistic modeling the energy absorption of a particle‐reinforced nonlinear hyperelastic matrix based on the volume fractions of the constituent phases instead of using wrong Voigt‐type models or impractical predefined gradation coefficients, (ii) considering non‐uniform distributions of the reinforcing particles, (iii) using a highly accurate asymmetric (all the available theories are symmetric) infinite‐order plate theory, (iv) including the inherent hyperelastic nature of the material in the definition of the parameters of the plate theory, (v) considering the thickness changes of the plate, (vi) including von Karman's kinematic nonlinearity, (vii) analyzing both the dynamic and impact behaviors, (viii) proposing an adaptive algorithm to match the description of the displacement field with the load/stress variations, (ix) updating not only the stiffness but also the mass matrix within the time steps, (x) incorporation of the nonlinear boundary conditions by the penalty method, and (xi) performing time‐dependent analyses instead of the natural frequency analyses. Results reveal the drastic effects of the volume fraction of the reinforcing particles on the dynamic responses and report the impact responses of the FG hyperelastic plates, for the first time.

Nonlinear Impact Response Analysis of Partially Damped Plate with Acoustic Black Hole with Residual Thickness

Nonlinear Impact Response Analysis of Partially Damped Plate with Acoustic Black Hole with Residual Thickness

Low-velocity impact response of sandwich cylindrical panels with nanotube-reinforced and metal face sheet in thermal environment

ABSTRACTEmploying an analytical method, non-linear low-velocity impact response of carbon nanotube (CNT)-reinforced sandwich cylindrical panels in thermal environments is analysed. Two types of core (i.e. homogenous and functionally graded) are considered for sandwich panels. The face sheets of sandwich panels are multi-layer which consist of CNT-reinforced composite (CNTRC) and metal layers. Micromechanical models are used to estimate the material properties of CNTRCs. A higher-order shear deformation theory with a von Kármán-type of kinematic non-linearity provides the equations of motion. Temperature-dependent material properties are used to include the thermal effects. The equations of motion are solved using a two-step perturbation technique. Existing numerical results in the literature are used to validate the present method. The effect of nanotube volume fraction, material property gradient, impactor initial velocity, geometrical parameters of cylindrical panel, temperature change and edge boundary condition on the impact response of cylindrical panel structures is discussed. The quantitative results and analytical formulations can be helpful in better designing of CNTRC structures subjected to low-velocity impact in thermal environments.

Effects of the impactor geometrical shape on the non-linear low-velocity impact response of sandwich plate with CNTRC face sheets

In this study, non-linear low-velocity impact response of a simply supported sandwich plate with CNTRC face sheets subjected to the impactors with different geometrical shapes is investigated. It has been assumed that the sandwich plate is made up of two face sheets reinforced with CNTs graded along their thickness as X profile and a homogeneous core. In CNT-reinforced layers, a micromechanical model has been used to obtain the effective material properties and the analysis is performed in the framework of the Reddy's higher order shear deformation theory with regard to thermal effects. An analytical model is proposed to capture the response performance of the three-layer sandwich plates under different thermal environments. Through the proposed analytical study, in order to characterize the contact force between the sandwich plate and the impactors, the modified Hertz contact law is utilized. Rayleigh-Ritz method is applied to the Hamilton principle in order to find the set of equations of motion for the impactor as well as the CNTRC sandwich plate. Afterwards, the solution in the time domain is obtained based on Newmark's numerical time integration scheme. After validating the proposed approach, in order to examine the influences of various involved parameters, different parametric studies are conducted. It has been demonstrated that the variation of the initial kinetic energy as one of the parameters under study has a significant effect on the central displacement, contact force, and indentation in both conical and cylindrical impactors and the change in the radius of the cylinder has an insignificant effect on the central displacement. As well, in the case of equal masses, the cylindrical impactor causes more amount of indentation with respect to conical.

Nonlinear low-velocity impact response of FG-GRC laminated plates resting on visco-elastic foundations

Abstract The nonlinear transient response of functionally graded graphene reinforced composite (FG-GRC) laminated plates resting on visco-Pasternak foundations in thermal environments under impact load is investigated in this paper. Each layer of a laminated plate is assumed to have the same thickness, but the volume fraction of graphene is assumed to be functionally graded in a piece-wise pattern along the plate thickness direction. The stiffness of FG-GRC is then obtained by an extended Halpin-Tsai model, where the graphene efficiency parameters are introduced and determined by molecular dynamics (MD) simulations. The impactor is assumed to be a metal sphere and the contact process between the impactor and the laminated plate is described by a modified Hertz model. The effects of the visco-Pasternak foundation and the temperature variation as well as the initial load are taken into consideration. In the framework of von Karman type of kinematic nonlinearity, the motion equations of an FG-GRC laminated plate are established based on a higher-order shear deformation theory and solved by a two-step perturbation technique. Finally, the motion equations of the impactor and the FG-GRC laminated plate can be simultaneously solved by the Runge-Kutta approach. The numerical results illustrate the effects of functionally graded graphene distribution, foundation stiffness, temperature variation, initial in-plane load and different impactor velocities on the contact force and the deflection of the FG-GRC laminated plate.

Nonlinear low-velocity impact analysis of matrix cracked hybrid laminated plates containing CNTRC layers resting on visco-Pasternak foundation

Abstract This paper investigates the low-velocity impact response of a shear deformable laminated plate which contains both carbon nanotube reinforced composite (CNTRC) layers and fiber reinforced composite (FRC) layers. The effect of matrix cracks is considered and a refined self-consistent model (SCM) is selected to describe the degraded stiffness of the plate. The material properties of both FRC layers and CNTRC layers are assumed to be temperature-dependent. The plate rests on a visco-Pasternak foundation in thermal environments. A modified Hertz model is utilized to describe the contact force between the impactor and the plate. Based on a higher order shear deformation theory and von Karman nonlinear strain-displacement relationships, the motion equations of the plate are established and solved by means of a two-step perturbation approach. The effects of the crack density, CNT volume fraction, temperature variation and the foundation stiffness on the nonlinear low-velocity impact response of hybrid laminated plates with multiple matrix cracks are discussed in detail.

Nonlinear low-velocity impact response of functionally graded plate with nonlinear three-parameter elastic foundation in thermal field

Abstract In this paper a nonlinear investigation is presented for impact response of functionally graded material plates which are resting on a nonlinear three-parameter elastic foundation with simply supported end condition. In foundation, the influence of linear Winkler and Pasternak parameter is taken into account. The governing equations of the plate are derived based on a Reddy's higher order shear deformation theory with the von Karman-type of kinematic nonlinearity. The effect of thermal field is considered and material properties of the plates are assumed to be temperature dependent, as well and vary along the thickness according to Voigt model. In addition, by using a modified Hertz's contact law, the influence of material properties of the substrate layers on impact response is considered. The equations of motion are solved via an analytical procedure. The effects of deformation theories as well as thermal field, foundation parameters and impactor's parameters are discussed in results and discussion section.

An experimental and numerical study on nonlinear impact responses of steel-plated structures in an Arctic environment

Ships and offshore platforms that operate in Arctic regions at low temperatures are likely subjected to impact loads that arise from collisions with icebergs. The aim of this paper was to examine the nonlinear impact response of steel-plated structures in an Arctic environment. In addition to material tensile tests for characterisation of the mechanical properties of polar-class high-tensile steel of grade DH36, an experimental study was undertaken in a dropped-object test facility on steel-plated structure models under impact loads and at low temperatures equivalent to those in Arctic regions. LS-DYNA nonlinear finite element computations were also performed for the corresponding test models. We conclude that nonlinear finite element analyses are useful in the analysis of the nonlinear impact structural responses involving yielding, crushing and brittle fracture at low temperatures as long as the modelling techniques are adequate. The conclusions and insights developed in this paper should be useful in the safety design of ships and offshore platforms intended for operation in Arctic regions.

Impact analysis of strain-rate-dependent composite plates with SMA wires in thermal environments: Proposing refined coupled thermoelasticity, constitutive, and contact models

Effects of the strain-rate dependency of the elastic moduli of the composite and shape memory alloy (SMA) materials on responses of rectangular composite plates with embedded SMA wires subjected to impacts with spherical indenters is considered in the present research, for the first time. The plates are assumed to be placed in thermal environments; so that in contrast to all the available researches, the shape memory and ferroelasticity effects are also taken into account in addition to the superelasticity. The governing equations are derived based on a proposed enhanced phase version free energy function and refined constitutive equations with coupled expressions and solved by a virtual-work-type Galerkin-based finite element method. The resulting highly non-linear and piecewise-defined governing equations are solved through using biquadratic rectangular elements, an iterative solution scheme, and a special phase transformation tracing algorithm. Hertz contact law is also revised accordingly based on a proper micromechanical model. Results are obtained for a range of ambient temperatures that are either lower or higher than the austenite start temperature. Results show that complex combinations of the strain-rate dependency of the material properties, impact-induced temperature rise, and ambient temperature may significantly affect the phase transformation phenomenon and the non-linear impact responses.

Nonlinear impact response analysis of LNG FPSO cargo tank structures under sloshing loads

This is a sequel to a previous paper by the same authors, which proposed a probabilistic approach to determine the nominal values of tank sloshing loads in the structural hull design of liquefied natural gas, floating production, storage and offloading units (LNG FPSO or FLNG). This study presents a procedure for the numerical computation of nonlinear impact responses in FLNG cargo tank structures under sloshing loads. The computations are performed using ANSYS/LS-DYNA nonlinear finite element software. Applied examples using a hypothetical FLNG are presented. The insights and conclusions obtained from the study are documented.

Nonlinear low-velocity impact analysis of temperature-dependent nanotube-reinforced composite plates

A nonlinear analysis is presented for impact response of carbon nanotube-reinforced composite (CNTRC) structures under thermal conditions. Two plate configurations (i.e., single-layer and sandwich plates) are considered, and the nanotube reinforcement is either uniformly-distributed or functionally-graded in the plate thickness direction. The material properties of nanotube reinforced composites are estimated using micromechanical models. The equations of motion are based on a higher-order shear deformation theory with a von Kármán-type of kinematic nonlinearity, and the thermal effects are included by considering the nanotube reinforced composites as temperature-dependent. The equations of motion are solved with a two-step perturbation technique, and the initial stresses caused by either the thermal or in-plane edge loads as in-plane boundary conditions are introduced. The influences of material property gradient, volume fraction distribution, temperature change, initial stress, initial velocity of the impactor, and core-to-face sheet thickness ratio on impact response of plate structures are discussed. The analysis presented can help better understand the nonlinear impact response of functionally-graded materials and facilitate design and optimization of nanocomposite structures against impact and under thermal and other environments.

Nonlinear low-velocity impact response analysis of a radially preloaded two-directional-functionally graded circular plate: A refined contact stiffness approach

The available rare publications on low-velocity impact analysis of the functionally graded plates have mainly been performed using commercial finite element softwares and discrete models for variations of the material properties. In the present research, nonlinear low-velocity impact analysis of two-directionally-graded circular plates under radial preloads is presented. Some of the novelties of the present research are: (a) the problem is treated based on a complete formulation and accurately modeling of variations of the material properties, (b) considering a functionally graded material whose properties vary in both radial and transverse directions, (c) considering influence of the initial compressive/extensional radial loads, (d) using nonlinear von Karman-type strain–displacement relations for evaluating effects of the radial preloads, (e) employing a refined contact law that accounts for the material heterogeneity and plate thickness, and (f) using a Galerkin-type solution procedure to achieve more accurate results. Therefore, results may be used for radially-graded and transversely-graded circular plates as special cases. The nonlinear governing equations are solved employing an iterative numerical procedure during each Newmark’s time integration step. A comprehensive sensitivity analysis including effects of various material heterogeneity, geometric, and motion parameters is accomplished.

Analysis of Impact Responses for Box Structures Having Damping Layers Supported by Nonlinear Springs (Influences of Damping Couplings among Parts on Nonlinear Responses)

This paper describes vibration analysis using finite element method for box structures consisting of elastic flat plates and damping layers on their bottom plates. The box structures are supported by nonlinear concentrated springs on the bottom plate. The restoring force of the springs have cubic nonlinearity and linear hysteresis damping. Finite element for the nonlinear springs are expressed and are connected to the elastic plates modeled by linear solid finite elements in consideration of complex modulus of elasticity. Further, the discretized equations in physical coordinate are transformed into the nonlinear ordinary coupled equations using normal coordinate corresponding to linear natural modes. Using material damping and shares of strain energy for the parts (i.e. the plates, the damping layer and the springs), we evaluate damping couplings among the parts. Further, we clarify influences of the damping couplings on nonlinear impact responses.