Newmark Time Integration Method Research Articles

The efficient data-driven solution to estimate the nonlinear bending of sandwich doubly curved panel subjected to transient loading

This paper investigates nonlinear transient bending characteristics of sandwich doubly curved panels under transient loading which is extensively used in aerospace structures. Due to the lack of a dataset for the nonlinear transient bending of the sandwich doubly curved panel for the data-driven solution, mathematical modeling is used. The sandwich doubly curved panel is made of two graphene nanoplatelets (GPLs) reinforced face sheets, and a polymer core. In the mathematical modeling section, the effective Young's modulus is obtained via modified Halpin-Tsai methodology, and the role of the mixture is used to estimate other material properties of the composite face sheets. The presented structure is analyzed using Reddy's third-order shear deformation theory (RTSDT), which incorporates von Kármán nonlinear geometric assumptions and Hamilton's principle. The governing equations and associated boundary conditions are derived accurately by imposing shear stress-free conditions on the upper and lower surfaces of the panel. The meshfree radial point interpolation method (RPIM) with interpolation functions is utilized to determine the unknown degrees of freedom to numerically simulate the mid-plane of the sandwich doubly-curved panel. The Newton-Raphson approach is used to solve the nonlinear ordinary differential using the constant-average acceleration strategy from Newmark's time integration method. After obtaining the dataset, the data is collected, and using an efficient data-driven approach, the results are tested, validated, and trained. In future studies, the presented efficient data-driven approach can be used with low computational cost to simulate nonlinear transient bending characteristics of sandwich doubly curved panels under transient loading for related aerospace industries.

Wave propagation in beams with functionally graded porosity distribution under highly transient axial and transverse impacts

Recent advances in the manufacturing process provide a possibility of fabricating a new generation of porous materials denoted by functionally graded porous materials (FGPM). This paper aims to present a time domain analysis of wave propagation through the porous structures with functionally graded porosity distribution, which has not been completely studied before. For this purpose, the beams with different functionally graded porosity distributions subjected to both axial and transverse tip impact loads with a high-frequency content are investigated. The shear deformable cantilevered functionally graded porous beams with various porosity distributions through the beam thickness are studied. The governing differential equations are derived using the Hamiltonian principle based on the Timoshenko beam theory. A locking-free first-order shear deformable beam element is used to derive the finite element formulation of the equations. The Newmark time integration method is used to perform a time domain analysis of the equations of motion and to investigate the transient response of the beams. The axial and transverse wave propagation characteristics through functionally graded (FG) porous beams are found using time domain analysis of the results. Deflection and velocity time histories of the tip and each point of the beam, reflection time, and variation of support reactions are obtained. The influences of the porosity magnitude and porosity distribution on the wave propagation characteristics and overall time responses are investigated. The results reveal that porosity distribution has a significant effect on the wave amplitude, wave speed, and reflection from the boundary. Also, this study can help in a better understanding of porous structures' behavior subjected to high-transient impact loads in different engineering applications.

The Effect of Porous Media on Wave-Induced Sloshing in a Floating Tank

Placing porous media in a water tank can change the dynamic characteristics of the sloshing fluid. Its extra damping effect can mitigate sloshing and, thereby, protect the integrity of a liquefied natural gas tank. In addition, the out-of-phase sloshing force enables the water tank to serve as a dynamic vibration absorber for floating structures in the ocean environment. The influence of porous media on wave-induced sloshing fluid in a floating tank and the associated interaction with the substructure in the ambient wave field are the focus of this study. The numerical coupling algorithm includes the potential-based Eulerian–Lagrangian method for fluid simulation and the Newmark time-integration method for rigid-body dynamics. An equivalent mechanical model for the sloshing fluid in a rectangular tank subject to pitch motion is proposed and validated. In this approach, the degrees of freedom modeling of the sloshing fluid can be reduced so the numerical computation is fast and inexpensive. The results of the linear mechanical model and the nonlinear Eulerian–Lagrangian method are correlated. The dynamic interaction between the sloshing fluid and floating body is characterized. The effectiveness of the added porous media in controlling the vibration and mitigating the sloshing response is confirmed through frequency response analysis.

Failure analysis of fiberglass‐vinyl ester composite cylinders subjected to fire and asymmetric transient pressure

AbstractA hybrid numerical method is developed for failure prediction of glass fiber reinforced vinyl ester (GRV) composite cylinders subjected to fire and asymmetric transient pressure. The method is composed of layerwise theory, differential quadrature method, Fourier series expansion, and Newmark's time integration method. To achieve high‐accuracy solution, the char formation, resin decomposition, volatile convection, and temperature‐dependent material properties are considered. By comparing the developed results with the experimental and numerical results presented in the available literatures, the precision of this method is confirmed. The results reveal that although the polymeric composites are flammable, they are also strong thermal insulators compared to conventional metals, which reduces the flame spread rate from one section to another.

Dynamic fracture analysis of the linearly uncoupled and coupled physical phenomena by the variable-node multiscale XFEM

This paper aims to develop a variable-node multiscale extended finite element method (V-XFEM) for dynamic fracture analysis of the linearly uncoupled and coupled physical phenomena in a compact formula. The general governing equations for the linearly uncoupled and coupled physical phenomena are presented in a compact form. The local mesh refinement technique for modeling cracks is used to improve the accuracy and efficiency, in which variable-node elements without modifying the system matrix or impose additional boundary conditions are taken to connect/link different scale elements. In addition, the time-dependent equations are solved by the unconditionally stable implicit Newmark time integration method, and the dynamic intensity factors (DIFs) are derived from the domain forms of the interaction integrals. Numerical results of the linearly elastic and piezoelectric problems show that V-XFEM is an efficient numerical approach to simulate the dynamic fracture problems of the linearly uncoupled and coupled physical phenomena.

Dynamic analysis of functionally graded sandwich beams using a semi-analytic method named scaled boundary finite element method

In this research, free and forced vibrations of the functionally graded material (FGM) sandwich beams are investigated by using the scaled boundary finite element method (SBFEM). The innovation of this method is that the discretization only exists in the axial direction of the beam, which reduces the spatial dimension of problem by one, the time-consuming mesh generation processes are greatly reduced. The homogeneous second-order differential equations of the beams are derived by the method of virtual work principle with the radial coordinates as independent variables, which realizes the characteristics of the FGM changing along the radial direction. By using the state space method and the Padé series expansion method, the governing equations are further solved analytically, and the mass and stiffness matrices of each layer of the FGM sandwich beams are obtained. The combination between layers of the FGM sandwich beams is realized according to continuity conditions of displacement. Therefore, the free and forced vibrations using Newmark time integration method of the FGM sandwich beams are further realized. A special attention is given to two different types of the FGM sandwich beams, one is the beam with FGM face sheets and the other is the beam with FGM core. Three different types of dynamic loadings are considered in the analysis of forced vibration. The convergence of the proposed method for solving the dynamic characteristics of the beams is verified by increasing the order of the higher order spectral elements. In order to prove the numerical stability of the current method for dynamic analysis of the FGM sandwich beams, the frequency of the FGM sandwich beams under various parameters and the transient vertical displacement of the beam loading points under three different loadings are solved. The numerical results of the current method are compared with the results obtained by using different theories in the other literature, which shows a good agreement. In addition, on the basis of the research, the doped FGM core in the uniform core is discussed by using the current method, which provides some guidance for the optimal design of the dynamic characteristics of the beams.

Impact analysis of functionally-graded graphene nanoplatelets-reinforced composite plates laying on Winkler-Pasternak elastic foundations applying a meshless approach

In this paper, we investigated impact analysis of functionally-graded (FG) graphene nanoplatelets (GPLs)-reinforced composite plates with arbitrary boundary conditions and resting on Winkler-Pasternak elastic foundations. The element-free improved moving least-squares Ritz (IMLS-Ritz) approach and the higher-order shear deformation theory (HSDT) are used to develop the theoretical formulation. Target plates are set to have uniform and functionally graded GPLs distributions throughout their thickness. The modified Halpin-Tsai model is considered to calculate the effective Young’s modulus yet the rule of mixture is used to calculate the effective Poisson’s ratio and mass density. The modified nonlinear Hertz contact law is adopted to describe the contact force between the spherical impactor and target plates. In addition, Newmark time-integration method is employed to obtain dynamic response of plates as well as impactor’s displacement. An extensive parametric study is performed to examine effects of some essential parameters on results (distributions and volume fraction of GPLs, initial velocity and radius of impactor, plate’s width-to-thickness ratio, Winkler and Pasternak modulus parameters as well as boundary conditions).

Nonlinear supersonic post-flutter motion of panels with adjacent bays and thermal effects

Aerospace vehicle structures in the supersonic regime flight have their outer skin subjected to unsteady aerodynamic and thermal loading, which may lead to aeroelastic instability. Typical aerospace structures are built as multiple adjacent panels, the so-called multi-bay configuration, but early efforts to predict the supersonic flutter were based on a single panel arrangement. This work evaluates the aeroelastic behavior of supersonic multi-bay fluttering panels under thermal effects, aiming to improve the understanding of adjacent panels interaction in the nonlinear regime. The aeroelastic model is established by using the first-order quasi-steady piston theory in conjunction with isotropic panel model using the von Kármán’s assumptions to account for geometrical nonlinearities. The Newmark time-integration method is used to evaluate the resulting equations of motion. The Hopf bifurcation behavior that determines the flutter onset, thermo-buckling loading, phase portrait plots, and bifurcation diagrams for two adjacent panels are presented. The numerical results show the detrimental aspect of thermal loading in the aeroelastic behavior of fluttering panels, and the new findings corroborate with some recent studies that highlight the difference in the nonlinear flutter behavior between a single panel and multi-bay panels. Moreover, the existence of limit cycle oscillations amplitude jumps from a certain level of flow dynamic pressure is also observed. The multi-bay panels configuration also shows the anticipation of the buckled to the limit cycle oscillation solutions, when compared with a single panel analysis. Results indicate that simplified single bay panel assumptions can underestimate the post-flutter oscillations amplitudes of the adjacent bay. Such dynamic behavior may lead to a negative impact on aircraft structural design and fatigue life estimation.

Transient responses of two mutually interacting single-walled boron nitride nanotubes induced by a moving nanoparticle

This paper reports a theoretical investigation on the dynamic behaviour of two mutually interacting single-walled boron nitride nanotubes (BNNTs) under a moving nanoparticle. Both the electromechanical coupling effect and nonlocal effect are considered by employing respectively the theory of piezoelectricity and nonlocal elasticity. The interaction between the two BNNTs is considered by calculating the van der Waals (vdW) force between atoms on the respective nanotubes. The Hamilton's principle is then used to derive the governing equations of motion based on the Rayleigh and Timoshenko beam model. The incremental harmonic balance method, Galerkin method and the Newmark time integration method are jointly employed to numerically obtain the transient vibration responses of the nanotubes. The influences of the size effect, aspect ratio, inertial force, electrical potential, as well as the mass and velocity of the nanoparticle on the transient responses are discussed.

Active control of functionally graded carbon nanotube–reinforced composite plates with piezoelectric layers subjected to impact loading

To the best of the authors’ knowledge, this is the first attempt in the open literature to study the active control of the dynamic response of functionally graded carbon nanotube–reinforced composite plates with piezoelectric layers, as target composite plates, subjected to impact loading. The theoretical formulation of the composite plates with piezoelectric layers is developed using the element-free improved moving least-squares Ritz model and the higher-order shear deformation theory. The effective material properties of the carbon nanotube–reinforced composite layer are estimated by the Mori–Tanaka method. The modified nonlinear Hertz contact law is used to identify the contact force between the target composite plates and the spherical impactor. The Newmark time integration method is utilized to calculate the resulting dynamic response. A constant velocity feedback controller is efficiently used for the active control of the dynamic response of the target plates subjected to impact loading. The results revealed that the current model can successfully reduce and suppress the resulting displacement caused by impact loading. Additionally, the effects of some passive configurations on the target plates’ dynamic response are presented. The effect of altering both active and passive control configurations together on the target plates’ dynamic response is discussed as well.

Wavelet based damage identification and dynamic pull-in instability analysis of electrostatically actuated coupled domain microsystems using generalized differential quadrature method

Abstract In this study, the effects of edged-crack on dynamic pull-in instability of fixed-fixed microbeams under suddenly applied electrostatic excitations and nonlinear squeeze film damping are investigated. The deformable electrode is modeled based on size dependent Euler–bernoulli beam formulations with modified couple stress theory. Also fluid interaction with electrode is modeled by nonlinear Reynolds equation. The model accounts for the von Karman nonlinear strains and edge crack in the domain. The edged crack is modeled as a massless torsional spring and is incorporated in the continuity equations of micro-beam formulations. Employing the Hamilton's principle, the governing nonlinear equations are attained and are then discretized by generalized differential quadrature method. This approach is combined with Newmark time integration and direct iteration method and is employed to investigate dynamic pull-in instability of the microsystem. The stability analysis of the cracked microbeam is also implemented by evaluating the largest Lyapunov exponent, the sign of which describes the character of the time dependent response. Wavelet transform based on Gabor function is applied for identifying the damage in microstructure. The location of damage is determined from the sudden peaks in the spatial variation of the transformed response of damped microbeam by this algorithm. Finally, a comprehensive study is carried out to examine the influence of the crack depth and crack position on pull-in instability characteristics of microbeams. Also, the efficiency of proposed wavelet analysis for damage detection in microstructures is assessed.

Structural damage detection using time domain responses and an optimization method

ABSTRACTAn efficient method is proposed to determine the location and severity of structural damage using time domain responses and an optimization method. The time domain responses utilized here are the nodal accelerations measured at the limited points of a structure subjected to an impulse load. The nodal accelerations of the structure are obtained by Newmark time integration method. Firstly, using nodal accelerations extracted for the damaged structure and an analytical model of the structure, an objective function is defined for optimization. Then, the optimization-based damaged detection problem is solved via a differential evolution algorithm for finding the location and severity of damage. In order to assess the accuracy of the proposed method, four numerical examples are considered. Simulation results reveal the efficiency of the method for properly identifying damage with considering measurement noise.

Analysis of A Uniform Bernoulli – Euler Beam on Winkler Foundation Subjected to Harmonic moving load

This paper established Galerkin Finite element method coupled with Newmark Beta time integration method to analyze Winkler foundation subjected to a harmonic moving load on a uniform Bernoulli – Euler Beam. MATLAB software was used to implement the Newmark time integration method to obtain the Analysis. The deflection of the Beam increase when the acceleration of the load was change from am = 2m/s2 to am = 15m/s2. Also when the position of the load was change from n = 5 to n = 10. It was observed from the results that the position of the load and the acceleration of the moving load affect the deflection of the Beam.

Iterative global-local approach to consider the local effects in dynamic analysis of beams

This paper introduces a numerical procedure to incorporate elasto-plastic local deformation effects in the dynamic analysis of beams. The appealing feature is that simple beam type finite elements can be used for the global model which needs not to be altered by the localized elasto-plastic deformations. An overlapping local sophisticated 2D membrane model replaces the internal forces of the beam elements in the predefined region where the localized deformations take place. An iterative coupling technique is used to perform this replacement. Comparisons with full membrane analysis are provided in order to illustrate the accuracy and efficiency of the method developed herein. In this study, the membrane formulation is able to capture the elasto-plastic material behaviour based on the von Misses yield criterion and the associated flow rule for plane stress. The Newmark time integration method is adopted for the step-by-step dynamic analysis.

Impact analysis of CNT-reinforced composite plates integrated with piezoelectric layers based on Reddy's higher-order shear deformation theory

Abstract As a first endeavor in the open literature, the impact analysis of carbon nanotube reinforced composite (CNTRC) plates integrated with piezoelectric layers is studied. In this paper, a novel element-free IMLS-Ritz model with Reddy's higher-order shear deformation theory is employed considering four distributions of carbon nanotubes. The effective material properties of the CNTRC plates are estimated by the Mori-Tanaka method. The modified non-linear Hertz contact law is utilized to define the contact force between the target CNTRC plates integrated with piezoelectric layers and the spherical impactor during the impact duration. Newmark time integration method is employed to identify the dynamic response of the target plates and the impactor displacement. The impactor is assumed to strike the target plate either at CNTRC layer or the piezoelectric one. Novel results for the two cases are presented.

Flutter stability analysis of a perforated damping blade for large wind turbines

The flutter stability of wind turbine blades is one of the important contents in the research of wind turbines. The bending stiffness of blades has decreased with the development of large-sized wind turbines. To achieve damping flutter-suppressing on the long spanwise blades, perforated damping blade was proposed under the consideration of the structural damping factor and the structural stiffness in this paper. Through the study of the unit cell, the deformation model was established and the structural loss factor of the perforated damping blade was derived. The undamped blade and the perforated damping blade, combined with the relevant parameters of a 1500 kW wind turbine blade, were established to simulate the flutter-suppressing abilities and the structural stability. The dynamic response analysis was accomplished with the large deformation theory, and the MPC algorithm was used to realize grid mobile and data delivery, according to the Newmark time integration method. The comparison results show that the perforated damping blade has both a higher structural damping factor and a better structural stiffness.

Impact analysis of CNT-reinforced composite plates based on Reddy’s higher-order shear deformation theory using an element-free approach

To the best of our knowledge, the available literature investigating the impact analysis of functionally graded carbon nanotube reinforced composite (CNTRC) plates is very limited and missing in the case of utilizing any of the element-free methods. In this paper, a novel element-free IMLS-Ritz model in association with Reddy’s higher-order shear deformation theory is presented to study the impact analysis of CNTRC plates with both uniform and functionally graded carbon nanotubes (CNTs) distributions. The modified non-linear Hertz contact law is used to define the contact force between the CNTRC target plates and the spherical impactor during the impact duration. Newmark time integration method is employed to identify the dynamic response of the CNTRC plates and the impactor displacement. Two Mori–Tanaka methods are utilized to calculate the effective material properties of the composites reinforced with randomly oriented or aligned straight CNTs. The current approach accuracy is validated with the available open literature results showing a clear agreement. Detailed parametric studies are performed to study the effects of CNTs distributions, plate’s width-to-thickness ratio, impactor’s initial velocity, impactor’s radius and CNTs volume fraction on the results. Furthermore, a comparison between the results obtained by the two Mori-Tanka methods is presented.

Dynamic analysis of functionally graded piezoelectric cylindrical panels by a three-dimensional mesh-free model

In this work, dynamic analysis of functionally graded piezoelectric cylindrical panels is carried out under different mechanical and electrical loads and boundary conditions by a three-dimensional mesh-free model. Moving least squares approximation is used in the weak form of governing equations including three-dimensional equations of motion and Maxwell’s equation. Transformation method is applied to impose the essential boundary conditions. A power-law distribution is used to determine the effective material properties in the panel. The resulting system of differential equations is solved using Newmark time integration method. After validation of the proposed model, parametric study is carried out to investigate the effects of boundary conditions, geometry of panel, and distribution of constituent materials on natural frequencies and dynamic response of functionally graded piezoelectric panel.

Nonlinear two-dimensional finite element model for transient and damping analysis of cylindrical sandwich panels with pseudoelastic shape memory alloy composite face sheets

A new nonlinear finite element model is proposed for the dynamic analysis of cylindrical sandwich panels with shape memory alloy hybrid composite face sheets and flexible core. In order to present a realistic transient vibration analysis, all the material complexities arising from the instantaneous and spatial martensite phase transformation of the shape memory alloy wires are taken into consideration. The one-dimensional constitutive equation proposed by Boyd and Lagoudas is used for modeling the pseudoelastic behavior of the shape memory alloy wires. Since the martensite volume fraction at each point depends on the stress at that point, the phase transformation kinetic equations and the governing equations are coupled together. Therefore, at each time step, an iterative method should be used to solve the highly nonlinear equations. Moreover, considering that the stress resultants generated by the martensite phase transformation in the wires are path-dependent values, an incremental method is used to estimate the increment of the stress resultants at each time step. The governing equations are derived based on the energy method and Newmark time integration method is used to solve the discretized finite element equations. Finally, several numerical examples are presented to examine the effect of various parameters such as intensity of applied pressure load, operating temperature, location of shape memory alloy wires, volume fraction of the shape memory alloy wires, and also boundary conditions upon the loss factor for panels with different aspect ratios.

Thermal-structural post-bucking and limit-cycle oscillation of Functionally Graded Materials

Thermal post-buckling and limit-cycle oscillation characteristics of Functionally Graded Material (FGM) structures are investigated based on the neutral surface concept. In particular, the material properties are non-homogeneous and vary gradually from one surface to the other. Furthermore, the properties are to be considered as temperature-dependent characteristics, and the neutral surface concept is adopted instead of the mid-plane to consider the reference plane due to the asymmetric properties in the thickness direction of model. In the formulation, the First-order Shear Deformation Theory (FSDT) of plate is used, and the geometric nonlinearity is accounted for by the von Karman strain-displacement relations. Also, steady state thermal conduction effects are assumed as a one dimensional heat transfer on the surface of the structure. For the numerical analysis, the Newton-Raphson method is applied to solve the thermal post-buckling behavior, while Newmark's time integration method is employed to resolve the limit-cycle oscillation. In order to validate the analysis results, the results of this paper based on the neutral surface are compared with the data from previous papers using the conventional approach for FGMs model. Finally, effects of the neutral surface on the non-linear thermo-mechanic behavior of structure are discussed in detail.