Abstract: The complex variable moving least-squares (CVMLS) approximation is discussed in this paper, and the mathematical and physical meaning of the complex functional in the CVMLS approximation is presented. With the CVMLS approximation, the trial function of a two-dimensional problem is formed with a one-dimensional basis function. Then combining the CVMLS approximation and the Galerkin weak form, we investigate the complex variable element-free Galerkin (CVEFG) method for two-dimensional elastodynamics problems. The penalty method is used to apply the essential boundary conditions, and the implicit time integration method, which is the Newmark method, is used for time history analysis. Then the corresponding formulae of the CVEFG method for two-dimensional elastodynamics problems are obtained. For the purposes of demonstration, some selected numerical examples are solved using the CVEFG method. Compared with the EFG method, the CVEFG method has greater precision.

Abstract: Introduction.- Analytical solutions.- Semi-analytical methods.- Review of numerical methods of solution.- Classical numerical methods of time integration.- Space-time finite element method.- Space-time finite elements and a moving load.- The Newmark method and a moving inertial load.- Meshfree methods in moving load problems.- Examples of applications.

Abstract: As numerical technology continues to grow and evolve with industrial applications, understanding the explicit finite element method has become increasingly important, particularly in the areas of crashworthiness, metal forming, and impact engineering. Introduction to the Explicit Finite Element Method for Nonlinear Transient Dynamics is the first book to address specifically what is now accepted as the most successful numerical tool for nonlinear transient dynamics. The book aids readers in mastering the explicit finite element method and programming code without requiring extensive background knowledge of the general finite element.

Abstract: A new method is developed to obtain guaranteed error bounds on pointwise quantities of interest for linear transient viscodynamics problems. The calculation of strict error bounds is based on the concept of "constitutive relation error" (CRE) and the solution of an adjoint problem. The central and original point of this work is the treatment of the singularity in space and time introduced by the loading of the adjoint problem. Hence, the adjoint solution is decomposed into two parts: (i) an analytical part determined from Green's functions; (ii) a residual part approximated with classical numerical tools (finite element method, Newmark integration scheme). The capabilities and the limits of the proposed approach are analyzed on a 2D example.

Abstract: The dynamic analysis of laminated plates with various loading and boundary conditions is presented employing generalized differential quadrature (GDQ) method. The first-order shear deformation theory is considered to model the transient response of the plate. The GDQ technique together with Newmark integration scheme is employed to solve the system of transient equations governing dynamics of the plate. Different symmetric and asymmetric lamination sequences together with various combinations of clamped, simply supported, and free boundary conditions are considered. Particular interest of this study regards to asymmetric orthotropic plates having free edge and mixed boundary conditions. It is shown that the method provides reasonably accurate results with relatively small number of grid points. Comparison of the results with those of other methods demonstrates a very good agreement. It is also revealed that the present method offers similar order of accuracy for all variables including displacements and stress resultants.

Abstract: Active control of multi-storey frame structures with nonlinear hysteretic response has been studied in this paper. A new nonlinear optimal control algorithm based on nonlinear Newmark integration method and distributed genetic algorithm (DGA) has been developed. The objective has been to reduce the response to below any desired level. In this study, DGA has been used to determine the weights in the control law corresponding to displacement, velocity and acceleration. The capabilities of the method has been assessed through simulation where an eight-storey frame with bilinear hysteretic behaviour has been subjected to a white noise ground acceleration and controlled by the controllers designed by the new algorithm. An active tendon control system comprised of prestressed tendons and either a single actuator, which could apply a force to one of the floors, or eight actuators, which could fully control the frame, has been used. Also, the optimum actuator placement in the single actuator case has been studied. The designed controllers have been tested under both near and far-field earthquakes and have performed successfully. Copyright © 2009 John Wiley & Sons, Ltd.

Abstract: In this study, a three-dimensional numerical model was developed based on a modal analysis and substructure method. The devised model was employed for an evaluation of the dynamic response of a bottom-mounted platform with a pile-soil foundation system that was subjected to random waves and currents. A two-dimensional numerical scheme with the Newmark β method was extended to three dimensions. The equation of motion was solved by using cylindrical beam elements to analyze the response of the superstructure, and the impedance function method was employed to model the pile-soil foundation system. The displacement and bending stress at selected nodal points of the structure were computed using various input parameters, such as the shear-wave velocity of the soil and the mean wave height and period. The effect of the current on the structural response was also evaluated. Using the reliability index obtained from the Monte Carlo simulation method, the reliability of the dynamic response at critical structural members, which contained uncertainties due to dynamic forces and structural properties, was assessed.

Abstract: In this paper, we study a numerical method for solving Nth-Order fuzzy differential equation (NOFDE). A Characterization Theorem that is presented shows that the NOFDE is equivalent to system of ODEs. So the numerical method for ODE can be used for NOFDE. Two examples are provided.

Abstract: Numerical simulations for the blood flow are carried out to investigate the effect of the flexible artery wall on the flow field and to determine the wall shear stresses in the carotid artery wall. To solve the equation of motion for the structure in typical fluid-structure interaction (FSI) problems, it is necessary to calculate the fluid force on the surface of the structure explicitly. To avoid complexity due to the necessity of additional mechanical constraints, we use the combined formulation including both the fluid and structure equations of motion into a single coupled variational equation. The Navier-Stokes equations for fluid flow are solved using a P2P1 Galerkin finite element method (FEM) and mesh movement is achieved using arbitrary Lagrangian-Eulerian (ALE) formulation. The Newmark method is employed to solve the dynamic equilibrium equations for linear elastic solid mechanics. The time-dependent, three-dimensional, incompressible flows of Newtonian fluids constrained in the flexible wall are analyzed. The study shows strongly skewed axial velocity and flow separation in the internal carotid artery (ICA). Flow separation results in locally low wall shear stress. Further, strong secondary motion in the ICA is observed.

Abstract: A simulation technique to deal with transient dynamic contact of tire rubber compounds on rough road surfaces is presented. The segment-to-surface approach is used for modeling the contact between tire tread rubber and road track. While the rubber components are deformable and described by a sophisticated viscoelastic damage constitutive model, the road surface is assumed to be rigid and characterized by an analytical function. A spectral approach based on an inverse computation of the 2D-Fast Fourier transform has been suggested for the reconstruction of rough surface profiles. The Newmark time-stepping method is used for the integration of transient dynamic equations. With the so-called contact-stabilized Newmark method the spurious oscillation at contact boundary has been removed. The detailed investigation on the dynamic contact of inelastic rubber block with rough road surfaces has been made. The robustness of the contact-stabilized Newmark method within a finite deformation framework is underlined by numerical studies, in which it is compared with several dissipation-based stabilization techniques selected from literature.

Abstract: In this study, a NURBS-based isogeometric approach is developed for transient analysis of laminated composite plates using the classical laminated plate theory (CLPT). Based on the isoparametric concept, the NURBS basis function is employed for both the parameterization of the geometry and the approximation of the plate deflection. An efficient and easy to implement technique is used for imposition of essential boundary conditions by simply fixing the deflection of the first row or first two rows of control points from the desired boundary for simply supported or clamped boundaries, respectively. Some numerical examples for transient response analysis of laminated plates with various boundary conditions under dynamic loadings are considered. The numerical results are obtained and compared with other available solutions in the literature. The comparisons demonstrate the efficiency and accuracy of the proposed approach for such problems.

Abstract: This paper presents the development of a finite element procedure for the dynamic analysis of flexible rotors supported on fluid-film elliptical journal bearings operating under several operating conditions. The rotating shaft is modeled by using Timoshenko beam theory and the coupled rotating components, such as disks and impellers, are modeled by using lumped masses. The modeling of the elliptical journal bearings is performed by solving the lubrication equations generated from the application of a linearized perturbation method on the classical Reynolds equation. The bearing carrying-load capacity and the linearized dynamic force coefficients can be predicted for elliptical bearings with different preloads and journal eccentricities. The rotor transient whirling unbalance response is estimated by performing the time integration of the finite element equations using Newmark method. Experimental whirling unbalance response of a rotating shaft supported at two identical journal bearings is used to validate the finite element procedure. A comparative analysis of the dynamic response of flexible rotors supported on both cylindrical and elliptical journal bearings is performed to show that some elliptical bearings are capable of attenuating the rotor unbalance response more efficiently than cylindrical bearings are.

Abstract: A sequential coupled field analysis of electromagnetic free bulging was performed by using FEM. A 2D axi-symmetric electromagnetic model based on the magnetic vector potential is proposed for the calculation of magnetic field and Lorentz’s forces. The Newmark integration method is used to calculate the transient dynamic plastic deformation of sheet during free bulging. In the finite element model, the effect of sheet deformation on the electromagnetic field analysis is taken into consideration. In order to confirm the sequential electromagnetic-mechanical coupling analysis, an experiment with an electromagnetic forming apparatus was conducted. The results showed that the final bulge height of the sheet predicted from the proposed method is in good agreement with experimentally measured height. Key Words : Electromagnetic Forming, Sequential Coupling Simulation, Electromagnetic-Structural Coupling, ANSYS /Multiphysics, High Speed Forming , Morphing , Lorentz’s Force

Abstract: This paper developed an effective optimization method, i.e., gradient-Hessian matrix-based method or second order method, of frame structures subjected to the transient loads. An algorithm of first and second derivatives of dynamic displacement and stress withrespect to design variables is formulated based on the Newmark method. The inequality time-dependent constraint problem is converted intoa sequence of appropriately formed time-independent unconstrained problems using the integral interior point penalty function method. The gradient and Hessian matrixes of the integral interior point penalty functions are also computed. Then the Marquardt's method is employed to solve unconstrained problems. The numerical results show that the optimal design method proposed in this paper can obtain the local optimum design of frame structures and sometimes is more efficient than the augmented Lagrange multiplier method.

Abstract: The vortex-induced vibration (VIV) phenomenon has drawn the attention of researchers in Engineering for several decades. An example is the riser used for petroleum exploration, in which it is subjected to marine flows that may cause oscillations due to vortex shedding. In this paper, numerical analyses of the phenomena that occur in the interaction among flows at low Reynolds numbers and elastically mounted cylinders are presented. The simulation is carried out by using the numerical model Ifeinco that uses a semi-implicit two-step Taylor-Galerkin method to discretize the Navier-Stokes equations and the arbitrary Lagrangean-Eulerian formulation to follow the cylinder motion. The rigid body motion description is calculated by using the Newmark method. Firstly, the characteristics of the vortex generation process for the fixed cylinder are analyzed. In this case, the Strouhal number, the mean drag and the RMS lift coefficients for Reynolds numbers ranging from 90 to 140 are shown. Afterwards, an analysis of a flexible supported cylinder (with a spring and a damper) in transverse direction subject to flows with Reynolds numbers ranging from 90 to 140 is carried out. The cylinder displacement and the vibration frequencies are studied; the synchronization between the vortex shedding and the vibration frequency (lock-in) is analyzed. Similar results to the experimental ones developed by Anagnostopoulos and Bearman (1992) were obtained in this study.

Abstract: The MLS(Moving Least Squares) Difference Method is a numerical scheme that combines the MLS method of Meshfree method and Taylor expansion involving not numerical quadrature or mesh structure but only nodes. This paper presents an dynamic algorithm of MLS difference method for solving transient solid mechanics problems. The developed algorithm performs time integration by using Newmark method and directly discretizes strong forms. It is very convenient to increase the order of Taylor polynomial because derivative approximations are obtained by the Taylor series expanded by MLS method without real differentiation. The accuracy and efficiency of the dynamic algorithm are verified through numerical experiments. Numerical results converge very well to the closed-form solutions and show less oscillation and periodic error than FEM(Finite Element Method).

Abstract: This paper presents a new method for direct time integration of nonlinear structural dynamic problems. In the proposed method, the order of time integration scheme is higher than the conventional Newmark’s family of methods. This method assumes second-order variation of the acceleration at each time step. Two variable parameters are used to increase the stability and accuracy of the method. The result obtained from this new higher-order method is compared with two implicit methods, namely the Wilson-θ and the Newmark’s average acceleration methods. The proposed method is an alternative quick method that can be written using matrix laboratory (MATLAB) for checking results from a more refined analysis or for a quick calculation with adequate accuracy.

Abstract: Stability characteristics of inclined rotor bearing system are investigated by numerical and experimental research. The dynamic equation is established based on finite element method. To describe the oil film force of journal bearing, Capone’s short bearing model and a variational approximate finite bearing model are employed separately and compared. Different inclination states are considered as different radial loads on journal bearing. Newmark method employed to solve the dynamic equation and stability characteristics are discussed. The numerical results show that the short and finite bearing models have differences on describing the oil force induced oil whirl and whip. Compared with the short bearing model results, unstable zones given by finite bearing model have larger breadth and larger whirl/whip amplitude. With the development of rotor inclination, the unstable threshold decreases and the unstable zone become wider. Influences of parameters on unstable thresholds are also affected by rotor incli...

Abstract: This study develops an adaptive time-stepping procedure of Newmark integration scheme for transient elastodynamic problems, based on the semi-analytical scaled boundary finite element method (SBFEM). In each time step, a posteriori local error estimator based on the linear distributed acceleration is employed to estimate the error caused by the time discretization. The total energy of the domain, consisting of the kinetic energy and the strain energy, is calculated semi-analytically. The time increment is automatically adjusted according to a simple criterion. Three examples with stress wave propagation were modeled. The numerical results show that the developed method is capable of limiting the local error estimator within specified targets by using an optimal time increment in each time step.

Abstract: This paper presents the research work conducted to investigate the dynamics characteristics of the offshore riser pipeline due to vortex flow and to develop a model that could predict its vortex induced responses. Glass-fiber reinforced plastic (GRP) pipe is used for this study which has smaller density from the steel. A two-dimensional finite element computational method is implemented to describe the dynamic behavior of the riser. The governing equation of motion was based on Hamilton's principle, consists of the strain energy due to bending and axial deformation, kinetic energy due to both riser and internal fluid movement and also external force from currents and waves. A direct integration method namely Newmark integration scheme is proposed to solve the equation of motion. A MATLAB program code was developed to obtain the simulation results. The natural frequency and damping ratio are presented for each mode. Dynamic response of riser is shown in time-domain and the numerical results are discussed. Several parameter effects are used to investigate dynamic responses and the results show an agreement with the theory. Vortex shedding phenomenon also has been discussed in this paper. As a conclusion, the simulation results have successfully shown the vortex induced vibration responses for GRP pipeline.

Abstract: The natural element method (NEM) is a meshless method. The trial and test functions of the NEM are constructed using natural neighbor interpolations which are based on the Voronoi tessellation of a set of nodes. The NEM interpolation is linear between adjacent nodes on the boundary of the convex hull, which makes imposition of essential boundary conditions easy to implement. We investigate the performance of the NEM combined with the Newmark method for problems of elastodynamics in this article. Applications are considered for a cantilever beam with different initial load conditions. The NEM numerical results are compared with the finite element method. NEM shows promise for these applications.