Abstract: The numerical integration of dynamical contact problems often leads to instabilities at contact boundaries caused by the non-penetration condition between bodies in contact. Even an energy dissipative modification (see, e.g. (Comp. Meth. Appl. Mech. Eng. 1999; 180:1-26)), which discretizes the non-penetration constraints implicitly, is not able to circumvent artificial oscillations. For this reason, the present paper suggests a contact stabilization in function space, which avoids artificial oscillations at contact interfaces and is also energy dissipative. The key idea of this contact stabilization is an additional L 2 -projection at contact interfaces, which can be easily added to any existing time integration scheme. In case of a lumped mass matrix, this projection can be carried out completely locally, thus creating only negligible additional numerical cost. For the new scheme, an elementary analysis is given, which is confirmed by numerical findings in an illustrative test example (Hertzian two-body contact).

Abstract: This paper focuses on trajectory control of the 6-DOF body flxed reference frame located on a very ∞exible aircraft. The 6-DOF equations of motion of a reference point on the aircraft are coupled with the aeroelastic equations that govern the geometrically nonlinear structural response of the vehicle. A low-order strain-based nonlinear structural analysis coupled with unsteady flnite-state potential ∞ow aerodynamics form the basis for the aeroelastic model. The nonlinear beam flnite element structural model assumes constant strain over an element in extension, twist, and in/out of plane bending. The geometrically nonlinear structural formulation, the flnite state aerodynamic model, and the nonlinear rigid body equations together provide a low-order complete nonlinear aircraft analysis tool. Due to the inherent ∞exibility of the aircraft modeling, the low order structural frequencies are of the same order as the rigid body modes. This creates a coupling which cannot be separated by previous control schemes. The ∞exibility must be accounted for directly in the controller development. To accomplish this a heuristic approach based upon pilot behavior is developed. This approach separates the problem into two parts: a fast inner-loop and a slower outer-loop. Dominant kinematic nonlinearities are handled in the outer-loop while the inner loop is further separated into a lateral and longitudinal motion. Control of the inner-loop lateral motion is accomplished using a standard Linear Quadratic Regulator. For the longitudinal motion Dynamic Inversion is utilized. Difierences between the desired and actual trajectories are handled in the nonlinear outer-loop using traditional proportional-integral-derivative design guidelines. The closed loop time integration is accomplished using an implicit modifled Newmark method. Numerical simulations are presented highlighting the strengths and weaknesses of the method.

Abstract: New implicit higher-order accuracy (IHOA) time integration, which uses constant time step, is presented for dynamic analysis. By defining weighted factors, current displacement and velocity are assumed to be functions of the accelerations in the several previous time steps. Then, the optimum weighted factors are determined so that displacement and velocity errors in the Taylor series are minimized. The IHOA is conditionally stable and by using the Routh–Hurwitz criterion, permissible time step is obtained. For numerical verification of the proposed technique, some linear and nonlinear dynamic systems from finite element and finite difference will be analyzed and the results are compared with common implicit methods such as Newmark- β and Wilson- θ approach. Further, the dynamic relaxation method is applied to solve equivalent static systems, obtained in implicit algorithms. Results show that the proposed time integration is stable for common time steps and exhibits improved accuracy. The highly accurate, ...

Abstract: Direct integration algorithms are typically used to solve temporally discretized equations of motion to evaluate the performance of structures under dynamic loading. The stability of these direct integration algorithms are usually investigated for linear elastic structures. However integration algorithms are often applied to structures with nonlinear behavior. This paper presents a procedure based on discrete control theory to investigate the stability of direct integration algorithms applied to multidegree-of-freedom (MDOF) nonlinear structures. The discrete root locus approach is used to investigate properties of the poles of the discrete transfer function matrix representing the nonlinear structural dynamics and to assess the stability of the integration algorithm. The procedure is illustrated using a nonlinear shear building MDOF system to investigate the stability of popular direct integration algorithms, including the Newmark family of integration algorithms, the Hilber-Hughes-Taylor α -method, and ...

Abstract: In this study, dynamic behavior and earthquake resistance of Alibey earth dam was investigated. The dam was modeled with four node plane-strain finite elements (FE) and displacement-pore pressure coupled FE analyses were performed. Nonlinear material models such as pressure dependent and independent multi yield materials were implemented during the analyses. Transient dynamic FE analyses were performed with Newmark method. The Newton-Raphson solution scheme was adopted to solve the equations. Liquefaction and/or cyclic mobility effects were considered during the analysis. For the FE analyses, OpenSees (Open System for Earthquake Engineering Simulation) framework was adopted.

Abstract: The MEMS capacitive switch based on fixed-fixed microbeam has garnered significant attention due to their geometric simplicity and broad applicability. The accurate model which describes the multiphysical coupled-field of MEMS capacitive switch should be developed to predict their electromechanical behaviors. The improved macromodel of the fixed-fixed microbeam-based MEMS capacitive switch is presented to investigate the behavior of electrically actuated MEMS capacitive switch in this paper, the macromodel provides an effective and accurate design tool for this class of MEMS devices because of taking account into some effects simultaneously including fringing field effect, midplane stretching effect, residual stress and multiphysical coupled-field effect. The numerical analysis of mechanical characterizations of electrically actuated microbeam-based MEMS capacitive switch are performed by the finite element Newmark method, and the performances of static and dynamic of MEMS capacitive switch are obtained. The numerical results show that, with only a few nodes used in the computation, the FEM-Newmark gives the identical results to other numerical methods, such as the shooting method and experiments. Moreover, the proposed model can offer proper and convenient approach for numerical calculations, and promote design of MEMS devices.

Abstract: This paper first compares the writers’ results of static and dynamic analyses of plates, cylindrical and spherical shells employing four-, eight-, and nine-noded elements with different integration rules with those of earlier investigators and including some of the recent composite theories. Thereafter, the nonlinear transient responses of laminated composite cylindrical and spherical shell panels with cutouts are investigated taking up additional examples that are yet to appear in the published literature. For these, the finite-element model is employed using eight-noded C0 continuity, an isoparametric quadrilateral element considering von Karman large deflection assumptions. In the time integration, the Newmark average acceleration method is used in conjunction with a modified Newton–Raphson iteration scheme. Important conclusions with respect to nonlinear transient responses are summarized for cylindrical and spherical shells with and without cutouts.

Abstract: The dynamic response of prestressed Timoshenko beams fully and partially resting on a two-parameter elastic foundation to a moving harmonic load is investigated by the finite element method. A beam element with shear deformation taking the effect of prestress and foundation support for the dynamic analysis is formulated in the context of the field consistent approach. Using the formulated element, the dynamic response of the beams having different boundary conditions is computed by using the direct integration Newmark method. The effects of prestress, foundation support, moving velocity and excitation frequency on the dynamic characteristics of the beams are studied and described in detail. The numerical results show that the effects of the axial force and the moving velocity on the dynamic response of the beams are governed by the excitation frequency. The influence of acceleration, partial support by the elastic foundation and the significance of the second foundation parameter are also examined and highlighted.

Abstract: A brief presentation on how to solve using the finite element method and the application of the method to microstrip problem are discussed.

Abstract: Geometrically nonlinear static and dynamic behaviour of laminate composite shells are analyzed in this work using the Finite Element Method (FEM). Triangular elements with three nodes and six degrees of freedom per node (three displacement and three rotation components) are used. For static analysis the nonlinear equilibrium equations are solved using the Generalized Displacement Control Method (GDCM) while the dynamic solution is performed using the classical Newmark Method with an Updated Lagrangean Formulation (ULF). The system of equations is solved using the Gradient Cojugate Method (GCM) and in nonlinear cases with finite rotations and displacements an iterative-incremental scheme is employed. Numerical examples are presented and compared with results obtained by other authors with different kind of elements and different schemes.

Abstract: This paper presents a simple implicit time integration scheme for transient response solution of structures under large deformations and long-time durations. The authors focus on a practical method using implicit time integration scheme applied to structural dynamic analyses in which the widely used Newmark time integration procedure is unstable, and not energy-momentum conserving. In this integration scheme, the time step is divided in two substeps. For too large time steps, the method is stable but shows excessive numerical dissipation. The influence of different substep sizes on the numerical dissipation of the method is studied throughout three practical examples. The method shows good performance and may be considered good for nonlinear transient response of structures.

Abstract: Current accuracy evaluation of a step-by-step integration method is generally based on the numerical solution itself and the exact solution is not referred to except for period distortion. Furthermore, the numerical accuracy associated with external force is generally not considered. In this study, an evaluation technique is proposed to assess the numerical accuracy, including the accuracy associated with a linear step loading type, of the Newmark method by comparing the numerical solution to the exact solution. No errors are found in the steady-state response. Period distortion in the cosine term of the transient response is different from that in the sine term except for the subfamily of γ = 1/2. A new measure of amplitude distortion is defined that incorporates the error in amplitude relative to the exact solution. This measure can reflect amplitude distortion more realistically in a numerical solution when compared to the current measures of numerical dissipation. In general, period and amplitude dist...

Abstract: Three dimensional coupled bending-torsion dynamic vibrations of thin-walled open section beam subjected to moving vehicle are investigated by transfer matrix method. Through adopting the idea of Newmark-? method, the partial differential equations of structural vibration can be transformed to the differential equations. Then, those differential equations are solved by transfer matrix method. An iterative scheme is proposed to deal with the coupled bending-torsion terms in the governing vibration equations. The accuracy of the presented method is verified through two numerical examples. Finally, with different eccentricities of vehicle, the torsional vibration of thin-walled open section beam and vertical and rolling vibration of truck body are investigated. It can be concluded from the numerical results that the torsional vibration of beam and rolling vibration of vehicle increase with the eccentricity of vehicle. Moreover, it can be observed that the torsional vibration of thin-walled open section beam may have a significant nonlinear influence on vertical vibration of truck body.

Abstract: A one-dimensional Klein-Gordon problem, which is a physical model for a quantumparticle submitted to a potential barrier, is studied numerically : using a variationalformulation and a Newmark numerical method, we compute the mean position andstandard deviation of the particle as well as their time evolution.Key words Klein-Gordon equation, Newmark method, mean and standard devia-tion, kernel smoothing, linear regression.AMS 35A15, 65M06, 65M12, 81Q05, 81Q10. 1 Introduction It has been well-known for a few years now that in quantum mechanics a particle canclimb up a step even if it has not enough energy a priori and it will be reflected thenwith a delay. In classical mechanics it would just try and go back to its position.Everything happens here as if the particle could go through a wall (cf. Fig. 5.1 in[17]) ! This phenomenon is called tunnel effect and has been a subject of interestfor physicians and mathematicians : the delay has been measured by the physicistsA. Haibel and G. Nimtz (cf. [16]). It seems that it is approximately equal to thereciprocal of their frequency and that it is independent of the shape of the barrier.The Workshop on Superluminal Velocities gathered some recent contributions inCologne in 1998 to describe transient phenomena concerning the tunnel effect (cf.[20]). In particular J. M. Deutch and F. E. Low were interested in 1993 (see [13])in superluminal effects of low-frequency Gaussian wave packets traversing a rectan-gular potential barrier.T. Hartman calculated in [19] the tunnelling time of Gaussian wave packets for one-dimensional rectangular potential barriers based on the time-dependent Schr¨odingerequation. An analytic expression is given in terms of the wave number. It is easyto adapt his calculations to obtain an expression for the delay of reflection.The main obstacle for a rigorous formulation comes from the fact that T. Hartman

Abstract: A heterogeneous space-time full approximation storage (HFAS) multilevel formulation for molecular dynamics simulations is developed. The method consists of a waveform Newton smoothing that produces initial space-time iterates and a coarse model correction. The formulation is coined as heterogeneous since it permits different interatomic potentials to be applied at different physical scales. This results in a flexible framework for physics coupling. Time integration is performed in windows using the implicit Newmark predictor-corrector method that permits larger time integration steps than the explicit method. The size of the time steps is governed by accuracy rather than by stability considerations of the algorithm. We study three different variants of the method: the Picard iteration, constrained dynamics and force splitting. Numerical examples show that FAS based on force splitting provides significant time savings compared to standard explicit methods and alternative implicit space-time schemes. Parallel studies of the Picard iteration on harmonic problems illustrate the time parallelization effect that leads to a superior parallel performance compared to explicit methods.

Abstract: The near-bed submarine pipeline is a widely used structure in the marine engineering. Due to the presence of the seabed resulting in an asymmetric flow, a large negative lift (attraction) can be induced on a pipeline in a horizontal current, which has significant influence on the behaviours of the pipeline. A coupled numerical approach is proposed in this paper to assess the nonlinear dynamic responses of this pipeline by combining the meshless technique and the boundary element method (BEM). BEM is firstly used to get the nonlinear dynamic fluid loading induced by the asymmetric flow. The meshless technique is used to discretize the structure of the pipeline, and the local weighted weak form using the spline weight function is employed to get the discrete system of equations for this nonlinear dynamic analysis. A numerical example for the static and dynamic analyses of a structure is firstly presented to verify the effectivity of the present method. Then, the coupled technique is used to simulate the nonlinear dynamic fluid-structure interaction problem of a near-bed pipeline. A Newton-Raphson iteration procedure is used herein to solve the nonlinear system of equations, and the Newmark method is adopted for the time integration. Our studies reveal that there exists a critical current velocity, above which the pipeline will become instable sharply. The detailed relationship between the critical velocity and the gap is given, and it has been found that the critical velocity is significantly affected by the initial gap from the pipeline to seabed. It has demonstrated that present approach is very effective to obtain numerical solutions for the nonlinear dynamic fluid-structure interaction analysis of a near-bed submarine pipeline.

Abstract: Using the obtained parameters of field shear velocity test,static and cyclic triaxial tests,the finite element method based analysis approach is presented for the seismic stability of extended municipal solid waste(MSW) landfill,and the seismic stability of extended MSW along internal circular sliding surfaces,along interface between extended and existing MSW as well as along back and base liners is analyzed respectively by the finite element method.During the earthquake,the extended MSW more tends to be failure along the interface between extended and existing MSW if the water level of the leachate in extended MSW is low.For the dynamic stability of the extended MSW along internal circular sliding surfaces,the computed dynamic factor of safety of the conventional total stress method will be larger than the real one due to that is cannot take into account the softening of MSW induced by the increasing dynamic pore water pressure during the earthquake.The permanent diplacements of six landfills with different vertical and horizontal extensions are computed by the Newmark method for two kinds of input accelerograms with different maximal horizontal accelerations.Results show that logarithm of seismic permanent displacement of extended MSW along interface between the existing and extended MSW is roughly linear to the ratio of the yield acceleration and the maximal horizontal acceleration.

Abstract: A sub-cycling algorithm presented by Belytschko and Mullen (Int. J. Numer. Meth. Engng 1978; 12(10):1575–1586) has been successfully applied in the finite element method. However, the problem of how to apply the sub-cycling to flexible multi-body dynamics (FMD) still lacks investigation. This paper presents a Newmark-based sub-cycling, which is suitable for solving condensed FMD models. Common-step update formulae and sub-step update formula for the sub-cycling are established based on the original Newmark integration algorithm. Stability of the procedure is validated by means of energy balance checking during the integral process. Numerical examples indicate that the sub-cycling is able to enhance the computational efficiency without dropping accuracy greatly. Copyright © 2007 John Wiley & Sons, Ltd.

Abstract: On the basis of Newmark-β method and superpasition principle,a new simplified numerical integration format for structural dynamics is deducted.The method is simple and convenient for elastic-plastic seismic response analysis because its calculated displacement is independent of velocity and acceleration.The starting condition and stability of this numerical integration format are discussed.Theoretical analysis and numerical examples showed that accuracy is better and stability is worse if the coefficient β changed from 1/4 to 1/8.