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Copyright of Engineering Mechanics / Gongcheng Lixue is the property of Engineering Mechanics Editorial Department and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The purpose of this paper is the evaluation of the Fourier transform of powers of the sinc function multiplied by monomials, also in the cases when log terms arise. Such evaluations appear only rarely in the literature. Some old sources are hardly available. Because of notations not in use today, several original works are difficult to read. We apply an approach by J. H. Michell in a variant of G. H. Hardy to integrals over sinc powers and their Fourier transforms. Moreover, the connection of such integrals with B‑splines is accentuated. [ABSTRACT FROM AUTHOR]

Abstract In this work, a method is put forward to obtain the dynamic solution efficiently and accurately for a large-scale train–track–substructure (TTS) system. It is called implicit-explicit integration and multi-time-step solution method (abbreviated as mI-nE-MTS method). The TTS system is divided into train–track subsystem and substructure subsystem. Considering that the root cause of low efficiency of obtaining TTS solution lies in solving the algebraic equation of the substructures, the high-efficient Zhai method, an explicit integration scheme, can be introduced to avoid matrix inversion process. The train–track system is solved by implicitly Park method. Moreover, it is known that the requirement of time step size differs for different sub-systems, integration methods and structural frequency response characteristics. A multi-time-step solution is proposed, in which time step size for the train–track subsystem and the substructure subsystem can be arbitrarily chosen once satisfying stability and precision demand, namely the time spent for m implicit integral steps is equal to n explicit integral steps, i.e., mI = nE as mentioned above. The numerical examples show the accuracy, efficiency, and engineering practicality of the proposed method.

This paper focuses mainly on developing single-step explicit integration algorithms considering the implicit treatment of velocity. A novel explicit algorithm (GSSI) is proposed and recommended as a self-starting dissipative alternative to the central difference methods in transient analysis. GSSI not only shares the same advantages as the central difference methods, such as second-order accuracy and computational cost, but also achieves flexible dissipation control and self-starting property. Remarkably, GSSI provides a significantly larger stability bound than the central difference methods in the damped case. GSSI imposes two algorithmic parameters ( ρ s and ρ b ) to flexibly adjust numerical dissipation at the bifurcation point. In general, the ρ b controls numerical dissipation at the bifurcation point, while the ρ s further adjusts the amount of dissipation in the low-frequency range. Spectral analysis and numerical examples are given solved to show the superiority of GSSI over the existing single-step explicit methods with respect to accuracy, stability, and dissipation control. [ABSTRACT FROM AUTHOR]

In this article, we present a novel explicit time‐integration algorithm for the coupled hydromechanical soil mechanics problems in a pseudo‐static regime. After introducing the finite element discretization, the semidiscrete ordinary system of equations is integrated explicitly in time with the Runge–Kutta method. It is noted that this formulation is conditionally stable in time. By introducing a stabilization technique, the Polynomial Pressure Projection, and selecting appropriately the stabilization parameter, the formulation becomes unconditionally stable. To illustrate the performance of the method several numerical analysis are reported, considering both elastic and elasto‐plastic soil behavior. [ABSTRACT FROM AUTHOR]

Step-function excitations are convenient abstractions for circuit turn on/off and for switching activities in general. However, they are ill-handled by SPICE-derived circuit simulators that employ implicit integration approximations and substitute steep ramps for steps. An ACES-derived explicit integration method efficiently handles step-functions, manages potential instability, and converges to the steady state. The resulting circuit simulator can be employed to find an initial state size and excursion-limited accuracy control. It also is able to accommodate resistance, capacitance, inductance, and nonlinear elements efficiently and accurately. [ABSTRACT FROM AUTHOR]

To reduce the computational time in the fields of dynamics, we introduce herein an efficient asynchronous step integration algorithm for a coupled finite-element–discrete-element method (FEM–DEM). Domain decomposition divides the whole model into an FEM subdomain and a DEM subdomain, where each subdomain selects the appropriate time step based on the element characteristics. The method of overlapping nodes and particles at the boundaries is adopted to handle the interface coupling problem, and the subcycling method is adopted to tackle the problem of transmission and matching of boundary data. Two numerical examples are presented to demonstrate the precision of the analysis and the overall efficiency. The algorithm provides the requisite calculation accuracy and significantly shortens the computer simulation. This approach further improves the efficiency of hybrid FEM–DEM modeling. [ABSTRACT FROM AUTHOR]

This paper focuses mainly on the development of composite sub-step explicit algorithms for solving nonlinear dynamic problems. The proposed explicit algorithms are required to achieve the truly self-starting property, so avoiding computing the initial acceleration vector, and the controllable numerical dissipation at the bifurcation point, so eliminating spurious high-frequency components. With these two requirements, the single and two sub-step explicit algorithms with truly self-starting property and dissipation control are developed and analyzed. The present single sub-step algorithm shares the same spectral accuracy as the known Tchamwa–Wielgosz scheme, but the former possesses some advantages for solving wave propagation problems. The present two sub-step algorithm provides a larger stability limit, twice than those of single step schemes, due to explicit solutions of linear systems twice within each time increment. Numerical examples are also simulated to show numerical performance and superiority of two novel explicit methods over other explicit schemes. [ABSTRACT FROM AUTHOR]

The finite element analysis of complex structure often requires a refine mesh in some local domain. To reduce the computation time, an explicit asynchronous step parallel computing method is proposed. The domain decomposition with overlapping node method is used to divide the model into different subdomains. The multiple overlapping nodes between different subdomains constitute the coupling region. Each subdomain selects the time step based on the mesh characteristics. The subcycling method is adopted to tackle the matching of asynchronous step boundary. The subdomain model, boundary information and calculation results are stored in parallel files which mean the overall finite element analysis process is implemented in parallel. The validity and efficiency of the proposed method are verified through three simulation cases which conducted on Tianhe 2 multi-core supercomputers. The results of simulation cases show that the proposed method has a higher accuracy than classic subcycling method under the same time step. The total speedup of the algorithm relates to the step ratios between subdomains, the number of subdomain and the load balance. This approach offers an efficient way to solve large-scale and super-scale structural dynamics analysis with local refine mesh. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this paper is to suggest a robust hybrid method for updating the stress and plastic internal variables in plasticity considering damage mechanics. Design/methodology/approach: By benefiting the properties of the well-known explicit and implicit integrations, a new mixed method is derived. In fact, the advantages of the mentioned techniques are used to achieve an efficient integration. Findings: The numerical studies demonstrate the high precision and robustness of the suggested algorithm. Research limitations: The perfect von-Mises plasticity together with Lemaitre damage model is considered within the realm of small deformations. Practical implications: Updating stress and plastic internal variables are of utmost importance in elastoplastic analyses of structures. The accuracy and efficiency of stress-updating methods significantly affect the final outcomes of nonlinear analyses. Originality/value: The idea which is used to derive the hybrid method leads to an efficient integration method for updating the constitutive equations of the damage mechanics. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Vibration Engineering is the property of Nanjing University of Aeronautics & Astronautics and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

We describe a novel algorithm for the robust approximation of elastic, inelastic, and frictional contact problems in explicit computations. The method is based on a master-slave concept and a predictor/corrector split of the dynamic update. In the predictor step, the bodies move ignoring all contact interactions; in the correction, the nodes that have penetrated a body are pushed back while correcting their velocities to preserve linear momentum and balance the kinetic energy. In contrast with existing predictor/corrector contact algorithms, no iterations nor global computations are required in the correction step. Moreover, thanks to the geometrical basis of the method, the choice of an artificial penalty parameter is avoided. The contact algorithm does not require the computation of the normal vectors at the contacting surfaces, making it especially useful for simulations that employ finite element and certain meshfree discretizations, and for the simulation of contact among bodies with non-smooth boundaries. [ABSTRACT FROM AUTHOR]

In the conventional Newmark family for time integration of hyperbolic problems, both explicit and implicit methods are inherently sequential in the time domain and not well suited for parallel implementations due to unavoidable processor communication at every time step. In this work we propose a Waveform Relaxation Newmark (WRN β ) algorithm for the solution of linear second-order hyperbolic systems of ODEs in time, which retains the unconditional stability of the implicit Newmark scheme with the advantage of the lower computational cost of explicit time integration schemes. This method is unstructured in the time domain and is well suited for parallel implementation. We consider a Jacobi and Gauss–Seidel type splitting and study their convergence and stability. The performance of the WRN β algorithm is compared to a standard implicit Newmark method and the obtained results confirm the effectiveness of the Waveform Relaxation Newmark algorithm as a new class of more efficient time integrators, which is applicable, as shown in the numerical examples, to both the finite element method and meshfree methods (e.g. the reproducing kernel particle method). [ABSTRACT FROM AUTHOR]

The dynamic interaction between the vehicle, rail, and bridges presents a huge computational challenge, especially for reliability analysis based on Monte Carlo simulations. In this study, an integrated algorithm is proposed for the vehicle- rail-bridge dynamic interaction problem. This algorithm divides the system into two subdomains, i.e. the vehicle-rail subdomain and the bridge subdomain. The vehicle-rail subdomain and the bridge subdomain are integrated by the Zhai algorithm and the Newmark-b algorithm, respectively. The integrated algorithm allows different time steps (or multitime steps) to be used for the two domains: a large time step for the bridge subdomain and a smaller one for the vehicle-rail subdomain. The stability region of the proposed algorithm was found through the two-degree-of-freedom model problem, when a single time step is used in both subdomains. The accuracy of the algorithm was numerically investigated through the two-degree-of-freedom model. The vehicle-rail-bridge vibration excited by rail irregularities and earthquakes was simulated using the multitime step algorithm. The effect of the time step ratio (ratio of the large time step to the small time step) on the accuracy of the vehicle-rail-bridge responses was investigated. It has been shown that the time step ratio of less than 50 produces vehicle-rail-bridge responses in an accurate manner for engineering purposes. The multitime step algorithm can solve the vehicle-rail-bridge problem 20 times faster than the single time step algorithms that are conventionally used in the vehicle-rail-bridge simulations. This multitime step algorithm provides an efficient alternative for solving the dynamic interaction between vehicle-rail and large-scale civil structures. [ABSTRACT FROM AUTHOR]

An effective form-finding method for form-fixed spatial network structures is presented in this paper. The adaptive form-finding method is introduced along with the example of designing an ellipsoidal network dome with bar length variations being as small as possible. A typical spherical geodesic network is selected as an initial state, having bar lengths in a limit group number. Next, this network is transformed into the ellipsoidal shape as desired by applying compressions on bars according to the bar length variations caused by transformation. Afterwards, the dynamic relaxation method is employed to explicitly integrate the node positions by applying residual forces. During the form-finding process, the boundary condition of constraining nodes on the ellipsoid surface is innovatively considered as reactions on the normal direction of the surface at node positions, which are balanced with the components of the nodal forces in a reverse direction induced by compressions on bars. The node positions are also corrected according to the fixed-form condition in each explicit iteration step. In the serial results of time history, the optimal solution is found from a time history of states by properly choosing convergence criteria, and the presented form-finding procedure is proved to be applicable for form-fixed problems. [ABSTRACT FROM AUTHOR]

Physics-based deformation simulation demands much time in integration process for solving motion equations. To ameliorate, in this paper we resort to structural mechanics and mathematical analysis to develop a novel unconditionally stable explicit integration method for both linear and nonlinear FEM. First we advocate an explicit integration formula with three adjustable parameters. Then we analyze the spectral radius of both linear and nonlinear dynamic transfer function’s amplification matrix to obtain limitations for these three parameters to meet unconditional stability conditions. Finally, we theoretically analyze the accuracy property of the proposed method so as to optimize the computational errors. The experimental results indicate that our method is unconditionally stable for both linear and nonlinear systems and its accuracy property is superior to both common and recent explicit and implicit methods. In addition, the proposed method can efficiently solve the problem of huge computation cost in integration procedure for FEM. [ABSTRACT FROM AUTHOR]

• We propose a new effective explicit time integration scheme. • Direct integration is used for transient response predictions. • The method is specifically developed for the solution of wave propagations. • We mathematically analyze the scheme and illustrate the solution effectiveness. In this paper we introduce the explicit β 1 / β 2 -Bathe method for solving dynamic problems, in particular wave propagations. Like for the implicit β 1 / β 2 -Bathe method, the proposed explicit scheme uses two sub-steps per time step and can be used directly as a first-order and a second-order method with the capability to suppress high spurious frequency response. In both sub-steps, standard Taylor series are employed resulting in an explicit solution scheme. The novelty is that we calculate the final displacements and velocities in each sub-step by applying correction terms using the generalized trapezoidal rule with control parameters β 1 and β 2. This approach makes the method a quite simple scheme. We consider the stability, accuracy and numerical dispersion and give recommendations on the parameter values β 1 and β 2 to be used in practice. We give the solutions of four problems, three of which are wave propagation problems, and compare the results with those obtained using other methods. While more experience in the use of the procedure is needed to understand its full solution capabilities, we can already conclude that the proposed method is effective in some wave propagation analyses. [ABSTRACT FROM AUTHOR]

As to the strength test of seatbelts anchorages which is a quasi-static problem,through comparative analysis of central difference method（ explicit integration） and Newmark method（ implicit integration） in elastodynamics,this paper used explicit solution method in LS-DYNA to compute the seatbelts FE model of domestic minibuses exported to Australia. Lots of studies were carried out herein on two key parameters: calculation time and load curve,and certain evaluation indexes were selected,to gradually improve simulation results consistency with the real test. The methed can be extended to other quasi-static strength analysis problems and gives some useful conclusions on improving simulation accuracy.

An adaptive substepping explicit integration scheme is developed for a porosity-dependent hydro-mechanical model for unsaturated soils. The model is referred to as the modified σ-Θ model in this paper, which features the employment of the subloading surface plasticity and the stress-saturation approach. On numerical aspects, convex/nonconvex subloading surfaces in the σ-Θ space may result in incorrect loading-unloading decisions during the integration. A new loading-unloading decision method is developed here to solve the problem and then embedded into the explicit integration scheme for the modified σ-Θ model. In addition, to enhance the accuracy of the explicit integration, local errors from both hydraulic and mechanical components are included in the error control for each substep. A drift correction method is also developed to ensure the state point lies on the subloading surface in the σ-Θ space within a set error level. The performance of the loading-unloading decision method for the modified σ-Θ model is discussed through comparing it with the conventional loading-unloading decision method. The importance of involving the hydraulic component in the error control is also demonstrated. The accuracy and efficiency of the proposed adaptive substepping explicit integration scheme for the modified p-Θ model are also studied via several numerical examples. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Higher-order elements frequently render accurate results and allow the reduction of the total number of elements required to represent a given structure. However, element order also affects the efficient time-history integration of the associated equations of motion in Lagrangian dynamics by an explicit method, which is only conditionally stable. The integration time step is affected by element type and must be sufficiently small to avoid instability of the computed solution and, simultaneously, should be sufficiently large for an economic analysis. The upper bound to the size of this step in an analysis is rigorously obtained from the solution of the eigenvalue problem to the global system of equations of the entire finite-element model. Common alternatives to this computation are to approximate the time step by much simpler one-dimensional node-to-node or individual elemental eigenvalue approaches. Robust higher-order finite-element formulations have recently been developed for explicit integration, but time-step determinations have been primarily limited to the one-dimensional approach. In this paper, the individual elemental eigenvalue approach is further used to study the critical time step for several practical higher-order element types (27-node bricks, 16-node thin plates, 15-node tetrahedra, and 21-node wedges). Parametric studies on the variables controlling their critical time steps are discussed. [ABSTRACT FROM AUTHOR]

Copyright of China Sciencepaper is the property of China Sciencepaper and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The increasing number of applications incorporating shape-memory alloy (SMA) components motivates the development of three-dimensional constitutive models to enhance their analysis and design. These models only reach their full utility if they are then implemented into numerical (e.g. often finite-element-based) frameworks. The present article addresses a topic rarely considered in the myriad of SMA computational analysis works in the literature: the analysis of the time and accuracy of implementation options. In particular, this work proposes to compare the performance of the implicit and explicit integration methods for two common three-dimensional phenomenological constitutive models: (i) the model by Lagoudas et al.; and (ii) the model by Auricchio et al. available in all installations of Abaqus. In doing so, the present work develops and implements an explicit algorithm for the model by Lagoudas et al. for the first time. The investigated models are compared in a chosen benchmark boundary value problem analysis considering both thermally induced actuation and isothermal stress-induced transformation of an SMA beam. The performance of the methods in terms of analysis time and parallelization efficiency are also investigated. [ABSTRACT FROM AUTHOR]

Despite numerous computational advances over the last few decades, molecular dynamics still favors explicit (and thus easily-parallelizable) time integrators for large scale numerical simulation. As a consequence, computational efficiency in solving its typically stiff oscillatory equations of motion is hampered by stringent stability requirements on the time step size. In this paper, we present a semi-analytical integration scheme that offers a total speedup of a factor 30 compared to the Verlet method on typical MD simulation by allowing over three orders of magnitude larger step sizes. By efficiently approximating the exact integration of the strong (harmonic) forces of covalent bonds through matrix functions, far improved stability with respect to time step size is achieved without sacrificing the explicit, symplectic, time-reversible, or fine-grained parallelizable nature of the integration scheme. We demonstrate the efficiency and scalability of our integrator on simulations ranging from DNA strand unbinding and protein folding to nanotube resonators. [ABSTRACT FROM AUTHOR]

This paper presents the adaptation of a semi-implicit time integration scheme that has been reported in the literature and its implementation for use in discrete element methods (DEM). The computational efficiency of DEM methods is primarily associated with the selection of time increment sizes, as dictated by stability requirements, and other factors that depend on the particulars of the DEM implementation and the problems solved. The proposed time integration scheme and the associated DEM are developed for problems pertaining to rigid-particle interaction and interaction of elastic bodies that are modeled as a cluster of rigid interconnected particles. Verification studies that consider nonlinear problems demonstrate that the proposed algorithm is unconditionally stable and accurate even for large time step sizes and when applicable does not require any inversions of the system matrices. Assessment studies on the accuracy, stability, and computational efficiency of the method have been conducted and discussed. The implementation of the proposed method is discussed and demonstrated through a showcase problem. [ABSTRACT FROM AUTHOR]

An adaptive substepping explicit integration scheme with a novel loading-unloading decision method is developed here for the non-isothermal unified hardening (UH) model. The non-isothermal UH model includes a convex subloading surface in the $$p$$ - $$q$$ plane and a nonconvex subloading surface in the $$p$$ - $$T$$ plane. Because of the convex/nonconvex subloading surfaces, the conventional loading-unloading decision method used in stress integration schemes may lead to incorrect elasticity/elastoplasticity judgements. In addition, the conventional loading-unloading decision method is unable to determine the division point that separates the elastic segment from the elastoplastic segment. A simple but robust method, the double cosine (DC) method, is proposed in this paper to solve loading-unloading decision problems. The proposed DC method is then embedded into an adaptive substepping explicit integration scheme to implement the non-isothermal UH model. The accuracy and efficiency of the DC method are discussed by comparing the method with the conventional loading-unloading decision method (the CV method) and the root-finding loading-unloading decision method (the RF method). The performance of the proposed scheme with the DC method is also discussed. [ABSTRACT FROM AUTHOR]

A finite element model of an aircraft seat subjected to static certification loads (Certification Specifications CS25.561) involves material, geometric and contact non-linearities. Implicit algorithms can model the physics of such problems appropriately but suffer from shortcomings such as significant finite element modelling efforts, high disk space and memory requirements and unconverged solutions. Explicit finite element schemes offer a more robust alternative for convergence for quasi-static loadcases but may come at an even higher computational cost as smaller solution time steps are required, in addition to unwanted inertial effects. A methodology to apply an explicit formulation for simulating static certification loading for an aircraft seat-structure is presented and validated in this article. The first part reviews the design novelties of the triple seat-structure considered, the safety regulations used in aircraft seat certification. The key theoretical aspects of an explicit solver are presented, together with the numerical challenges faced when applied to solving quasi-static problems. Time scaling, mass scaling and damping are common approaches to assist in artificially reducing the computational time but previous articles provide little insight into how to apply these techniques correctly and the level of checking that is required to ensure the quality of the results are unaffected by these modifications. The main focus of this article is to clearly define the procedure to establish appropriate factors for mass scaling, time scaling and damping. Quality checks, such as ratio of kinetic energy to internal energy and their time-histories have been investigated to ensure a quasi-static solution. finite element analysis results are validated against experimental testing for the 8.6 g downward loadcase. Parameters such as kinematic behaviour and deflections at key locations been used for comparison. An acceptable level of correlation between finite element analysis results and physical tests validates the proposed methodology, which will be extended in a future article (Part II) to consider additional contact complexities with the inclusion of body blocks. [ABSTRACT FROM AUTHOR]

Loading an aerospace and automotive seat statically through lap or body blocks is a complex and highly non-linear problem, as the key numerical challenge is to replicate the contact and slipping kinematics between seat, lap block and belt. In addition, severe element distortions and unexpected contact between parts can occur due to the large deformations involved, which result in implicit solvers struggling to find a converged solution. This paper focuses on the use of an explicit Finite Element Analysis (FEA) solver (LS-DYNA3D) for an aircraft seat subject to Certification Specifications CS25.561, although the ideas presented are equally applicable to automotive seat designers. Explicit codes are better able to overcome contact convergence issues and are often used with appropriate damping to achieve a quasi-static solution. This paper reviews the methodology presented in Part I, whereby issues relating to damping, mass and time scaling are outlined in order to overcome the high computational time step costs (Courant-Friedrichs-Lewy (CFL) condition), together with the procedural and error checks required to ensure a quasi-static response. This paper extends the methodology by considering load cases that use lap blocks, such as ‘forward 9g’ and ‘upward 3g’ certification requirements. Alternative modelling approaches to represent the loading mechanism and effect of lap block mass on solution accuracy are discussed. This paper concludes with a verification framework that outlines the quality checks on various model energies and their ratios, where the numerical results are validated against test in terms of displacements and seat kinematics. Thus, ‘Part I’ and ‘Part II’ cover all elements related with the application of an explicit dynamic integration scheme to demonstrate static seat compliance, and together, form a clear framework to assist a Computer Aided Engineering (CAE) analyst involved in applying an explicit integration scheme to solve non-linear quasi-static analyses. [ABSTRACT FROM PUBLISHER]

Abstract: Constitutive models of unsaturated soils, and in particular those based on constitutive variables which include both degree of saturation and suction, are characterised by strong non linearities due to hydromechanical coupling. In this paper, a refined Runge–Kutta–Dormand–Prince explicit algorithm and a fully implicit Euler scheme are compared for the integration of the latter class of models. The explicit and implicit procedures have been tested along different hydromechanical paths, involving various hydraulic and mechanical external control conditions. Accuracy and efficiency of the algorithms have been investigated. The results confirm that substepping is mandatory for the explicit algorithm to converge regardless the initial step size and to remain sufficiently accurate. The value of the incremental hydromechanical work per unit volume was calculated during the explicit integration procedure. The numerical results show that the maximum size of the substep which can be adopted to meet a given tolerance depends on the gradient of the incremental work per unit volume. Therefore, the latter appears a good candidate to identify problematic integration steps in terms of convergence. Accuracy of the implicit algorithm also depends on the chosen step size, although the algorithm proved to be convergent in all the paths analysed. [Copyright &y& Elsevier]

Abstract: Two integration algorithms, namely the implicit return mapping and explicit sub-stepping schemes, are adopted in the anisotropic bounding surface plasticity model for cyclic behaviours of saturated clay and are implemented into finite element code. The model is a representative of a series of bounding surface models that have typical characteristics, including isotropic and kinematic hardening rules and a rotational bounding surface to capture complex but important cyclic behaviours of soils, such as cyclic shakedown and degradation. However, there is no explicit current yield surface in the model to which the conventional implicit algorithm returns the stress state back or the sub-stepping integration corrects the drift of the stress state. Hence, necessary modifications have been made for both of the integration schemes. First, the image stress point is mapped or corrected to the bounding surface instead of mapping back or correcting the stress state to the yield surface. Second, the unloading–loading criterion is checked to determine the image stress point rather than checking the yield criterion after giving the trial stress state in a conventional way. Comparative studies on the accuracy, stability and efficiency of the two integration schemes are conducted not only at the element level but also in solving boundary value problems of monotonic and cyclic bearing behaviours of rigid footings on saturated clay. For smaller strain increments, there is no significant difference in the accuracy between the two integration schemes, but the explicit integration shows a higher efficiency and accuracy. For relatively larger increments, the implicit return mapping algorithm presents good accuracy and more robustness, while the sub-stepping algorithm shows deteriorating accuracy and suffers the convergence problem. With the tolerance used in the present model, the bearing capacity of the rigid footing predicted by the return mapping algorithm is closer to the available analytical and numerical solutions, while the bearing capacity predicted by the sub-stepping algorithm shows a marginal increase. [Copyright &y& Elsevier]

SUMMARY An efficient finite-discrete element method applicable for the analysis of quasi-static nonlinear soil-structure interaction problems involving large deformations in three-dimensional space was presented in this paper. The present method differs from previous approaches in that the use of very fine mesh and small time steps was not needed to stabilize the calculation. The domain involving the large displacement was modeled using discrete elements, whereas the rest of the domain was modeled using finite elements. Forces acting on the discrete and finite elements were related by introducing interface elements at the boundary of the two domains. To improve the stability of the developed method, we used explicit time integration with different damping schemes applied to each domain to relax the system and to reach stability condition. With appropriate damping schemes, a relatively coarse finite element mesh can be used, resulting in significant savings in the computation time. The proposed algorithm was validated using three different benchmark problems, and the numerical results were compared with existing analytical and numerical solutions. The algorithm performance in solving practical soil-structure interaction problems was also investigated by simulating a large-scale soft ground tunneling problem involving soil loss near an existing lining. Copyright © 2011 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

We discuss explicit integration and bifurcation analysis of two non-holonomic problems. One of them is the Chaplygin's problem on no-slip rolling of a balanced dynamically non-symmetric ball on a horizontal plane. The other, first posed by Yu. N. Fedorov, deals with the motion of a rigid body in a spherical support. For Chaplygin's problem we consider in detail the transformation that Chaplygin used to integrate the equations when the constant of areas is zero. We revisit Chaplygin's approach to clarify the geometry of this very important transformation, because in the original paper the transformation looks a cumbersome collection of highly non-transparent analytic manipulations. Understanding its geometry seriously facilitate the extension of the transformation to the case of a rigid body in a spherical support - the problem where almost no progress has been made since Yu.N. Fedorov posed it in 1988. In this paper we show that extending the transformation to the case of a spherical support allows us to integrate the equations of motion explicitly in terms of quadratures, detect mostly remarkable critical trajectories and study their stability, and perform an exhaustive qualitative analysis of motion. Some of the results may find their application in various technical devices and robot design. We also show that adding a gyrostat with constant angular momentum to the spherical-support system does not affect its integrability. [ABSTRACT FROM AUTHOR]

Abstract: This paper details the numerical implementation of a constitutive model for unidirectional (UD) polymer-matrix fibre-reinforced composites, which is able to accurately represent the full non-linear mechanical response. Features such as hydrostatic pressure sensitivity, the effect of multiaxial loading and the dependence of the yield stress on the applied pressure are often neglected in constitutive modelling, but are included in this model. The constitutive model includes a novel yield function, non-associative flow rule and a non-linear kinematic hardening rule. It is combined with suitable failure criteria and associated damage model. The complete model is implemented in an explicit finite element code. Experimental test data is used to show that the model is able to predict the non-linear response of both unidirectional and multidirectional composite laminates. The model is shown to accurately predict the constitutive response under complex multiaxial loading and unloading, including significant hydrostatic pressure. Predictions are also shown to compare favourably for the evolution of matrix cracking after initial matrix cracking is detected by the failure criteria. [Copyright &y& Elsevier]

Abstract: In this paper a robust static-dynamic procedure has been developed. The development extends the capability of the Vulcan software to model the dynamic and static behaviour of steel buildings during both local and global progressive collapse of the structures under fire conditions. The explicit integration method was adopted in the dynamic procedure. This model can be utilized to allow a structural analysis to continue beyond the temporary instabilities which would cause singularities in the full static analyses. The automatic switch between static and dynamic analysis makes the Vulcan a powerful tool to investigate the mechanism of the progressive collapse of the structures generated by the local failure of components. The procedure was validated against several practical cases. Some preliminary studies of the collapse mechanism of steel frame due to columns’ failure under fire conditions are also presented. It is concluded that for un-braced frame the lower loading ratio and bigger beam section can give higher failure temperature in which the global structural collapse happens. However, the localised collapse of the frame with the higher loading ratio and smaller beam section can more easily be generated. The bracing system is helpful to prevent the frame from progressive collapse. The higher lateral stiffness of the frame can generate the smaller vertical deformation of the failed column at the re-stable position. However, the global failure temperature of the frame is not sensitive to the lateral stiffness of the frame. [Copyright &y& Elsevier]

Abstract: Numerical analyses of bird impact damage in complex aircraft structures have been performed using ABAQUS/Explicit. A Lagrangian formulation was used for the bird model in combination with various material models. Several failure and damage modes have been considered for different material models used in the inboard flap of a typical large transport aircraft. A submodeling approach has been used to reduce computational time. Parametric analyses have been performed using different bird sizes, impact locations and velocity vectors. [Copyright &y& Elsevier]

Abstract: The aim of this paper is to comprehensively analyse the performance of a new ring-type brake energy dissipator through the finite element method (FEM) (formulation and finite element approximation of contact in nonlinear mechanics) and experimental comparison. This new structural device is used as a system component in rockfall barriers and fences and it is composed of steel bearing ropes, bent pipes and aluminium compression sleeves. The bearing ropes are guided through pipes bent into double-loops and held by compression sleeves. These elements work as brake rings. In important events the brake rings contract and so dissipate residual energy out of the ring net, without damaging the ropes. The rope’s breaking load is not diminished by activation of the brake. The full understanding of this problem implies the simultaneous study of three nonlinearities: material nonlinearity (plastic behaviour) and failure criteria, large displacements (geometric nonlinearity) and friction-contact phenomena among brake ring components. The explicit dynamic analysis procedure is carried out by means of the implementation of an explicit integration rule together with the use of diagonal element mass matrices. The equations of motion for the brake ring are integrated using the explicit central difference integration rule. The presence of the contact phenomenon implies the existence of inequality constraints. The conditions for normal contact are and , where is the normal traction component and g is the gap function for the contact surface pair. To include frictional conditions, let us assume that Coulomb’s law of friction holds pointwise on the different contact surfaces, being the dynamic coefficient of friction. Next, we define the non-dimensional variable by means of the expression , where is the frictional resistance and t is the tangential traction component. In order to find the best brake performance, different dynamic friction coefficients corresponding to the pressures of the compression sleeves have been adopted and simulated numerically by FEM and then we have compared them with the results from full-scale experimental tests. Finally, the most important conclusions of this study are given. [Copyright &y& Elsevier]

No literature has reported an explicit integration algorithm to achieve controllable numerical dissipation and identical third-order accuracy simultaneously. This paper develops two novel explicit integration algorithms to achieve this goal well without increasing computational complexity. In detail, two novel methods are identical third-order accuracy, so avoiding the order reduction for solving damped and forced vibrations, and both of them provide a full range of dissipation control via adjusting their unique algorithmic parameter. Apart from these two highlights, two novel methods embed another two enjoyably advantages. One is to present a significantly larger stability limit than the published third-order explicit schemes. Two novel methods provide the maximum stability limit, reaching 2 3 in the non-dissipative case, getting close to four. The other is to maintain a relatively little computational cost. Two novel methods require explicit solutions only twice within each time step. Therefore, two novel methods are significantly superior to other composite sub-step explicit schemes with respect to the accuracy, stability, dissipation control, and computational cost. Numerical examples are also performed to confirm the numerical performance and superiority of two novel explicit methods. • Two novel fully explicit methods are proposed based on the composite two-sub-step technique. • Two novel methods are identically third-order accurate for solving general structures. • Two novel methods can control numerical dissipation imposed at the bifurcation point. • Two novel methods provide a larger stability limit and require a relatively little computational cost. [ABSTRACT FROM AUTHOR]

Abstract: An explicit numerical implementation is described, for a constitutive model of glassy polymers, previously proposed and validated. Then it is exploited within a Finite Element continuum model, to simulate spontaneous strain localization (necking) occurring during extension of a prismatic bar of a typical glassy polymer. Material parameters for atactic polystyrene are employed. The material model is physically based and highly non-linearly viscoelastic. Three of its principal features are critical in simulations of strain localization: rate-dependence of plastic flow stress; strain-induced structural rejuvenation, represented by increase of Tool’s fictive temperature and leading to pronounced post-yield strain softening; and molecular alignment during extension, giving rise to strain-hardening. In all simulations there is a peak in nominal stress, satisfying the condition for localization to occur. Nevertheless, the simulations show that the process of strain localization varies considerably, depending on details of the extension sequence and on assumed values for certain material parameters. A characteristic feature observed is that strain localization in such a material occurs in two stages. There is an initial spurt associated with strain-softening, followed by a slower growth of localization that eventually subsides, ultimately giving way to uniform extension of the neck. But the details of evolution of the strain distribution vary greatly. The rapidity and severity of localization are increased by decreased temperature, increased strain-rate or greater structural rejuvenation. A simple one-dimensional stability analysis is successful in explaining the results. [Copyright &y& Elsevier]