A Convolution Approach for the Transient Analysis of Locally Nonlinear Rotor Systems

The results of a theoretical and experimental investigation regarding the static and dynamic characteristics of shear walls are described. Solutions were obtained for the natural frequencies, mode shapes, and response quantities for an appropriate mathematical model, consisting of a distributed mass shear panel having a concentrated roof load mass at its top. Damping for such a structure may be represented in terms of an experimentally determined equivalent viscous damping ratio, veq. Using numerical analysis techniques, appropriate equations were derived and programmed, and a digital computer used to obtain the desired response quantitites resulting from either harmonic or arbitrary forcing functions. The 1940 El Centro earthquake, N-S component ground accelerations were utilized for most of the latter calculations. Using experimentally obtained static-cyclic load-deflection curves, values of veq were found to average 0.08-0.10 for low design-type loads, a range which was further verified by vibration generator and “snap” test dynamic testing. It was thus deemed satisfactory to recommend constant damping ratios of 0.07-0.08 for response calculations. Numerical accuracy of the computer solutions was investigated, with it being noted the acceleration values provided a good criterion for stability of solutions. Being least accurate because of the numerical procedure used, the accelerations always became unstable at a time prior to that of the displacements, thus giving a simple check as to the time span of correct solutions. Another effective procedure simply involved making two computer runs with the same input data, but different time increments, and then comparing results. If results were basically the same, the larger time increment was adequate; otherwise, another run was made with an even smaller time increment, answers compared, etc., until results essentially agreed.

A large time increment approach for cyclic viscoplasticity

This paper simulates the 2D transient magnetohydrodynamic (MHD) flow in a rectangular duct in terms of the velocity of the fluid and the induced magnetic field by using the radial basis function (RBF) approximation.  The inhomogeneities in the Poisson’s type MHD equations are approximated using the polynomial functions (1+r) and the particular solution is found satisfying both the equations and the boundary conditions (no-slip and insulated walls).  The Euler scheme is used for advancing the solution to steady-state with a time increment and a relaxation parameter which are determined for achieving stable solution.  It is shown that, as Hartmann number increases, the fluid becomes stagnant at the center of the duct, the flow is flattened and boundary layers are developed on the Hartmann and side walls.  These are the well-known characteristics of the MHD duct flow.  The stability analysis is also carried in terms of the spectral radius of the coefficient matrix of the discretized coupled system.  Stable solutions are obtained with RBF by using quite large time increment and suitable relaxation parameters on the expense of explicit Euler time-integration scheme used.

Distinct element method (DEM) requires enormous computation time because it needs small time increments that are sufficient to follow high frequency fluctuations in contact dynamic model. In general, the equations of motion of particles are solved by the second order Adams-Bashforth method, which estimates the contact force for the next time step by linear extrapolation, or by multistep methods such as predictor-corrector method. In order to overcome the deficit of conventional methods, we propose a Contact Force Prediction Method that allows us to use larger time increments. The method incorporates the contact force at every contact point obtained as the exact solutions or numerical solutions of differential equations that describe two particle contacts. It is confirmed that the proposed method gives the simulation results for packing and discharge of particles which are consistent with the experimental data, while accelerating DEM computation by 3 to 8 times.

This contribution focuses on the use of a new method to reduce the computational demands of fatigue damage computations using continuum damage mechanics. The LArge Time INcrement (LATIN) method incorporates a model order reduction approach namely the proper generalised decomposition (PGD). LATIN has been extended to tackle damage problems. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Most of today's numerical computations are performed using floating-point data operations for representing real numbers. The precision of the related data types should be adapted in order to guarantee a desired overall rounding error and to strengthen the performance of programs. This adaptation lies to the precision tuning technique, which consists of finding the least floating-point formats enabling a program to compute some results with an accuracy requirement. Precision tuning is important for several applications from a wide variety of domains including embedded systems, Internet of Things (IoT), etc. In this work, we evaluate the performance of POP, our static analysis tool, in several manners. First, we compare two ways of optimizing programs in POP throughout the definition of different cost functions given to the solver. Second, we measure the runtime errors between the exact results given by an execution in multiple precision and the results of tuned programs by POP and show that the measured error is always less than the accuracy requirements given by the user for several examples. Third, we provide a detailed comparison of POP versus the prior state-of-the-art tool, Precimonious.

Operator splitting ADI schemes for pseudo-time coupled nonlinear solvation simulations

As a direct extension of the asymptotic spatial homogenization method we develop a temporal homogenization scheme for a class of homogeneous solids with an intrinsic time scale significantly longer than a period of prescribed loading. Two rate-dependent material models, the Maxwell viscoelastic model and the power-law viscoplastic model, are studied as an illustrative examples. Double scale asymptotic analysis in time domain is utilized to obtain a sequence of initial-boundary value problems with various orders of temporal scaling parameter. It is shown that various order initial-boundary value problems can be further decomposed into: (i) the global initial-boundary value problem with smooth loading for the entire loading history, and (ii) the local initial-boundary value problem with the remaining (oscillatory) portion of loading for a single load period. Large time increments can be used for integrating the global problem due to smooth loading, whereas the integration of the local initial-boundary value problem requires a significantly smaller time step, but only locally in a single load period. The present temporal homogenization approach has been found to be in good agreement with a closed-form analytical solution for one-dimensional case and with a numerical solution in multidimensional case obtained by using a sufficiently small time step required to resolve the load oscillations.

In this work, the problem of the unsteady natural convection in an -water filled nanofluids influenced by an uniform magnetic field is analysed numerically. Governing equations are given in terms of the streamlines, the vorticity and the temperature of the fluid. Dual Reciprocity Boundary Element Method (DRBEM) is performed as a solution technique. Both the fundamental solutions of Laplace equation and modified Helmholtz equation are used in the derivation of the method. The numerical analysis are done for physical parameters Rayleigh number (), Hartmann number () and particle volume fraction (). From the results, it is observed that the behaviours of all the variables are influenced by the changing values of parameters. The solution procedure of the all variables needs considerably small number of iterations and large time increments with suitable values of relaxation parameters which occur in the argument of Bessel function .

A kinetic two-scale damage model for high-cycle fatigue simulation using multi-temporal Latin framework

A scaled boundary finite element formulation for solving plane-strain viscoelastic problems

A novel constrained LArge Time INcrement method for modelling quasi-brittle failure

A variationally consistent formulation is presented to devise a method of fully implicit analysis for predicting thermo-mechanically coupled behavior of thermosetting resin subjected to cure in finite strain theory. To characterize the finite thermo-viscoelasticity coupled with cure kinetics, the dual dissipation potential (DDP) is originally defined in the thermodynamically consistent formulation, which begins with the definition of stored energy. The governing equations are derived as stationary conditions of the relevant total energy rate potential containing internal energy, and viscous and curing DDPs, and then discretized in time and space in order. In the temporal discretization process within a time interval, we utilize the function form of the equilibrium temperature obtained from the Legendre–Fenchel transformation of internal energy. The obtained time discretized equations are spatially discretized by means of the standard finite element method. The present formulation results in a fully implicit algorithm with separate systems of governing equations that can be solved in a monolithic manner. Two representative numerical examples are presented to demonstrate that, while allowing relatively large time increments, the devised analysis method provides a more realistic prediction than the previous method formulated within the framework of small strain theory.

Two different approaches for simulation of contact mechanics problems are investigated. First, the equivalence of the Large Time INcrement (LATIN) method for unilateral contact problems, in terms of an augmented Lagrangian approach dedicated to nonsmooth problems, is proved (with the non trivial introduction of two constraints: an equality constraint and an inequality-type constraint). Second, the Finite Element Tearing and Interconnecting method for Contact (FETI-C) is interpreted as a projected gradient with projection, acting on the dual problem. An extension to frictional contact is presented in the context of granular media.

Mathematical models are coming into increasing use as a means of investigating unsteady river and channel flow. Their potential scope is briefly described. The Saint-Venant equations for gradually varying unsteady flow constitue a hyperbolic quasi-linear system. They can be integrated by two basic numerical methods : explicit methods requiring a stability condition, and implicit methods which may be unconditionally stable. The choice of which method to use is very often given by the type of problem, for whereas the increment along the abscissa depends on river or channel bed geometry and water level definition accuracy, the time increment, on the other hand, must account for significant variations. In the case of a flood (a 'slow' phenomenon) the implicit method is the obvious one as it can cope with a comparatively large time increment. Very rapidly developing phenomena, on the other hand, require a short time increment, which satisfies the stability condition of explicit methods. Each problem is represented by a hydraulic scheme allowing for the various ramifications and featuring all the weirs, flow inputs, cross-sectional changes, diversions and other special points in the system. One or two conditions (hydrograph or level chart) will be given upstream from each branch, and a stage/discharge relationship or a level record downstream from the model, also an operating relationship for each singular point. The initial conditions also require defining. They can be calculated for steady flow, but if the phenomenon is already developing at the point at which the calculation starts, they have to be assumed ; they are usually of little importance, however, as their effects are no longer felt after a certain time. Reference is made to examples of a few applications to illustrate the potential usefulness of mathematical models in this field. Examples of flood-routing studies mentioned are a study of the Rhine at Karlsruhe and one of the Rhone above Lyons. The Rhine's hydraulic scheme features a number of hydro-power plants and that of the Rhone several weirs (Fig. 1 to 8). Under the heading of hydro-power development an example of a surge wave study arises in the problem of 'by the lockful' operation (Fig. 9 to 17). In this particular case, the implicit method could be used to reduce the computing time requirements, but it should be noted that the explicit one is preferable for cases involving more rapid operation. A scheme with power governed by water level is mentioned as a further example. It features a reservoir, a canal, a pressure tunnel with two surge tanks and a penstock. Turbine discharge is governed by reservoir level (Fig. 18.) Downstream and upstream boundary conditions remain permanently interdependent in this example. Mathematical models have also been used to study tidal propagation. Figures 19, 20 and 21 show the close agreement reached between observed and calculated data in a study of the Seine and the formation of a tidal bore which, if considered as a weak shock wave, can be dealt with by the explicit method. In a tidal propagation problem in a small river the downstream condition represents a floodgate system keeping the sea out at rising tide and opening at the ebb tide (Fig. 23). In a study of a cooling system for a thermal power station using water from the Loire and discharging it back to a shallow river arm the mathematical model features control sections at the ends of the river arm when the latter are high and dry at low water (Fig. 22). The various examples are merely mentioned as an illustration of the potential scope of mathematical models ; a brief discussion on numerical integration methods is given in an Appendix.