Explicit Integration Algorithm Research Articles

Two Stage Singular Perturbation Model Reduction for Gas Transmission Networks

The instationary gasflow in large gas transmission networks is modelled by a coupled system of partial differential equations. The simulation model for a single pipeline can be normalized in a way that exploits the dominant role of the mach number (M) and the tube factor (RW) for characterizing the flow's and the pipeline's parameters. Introducing a spatial discretization leads to a nonlinear system of ordinary differential equations that - dependent on the values of M and RW - is stiff. In the first stage the discretized model for a single pipeline is reduced by the means of ‘Singular Perturbation’. Inspecting the eigenvalues of the appertaining Jacobian Matrix shows a good representation of the slow modes. The network's dynamic model consists of several reduced models for a single pipeline and an auxilary flow and pressure condition at the nodes. By defining time constants it is shown that also the network model may be stiff. In the second stage the network's dynamic model is reduced by explicit and implicit ‘Singular Perturbation’ methods. Using the reduced model makes it possible to adapt simple explicit integration algorithms which decrease the computing time for simulation.

Elimination of spurious higher‐mode response in pseudodynamic tests

AbstractIn a pseudodynamic test, errors in restoring‐force feedback are introduced into numerical computations. Some of these errors can excite the higher‐frequency response of the specimen. In this paper, the use of viscous and numerical dampings to eliminate spurious higher‐frequency effects is studied. Since the tangent stiffness of a non‐linear specimen cannot be measured accurately, initial‐stiffness‐dependent viscous damping is considered. In addition, an explicit integration algorithm with desired numerical damping properties is proposed and examined. The analytical and numerical studies presented indicate that viscous‐damping properties can be substantially changed by non‐linear deformations. For this reason, the use of numerical damping appears to be more advantageous.

Explicit multi-time step integration for the non-linear thermal analysis of structures

An explicit integration algorithm is presented which uses different time steps to integrate different element subdomains of a mesh. The method is applicable to non-linear first order finite element systems. Stability is shown by considering an energy norm which decreases and the critical time step is given in terms of element eigenvalues. Several numerical examples are presented.

Numerical analysis of longitudinal elastic-plastic waves with radial effects

The two-dimensional problem of longitudinal elastic-plastic waves in circular rods taking radial-inertia effects into account is solved based on the finite-element method and an explicit integration algorithm. The elastic-plastic constitutive equations are the yield criterion of von Mises with isotropic work hardening and the Prandtl-Reuss flow rule. Numerical results are shown for the region near the impact end of a semi-infinite rod for two sets of boundary conditions, namely prescribed longitudinal velocity and prescribed longitudinal stress at the bar end. The lateral motion of the struck end is assumed to be unrestrained (zero shear stress). The numerical results show response characteristics which deviate from the one-dimensional solution and which are in a good qualitative agreement with a number of experimental observations reported in the literature. These impact test results have been examined with respect to the predictions in order to separate radial- and strain-rate effects. Several specific calculations for the various test conditions have been performed to obtain quantitative agreement with experimental observations.

Eigenvalues and stable time steps for the bilinear Mindlin plate element

AbstractEigenvalues are obtained for the 4‐node Mindlin plate element with one‐point quadrature. Both isotropic and some anisotropic matenals are considered, but for the latter only bounds are obtained on the eigenvalues. These eigenvalues provide stable time steps for explicit time integration algorithms.

Quasi-Static Control of Explicit Algorithms for Transient Analysis

A linearized state-variable formulation of the lumped circuit simulation problem shows the results of some simpler related dc analyses to be useful in the time step size stability control of explicit integration algorithms. These analyses result also in a stable explicit integration algorithm that is often applicable. Because the various results obtained are amenable to simple physical interpretation, their use is not limited to state variable formulations of the lumped circuit simulation problem.

Integration system of a nonlinear transient network-analysis program

Users of nonlinear transient network-analysis programs, which use explicit integration procedures, have reported that excessive computer time is required to compute the transient response of networks containing widely separated time constants. Several recent papers have shown that for these problems significant computation-time reductions can be obtained by using implicit integration formulas. This paper is concerned with the selection and implementation of an implicit integration formula used in the CIRPAC nonlinear transient network-analysis program. Time-comparison data presented here indicate that the integration system that is described in this paper is significantly faster than the integration system of a network-analysis program that uses an explicit integration algorithm.

Numerical Simulation Of Middle-AmericaTrench Generated Tsunamis, Their CoastalArrival And Inundation Patterns In Mexico

To assess the extent and consequences of Middle America Trench generated tsunami impact to Eastern Pacific coastal communities of Mexico, computer simulations are performed. The tsunami source is described as an ocean water disturbance generated by an earthquake sea-floor deformation, assumed as a mirror sea-surface motion image. Deep water linear wave theory for the generation and far ocean propagation, and shallow water non-linear wave theory close to the shore are considered. Nonlinear discharge-depth relationships conditioned to the state of the water level at the boundaries, are used to model the flooding and recession at the coast. The computations are carried out through an explicit finite-difference numerical integration algorithm for interconnected discrete grids of different sizes. One of the most recent and well documented tsunamis in Mexico, considered as representatives of highly probable average cases, is satisfactorily modeled. Source parameters from large tsunamigenic past-earthquakes at seismic gaps off the Middle America Trench are used to simulate extreme future tsunamis. Inundation maps showing water runup and extension of flooding for some densely populated coastal areas and major industrially developed ports of the Eastern Pacific coast of Mexico, are produced for civil protection purposes.