Time integration in the context of energy control and locking free finite elements

Summary In the present paper two main research areas of computational mechanics, namely the finite element development and the design of time integration algorithms are reviewed and discussed with a special emphasis on their combination. The finite element techniques are designed to prevent locking and the time integration schemes to guarantee numerical stability in non-linear elastodynamics. If classical finite element techniques are used, their combination with time integration schemes allow to avoid any modifications on the element or algorithmic level. It is pointed out, that on the other hand Assumed Stress and Enhanced Assumed Strain elements have to be modified if they are combined with energy conserving or decaying time integration schemes, especially the Energy-Momentum Method in its original and generalized form. The paper focusses on the necessary algorithmic formulation of Enhanced Assumed Strain elements which will be developed by the reformulation of the Generalized Energy-Momentum Method based on a classical one-field functional, the extension to a modifiedHu-Washizu three-field functional including enhanced strains and a suitable time discretization of the additional strain terms. The proposed method is applied to non-linear shell dynamics using a shell element which allows for shear deformation and thickness change, and in which the Enhanced Assumed Strain Concept is introduced to avoid artificial thickness locking. Selected examples illustrate the locking free and numerically stable analysis.     

Numerical integration for the inverse dynamics of a large class of cranes

Multibody System Dynamics - A recently developed index reduction method is applied to comparatively complicated underactuated mechanical systems in the context of inverse dynamics. The inverse...     

A new factorization of the mass matrix for optimal serial and parallel calculation of multibody dynamics

This paper describes a new factorization of the inverse of the joint-space inertia matrix M. In this factorization, M ^?1 is directly obtained as the product of a set of sparse matrices wherein, for a serial chain, only the inversion of a block-tridiagonal matrix is needed. In other words, this factorization reduces the inversion of a dense matrix to that of a block-tridiagonal one. As a result, this factorization leads to both an optimal serial and an optimal parallel algorithm, that is, a serial algorithm with a complexity of O(N) and a parallel algorithm with a time complexity of O(logN) on a computer with O(N) processors. The novel feature of this algorithm is that it first calculates the interbody forces. Once these forces are known, the accelerations are easily calculated. We discuss the extension of the algorithm to the task of calculating the forward dynamics of a kinematic tree consisting of a single main chain plus any number of short side branches. We also show that this new factorization of M ^?1 leads to a new factorization of the operational-space inverse inertia, Λ ^?1, in the form of a product involving sparse matrices. We show that this factorization can be exploited for optimal serial and parallel computation of Λ ^?1, that is, a serial algorithm with a complexity of O(N) and a parallel algorithm with a time complexity of O(logN) on a computer with O(N) processors.     

Data errors in the computation of free motion

Input data in the computation of free motion (the inertia and stiffness matrices) contain some errors. These errors generate errors of output data (the natural frequency vector, the natural mode vectors). In this paper the relationships between errors of input and output data in the computation of free motion are derived. This analysis is applied to the finite element method. The paper presents program ERROR, which computes the errors of the natural frequencies created by the inertia matrix errors. An example of the influence of the errors of the mass and of the mass moment of inertia on the natural frequencies of a ship hull is presented.     

Simulation and integration of geometric and rigid body kinematics errors for assembly variation analysis

Rigid and compliant models have been developed in parallel in the literature for variation analysis of different assembly processes. For a complex assembly system, it is desirable to balance accuracy and simplicity by introducing a rigid-compliant hybrid model. This paper develops a new method aimed at providing an interface between rigid and compliant assembly models. Part geometric errors (PGE) and rigid body kinematics stackup error (RE) are simulated and integrated in rigid assembly processes. A covariance matrix of PGE and RE is then constructed, providing input to subsequent compliant assembly models. Algorithms are developed (1) to predict RE by using the stream of variation (SOVA) model; (2) to simulate PGE based on statistical modal analysis (SMA) and specified tolerances; and (3) to integrate RE and PGE in rigid assembly processes for covariance matrix construction. This is an initial step toward the development of a rigid-compliant hybrid assembly model for variation analysis in multistation manufacturing systems (MMS).     

Time integration and reject options for probabilistic output of pairwise LVQ

Learning vector quantization (LVQ) constitutes a very popular machine learning technology with applications, for example, in biomedical data analysis, predictive maintenance/quality as well as product individualization. Albeit probabilistic LVQ variants exist, its deterministic counterparts are often preferred due to their better efficiency. The latter do not allow an immediate probabilistic interpretation of its output; hence, a rejection of classification based on confidence values is not possible. In this contribution, we investigate different schemes how to extend and integrate pairwise LVQ schemes to an overall probabilistic output, in comparison with a recent heuristic surrogate measure for the security of the classification, which is directly based on LVQ’s multi-class classification scheme. Furthermore, we propose a canonic way how to fuse these values over a given time window in case a possibly disrupted measurement is taken over a longer time interval to counter the uncertainty of a single point in time. Experimental results indicate that an explicit probabilistic treatment often yields superior results as compared to a standard deterministic LVQ method, but metric learning is able to annul this difference. Fusion over a short time period is beneficial in case of an unclear classification.

     

Variational methods for a class of nonlocal functionals

The paper gives on overview of recent developments and presents some new results for variational problems involving functionals with nonlocal transformation of argument, in particular, argument deviation.     

Research on the new dynamics properties for a noise-induced excited system

Three induces are discussed to study the new dynamics properties both analytically and numerically for noise-induced Fitzhugh-Nagumo system; the three induces are as follows: Lyapunov exponent, the density distribution of trajectories and power spectrum; the numerical experiment indicated that the noise can induce the system to quite regular dynamics, including coherence resonance (in the case of uncoupling) and stochastic synchronization (in the case of coupling), noise can control the dynamics properties and some other new phenomena that the synchronization takes place only for some moderate noise intensity is also found for the first time.     

noloco: An efficient implementation of van der Waals density functionals based on a Monte-Carlo integration technique

The treatment of van der Waals interactions in density functional theory is an important field of ongoing research. Among different approaches developed recently to capture these non-local interactions, the van der Waals density functional (vdW-DF) developed in the groups of Langreth and Lundqvist is becoming increasingly popular. It does not rely on empirical parameters, and has been successfully applied to molecules, surface systems, and weakly-bound solids. As the vdW-DF requires the evaluation of a six-dimensional integral, it scales, however, unfavorably with system size. In this work, we present a numerically efficient implementation based on the Monte-Carlo technique for multi-dimensional integration. It can handle different versions of vdW-DF. Applications range from simple dimers to complex structures such as molecular crystals and organic molecules physisorbed on metal surfaces.     

A new architecture for integration of CORBA and OODB

Object oriented database system (OODB) supports an object oriented data model with the functionality of persistency and transaction semantics. In order to facilitate the use of OODB, the Object Database Management Group (ODMG) defined a standard for object database management systems. On the other hand, the Object Management Group (OMG) defined the Common Object Request Broker Architecture (CORBA), which is an emerging standard of distributed object technology providing the interconnection network between distributed objects. For the sake of matching these two object models, taking the advantages of merging both of them, and building a more sophisticated infrastructure, the integration of CORBA and OODB is currently an urgent and important issue in distributed object systems. Instead of using Object Database Adapter (ODA) suggested by the ODMG, we provide a novel way of reusing the Object Transaction Service (OTS) and wrapping techniques to introduce OODB into CORBA automatically. Through our design, CORBA clients or OODB object implementers do not need to learn any knowledge of each other. In addition, error recovery is also provided to guarantee the consistency of object states. The whole task for integrating CORBA and OODB is done transparently by our proposed preprocessor, which plays an important role in solving problems encountered by ORB and OODB vendors easily     

Gauging the performance of some density functionals including dispersion and nonlocal corrections for relative energies of water 20-mers

Currently, development of density functional theory approximations and their benchmarking for accurately modeling different types of molecular interactions become a very active field of research. In this report, performance of the dispersion (D3) and nonlocal (NL) corrected density functionals has been compared with generalized energy-based fragmentation approach at the complete basis set limit for predicting the relative energies of 10 low-energy isomers of water nanoclusters (H₂O)₂₀ as an illustrative example of hydrogen bonded systems. Considering a variety of exchange-correlation density functionals in combination with D3 and NL corrections we find that the D3 based approximations outperform the functionals incorporating NL correction. It is also shown that the LC-ωPBE-D3 and rPW86PBE-NL functionals have the best trend from the viewpoint of the order of stabilities in water nanoclusters under study.     

Error and timing analysis of multiple time-step integration methods for molecular dynamics

Molecular dynamics simulations of biomolecules performed using multiple time-step integration methods are hampered by resonance instabilities. We analyze the properties of a simple 1D linear system integrated with the symplectic reference system propagator MTS (r-RESPA) technique following earlier work by others. A closed form expression for the time step dependent Hamiltonian which corresponds to r-RESPA integration of the model is derived. This permits us to present an analytic formula for the dependence of the integration accuracy on short-range force cutoff range. A detailed analysis of the force decomposition for the standard Ewald summation method is then given as the Ewald method is a good candidate to achieve high scaling on modern massively parallel machines. We test the new analysis on a realistic system, a protein in water. Under Langevin dynamics with a weak friction coefficient (ζ=1 ps⁻¹) to maintain temperature control and using the SHAKE algorithm to freeze out high frequency vibrations, we show that the 5 fs resonance barrier present when all degrees of freedom are unconstrained is postponed to ≈12 fs. An iso-error boundary with respect to the short-range cutoff range and multiple time step size agrees well with the analytical results which are valid due to dominance of the high frequency modes in determining integrator accuracy. Using r-RESPA to treat the long range interactions results in a 6× increase in efficiency for the decomposition described in the text.     

A new algorithm for integration of dynamic systems

A high precision unconditionally stable algorithm for computation of linear dynamic structural systems is described. It shares the advantageous property (typical for lower order algorithms) of the amplification matrix preserving a banded form due to discretization in space. Hence in contrast to the known high precision algorithms employing full matrices, less computer space and fewer operations are needed. The new algorithm is free of artificial damping in the undamped case as well as of artificial oscillation in the postcritical damping region. Local truncation error analysis is made and rate of convergence is proved. Applications to problems allowing comparison with existing results are presented. Excellent agreement with exact solutions is achieved and engineering accuracy is attained with relatively few time steps.     

Linear estimation in the presence of errors in assumed plant dynamics

This paper is concerned with certain practical aspects of linear estimation theory. Several questions, which arise during most applications of the theory, are partially answered by considering the following problem: Obtain the linear minimum variance estimate of the systemx_{n+1} = (Phi_{n+1.n} + deltaPhi_{n+1.n})x_{n} + w_{n}y_{n} = M_{n}x_{n}when the assumed model is given byx_{n+1} = Phi_{n+1.n}x_{n} + w_{n}y_{n} = M_{n}x_{n}     

Performance of implicit A-stable time integration methods for multibody system dynamics

Multibody System Dynamics - This paper illustrates the performance of several representative implicit A-stable time integration methods with algorithmic dissipation for multibody system dynamics,...