Integration Algorithms (integration + algorithms)

Distribution by Scientific Domains

Selected Abstracts

Real-time hybrid testing using the unconditionally stable explicit CR integration algorithm

Cheng Chen
Abstract Real-time hybrid testing combines experimental testing and numerical simulation, and provides a viable alternative for the dynamic testing of structural systems. An integration algorithm is used in real-time hybrid testing to compute the structural response based on feedback restoring forces from experimental and analytical substructures. Explicit integration algorithms are usually preferred over implicit algorithms as they do not require iteration and are therefore computationally efficient. The time step size for explicit integration algorithms, which are typically conditionally stable, can be extremely small in order to avoid numerical stability when the number of degree-of-freedom of the structure becomes large. This paper presents the implementation and application of a newly developed unconditionally stable explicit integration algorithm for real-time hybrid testing. The development of the integration algorithm is briefly reviewed. An extrapolation procedure is introduced in the implementation of the algorithm for real-time testing to ensure the continuous movement of the servo-hydraulic actuator. The stability of the implemented integration algorithm is investigated using control theory. Real-time hybrid test results of single-degree-of-freedom and multi-degree-of-freedom structures with a passive elastomeric damper subjected to earthquake ground motion are presented. The explicit integration algorithm is shown to enable the exceptional real-time hybrid test results to be achieved. Copyright 2008 John Wiley & Sons, Ltd. [source]

A new family of generalized-, time integration algorithms without overshoot for structural dynamics

Yu KaiPing
Abstract A new family of generalized-, (G-,) algorithm without overshoot is presented by introducing seven free parameters into the single-step three-stage formulation for solution of structural dynamic problems. It is proved through finite difference analysis that these algorithms are unconditionally stable, second-order accurate and numerical dissipation controllable. The comparison of the new G-, algorithms with the commonly used G-, algorithms shows that the newly developed algorithms have the advantage of eliminating the overshooting characteristics exhibited by the commonly used algorithms while their excellent property of dissipation is preserved. The numerical simulation results obtained using a single-degree-of-freedom system and a two-degree-of-freedom system to represent the character of typical large systems coincide well with the results of theoretical analyses. Copyright 2008 John Wiley & Sons, Ltd. [source]

Generalized trapezoidal numerical integration of an advanced soil model

Yunming Yang
Abstract This paper investigates the numerical performance of the generalized trapezoidal integration rule by using an advanced soil model. The generalized trapezoidal integration rule can include many other integration algorithms by adjusting a single parameter , ranging from 1 to 0. The soil model used is the recently developed middle surface concept (MSC) sand model which simulates different soil response characteristics by using different pseudo-yield functions. The generalized trapezoidal rule and MSC sand model are used to simulate the responses of sand samples with different relative densities under various initial and loading conditions. Instead of a single step, multiple loading steps bring the sample to the vicinity of failure. These comprehensive investigations examine and compare the influences of various values of , on the numerical solution of integrated constitutive equations, the convergence of Newton's iterative scheme, and the integration accuracy. Copyright 2007 John Wiley & Sons, Ltd. [source]

An internally consistent integration method for critical state models,

Randall J. Hickman
Abstract A new procedure to integrate critical state models including Cam,Clay and modified Cam,Clay is proposed here. The proposed procedure makes use of the linearity of the virgin isotropic compression curve and the parallel anisotropic consolidation lines in e,ln p space which are basic features of the formulation of critical state models. Using this algorithm, a unique final stress state may be found as a function of a single unknown for elastoplastic loading. The key equations are given in this article for the Cam,Clay and modified Cam,Clay models. The use of the Newton,Raphson iterative method to minimize residuals and obtain a converged solution is described here. This new algorithm may be applied using the assumptions of linear elasticity or non-linear elasticity within a given loading step. The new algorithm proposed here is internally consistent and has computational advantages over the current numerical integration procedures. Numerical examples are presented to show the performance of the algorithm as compared to other integration algorithms. Published in 2005 by John Wiley & Sons, Ltd. [source]

A variationally consistent framework for the design of integrator and updates of generalized single step representations for structural dynamics

R. Kanapady
Abstract A variationally consistent framework leading to the concise design of both the ,integrator' and the associated ,updates' as related to the single step representations encompassing the so-called LMS methods for structural dynamics is described. The present paper shows for the first time, a consistent treatment involving both the ,integrator' and ,updates' that are inherent in the general context of designing the time integration process. Furthermore, the framework encompasses not only all the existing time integration algorithms that are dissipative and non-dissipative within the scope of LMS methods but also contains new optimal algorithms useful for practical applications,in the sense of accuracy, stability, numerical dissipation and dispersion, and overshoot characteristics of computational algorithms for time dependent problems encountered in structural dynamics. Copyright 2003 John Wiley & Sons, Ltd. [source]

Multi-time-step domain coupling method with energy control

N. Mahjoubi
Abstract A multi-time-step integration method is proposed for solving structural dynamics problems on multiple domains. The method generalizes earlier state-space integration algorithms by introducing displacement constraints via Lagrange multipliers, representing the time-integrated constraint forces over the individual time step. It is demonstrated that displacement continuity between the subdomains leads to cancelation of the interface contributions to the energy balance equation, and thus stability and algorithmic damping properties of the original algorithms are retained. The various subdomains can be integrated in time using different time steps and/or different state-space time integration schemes. The solution of the constrained system equations is obtained using a dual Schur formulation, allowing for maximum independence of the calculation of the subdomains. Stability and accuracy are illustrated by a numerical example using a refined mesh around concentrated forces. Copyright 2010 John Wiley & Sons, Ltd. [source]

Design, analysis, and synthesis of generalized single step single solve and optimal algorithms for structural dynamics

X. Zhou
Abstract The primary objectives of the present exposition are to: (i) provide a generalized unified mathematical framework and setting leading to the unique design of computational algorithms for structural dynamic problems encompassing the broad scope of linear multi-step (LMS) methods and within the limitation of the Dahlquist barrier theorem (Reference [3], G. Dahlquist, BIT 1963; 3: 27), and also leading to new designs of numerically dissipative methods with optimal algorithmic attributes that cannot be obtained employing existing frameworks in the literature, (ii) provide a meaningful characterization of various numerical dissipative/non-dissipative time integration algorithms both new and existing in the literature based on the overshoot behavior of algorithms leading to the notion of algorithms by design, (iii) provide design guidelines on selection of algorithms for structural dynamic analysis within the scope of LMS methods. For structural dynamics problems, first the so-called linear multi-step methods (LMS) are proven to be spectrally identical to a newly developed family of generalized single step single solve (GSSSS) algorithms. The design, synthesis and analysis of the unified framework of computational algorithms based on the overshooting behavior, and additional algorithmic properties such as second-order accuracy, and unconditional stability with numerical dissipative features yields three sub-classes of practical computational algorithms: (i) zero-order displacement and velocity overshoot (U0-V0) algorithms; (ii) zero-order displacement and first-order velocity overshoot (U0-V1) algorithms; and (iii) first-order displacement and zero-order velocity overshoot (U1-V0) algorithms (the remainder involving high-orders of overshooting behavior are not considered to be competitive from practical considerations). Within each sub-class of algorithms, further distinction is made between the design leading to optimal numerical dissipative and dispersive algorithms, the continuous acceleration algorithms and the discontinuous acceleration algorithms that are subsets, and correspond to the designed placement of the spurious root at the low-frequency limit or the high-frequency limit, respectively. The conclusion and design guidelines demonstrating that the U0-V1 algorithms are only suitable for given initial velocity problems, the U1-V0 algorithms are only suitable for given initial displacement problems, and the U0-V0 algorithms are ideal for either or both cases of given initial displacement and initial velocity problems are finally drawn. For the first time, the design leading to optimal algorithms in the context of a generalized single step single solve framework and within the limitation of the Dahlquist barrier that maintains second-order accuracy and unconditional stability with/without numerically dissipative features is described for structural dynamics computations; thereby, providing closure to the class of LMS methods. Copyright 2003 John Wiley & Sons, Ltd. [source]