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Two-point constitutive equations and integration algorithms for isotropic-hardening rate-independent elastoplastic materials in large deformation

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INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING 2008年第12期75卷 1435-1456页

作者： Wang, Zhi-Qiao Dui, Guan-Suo Beijing Jiaotong Univ Inst Engn Mech Beijing 100044 Peoples R China

This paper presents alternative forms of hyperelastic-plastic constitutive equations and their integration algorithms for isotropic-hardening materials at large strain, which are established in two-point tensor field, namely between the first Piola-Kirchhoff stress tensor and deformation gradient. The eigenvalue problems for symmetric and non-symmetric tensors are applied to kinematics of multiplicative plasticity, which imply the transformation relationships of eigenvectors in current, intermediate and initial configurations. Based on the principle of plastic maximum dissipation, the two-point hyperelastic stress-strain relationships and the evolution equations are achieved, in which it is considered that the plastic spin vanishes for isotropic plasticity. On the computational side, the exponential algorithm is used to integrate the plastic evolution equation. The return-mapping procedure in principal axes, with respect to logarithmic elastic strain, possesses the same structure as infinitesimal deformation theory. Then, the theory of derivatives of non-symmetric tensor functions is applied to derive the two-point closed-form consistent tangent modulus, which is useful for Newton's iterative solution of boundary value problem. Finally, the numerical simulation illustrates the application of the proposed formulations. Copyright (C) 2008 John Wiley & Sons, Ltd.

关键词： large-strain hyperelastic-plasticity constitutive equations integration algorithms first Piola-Kirchhoff stress deformation gradient consistent tangent modulus

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Optical solitons for Biswas-Arshed equation with multiplicative noise via Ito calculus using three integration algorithms

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OPTIK 2022年 258卷 168847-168847页

作者： Zayed, Elsayed M. E. Shohib, Reham M. A. Alngar, Mohamed E. M. Gepreel, Khaled A. Nofal, Taher A. Yildirim, Yakup Zagazig Univ Math Dept Fac Sci Zagazig 44519 Egypt Taif Univ Coll Sci Dept Math POB 11099 Taif 21944 Saudi Arabia Near East Univ Fac Arts & Sci Dept Math CY-99138 Nicosia Cyprus

The current paper studies optical solitons with the nonlinear stochastic Biswas-Arshed equation for the first time. Dark, bright, and singular solitons are presented via three integration technologies.

关键词： Multiplicative noise Solitons integration algorithms

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Simplified Design of Dual Quaternion Strapdown Inertial Navigation integration algorithms

Simplified Design of Dual Quaternion Strapdown Inertial Navi...

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International Conference on Measurement, Instrumentation and Automation (ICMIA 2012)

作者： Lin Yu-rong Chen Liang Fu Zhen-xian Harbin Inst Technol Dept Control Sci & Engn Harbin 150001 Peoples R China

ISBN: (纸本)9783037855454

Dual quaternion navigation algorithm gain higher accuracy than traditional strapdown inertial navigation algorithm at the cost of real-time performance. In order to reduce tremendous computation amount of the former, a simplified design scheme for navigation integration algorithms is presented in this paper. First, based on update principle and computation rules of dual quaternion we separate rotational and translational increment information from dual quaternion increment, and deduce exact solutions defined by the spiral vector for thrust velocity increment, gravitational velocity increment and displacement increment. Then, considering characteristics of a strapdown inertial navigation system, implementation schemes of simplified integration algorithms for dual quaternion differential equations in three frames, including thrust velocity coordinates, gravitational velocity coordinates and position coordinates, are designed separately. Under the premise of ensuring the accuracy advantage of the original dual quaternion inertial navigation algorithm, the proposed simplified algorithm significantly improve the computational efficiency. This will lay favorable foundation for engineering realization of the dual quaternion strapdown inertial navigation algorithm.

关键词： Dual quatrenion integration algorithms Simplified design Thrust velocity Gravitational velocity

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A semi-explicit integration algorithm with controllable numerical damping for real-time hybrid simulation

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STRUCTURES 2025年 74卷

作者： Lai, Zhenfeng Liu, Yanhui Tan, Ping Peng, Jinqiang Zhou, Fulin Guangzhou Univ Earthquake Engn Res & Test Ctr EERTC Guangzhou 510006 Peoples R China Minist Educ Key Lab Earthquake Resistance Earthquake Mitigat & Guangzhou 510006 Peoples R China Guangdong Prov Key Lab Earthquake Engn & Appl Tech Guangzhou 510006 Peoples R China

Real-time hybrid simulation (RTHS) is a cost-effective experimental method for evaluating the dynamic behavior of structures. In the numerical computation component of RTHS, the use of efficient, accurate, and stable integration algorithms is critical for its effective execution. This study presents a single-step semi-explicit integration algorithm SSE-alpha, designed to enhance the precision and robustness of numerical computations in RTHS. The numerical properties of the proposed algorithm, including stability, accuracy, and overshoot behavior, are evaluated. The results show that the SSE-alpha algorithm offers flexible and controllable numerical damping, offering unconditional stability for both linear and softened nonlinear systems. This algorithm features second-order accuracy and can effectively reduce or eliminate overshoot through parameter adjustment. The comparative analysis with the G-alpha, WBZ-alpha, and MKR-alpha algorithms demonstrates that the proposed algorithm exhibits superior stability, precision, computational efficiency, and numerical damping characteristics. Finally, the effectiveness and stability of the SSE-alpha algorithm are confirmed through its application to different structural systems in RTHS. This algorithm ensures improved real-time computational accuracy and stability for the assessment of structural systems, including critical infrastructure under seismic loading, contributing to advancements in structural dynamics.

关键词： Semi-explicit integration algorithms Real-time hybrid simulation Numerical damping Spectral radius Stability and accuracy

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On the integration of highly oscillatory functions:: algorithms based on critical points and semi-periodic zones in scalar diffraction

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COMPUTER PHYSICS COMMUNICATIONS 2001年第1期134卷 11-22页

作者： Ferré-Borrull, J Bosch, S Univ Barcelona Dept Fis Aplicada & Opt E-08028 Barcelona Spain

Two methods for the computation of the diffraction integrals appearing in the scalar approximation of the theory of diffraction of electromagnetic waves are developed. The methods are tuned since they avoid the oscillations of the integral kernel by dividing the integration domain in semi-periodic zones. A further optimization is applied hy taking advantage of the fact that the semi-periodic zones that contain a critical point have the main contribution to the result. (C) 2001 Elsevier Science B.V. All rights reserved.

关键词： diffraction integrals integration algorithms highly oscillatory functions semi-periodic zones critical points

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A Generalized Backward Euler algorithm for the numerical integration of a viscous breakage model

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INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS 2019年第1期43卷 3-29页

作者： Marinelli, Ferdinando Buscarnera, Giuseppe Northwestern Univ Dept Civil & Environm Engn 2145 Sheridan Rd Evanston IL 60208 USA

This paper discusses the formulation and the numerical performance of a fully implicit algorithm used to integrate a rate-dependent model defined within a breakage mechanics framework. For this purpose, a Generalized Backward Euler (GBE) algorithm has been implemented according to two different linearization strategies: The former is derived by a direct linearization of the constitutive equations, while the latter introduces rate effects through a consistency parameter. The accuracy and efficiency of the GBE algorithm have been investigated by (1) performing material point analyses and (2) solving initial boundary value problems. In both cases, the overall performance of the underlying algorithm is inspected for a range of loading rates, thus simulating comminution from slow to fast dynamic problems. As the viscous response of the breakage model can be recast through a viscous nucleus function, the presented algorithm can be considered as a general framework to integrate constitutive equations relying on the overstress approach typical of Perzyna-like viscoplastic models.

关键词： continuum breakage mechanics finite element method integration algorithms Perzyna viscoplasticity rate effects

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An investigation of GPU-based stiff chemical kinetics integration methods

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COMBUSTION AND FLAME 2017年第May.期179卷 312-324页

作者： Curtis, Nicholas J. Niemeyer, Kyle E. Sung, Chih-Jen Univ Connecticut Dept Mech Engn Storrs CT 06269 USA Oregon State Univ Sch Mech Ind & Mfg Engn Corvallis OR 97331 USA

A fifth-order implicit Runge-Kutta method and two fourth-order exponential integration methods equipped with Krylov subspace approximations were implemented for the GPU and paired with the analytical chemical kinetic Jacobian software pyJac. The performance of each algorithm was evaluated by integrating thermochemical state data sampled from stochastic partially stirred reactor simulations and compared with the commonly used CPU-based implicit integrator CVODE. We estimated that the implicit Runge-Kutta method running on a single Tesla C2075 GPU is equivalent to CVODE running on 12-38 Intel Xeon E5-4640 v2 CPU cores for integration of a single global integration time step of 10(-6)s with hydrogen and methane kinetic models. In the stiffest case studied-the methane model with a global integration time step of 10(-4)s-thread divergence and higher memory traffic significantly decreased GPU performance to the equivalent of CVODE running on approximately three CPU cores. The exponential integration algorithms performed more slowly than the implicit integrators on both the CPU and GPU. Thread divergence and memory traffic were identified as the main limiters of GPU integrator performance, and techniques to mitigate these issues were discussed. Use of a finite-difference Jacobian on the GPU-in place of the analytical Jacobian provided by pyJac-greatly decreased integrator performance due to thread divergence, resulting in maximum slowdowns of 7.11 - 240.96x;in comparison, the corresponding slowdowns on the CPU were just 1.39 - 2.61x, underscoring the importance of use of an analytical Jacobian for efficient GPU integration. Finally, future research directions for working towards enabling realistic chemistry in reactive-flow simulations via GPU/SIMT accelerated stiff chemical kinetics integration were identified.(C) 2017 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

关键词： Chemical kinetics Stiff chemistry integration algorithms GPU SIMT

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On continuity of integration methods for AUC. A note

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JOURNAL OF PHARMACOKINETICS AND BIOPHARMACEUTICS 1998年第1期26卷 125-130页

作者： Jawien, W Jagiellonian Univ Coll Med PL-30688 Krakow Poland

A lack of monotonicity and discontinuity of some integration methods for AUC, as a function of measured concentration, is demonstrated. Hybrid methods consisting of either parabolas-through-the-origin or the alpha-function method followed by the log-trapezoidal method were found to be discontinuous at the switching point. The stable piecewise third-order polynomial method appeared to be nonmonotonic as well as discontinuous.

关键词： area-under-the-curve model-independent pharmacokinetics integration algorithms

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Knowledge Generalization during Hierarchical Structures integration

Knowledge Generalization during Hierarchical Structures Inte...

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6th Asian Conference on Intelligent Information and Database Systems (ACIIDS)

作者： Maleszka, Marcin Wroclaw Univ Technol PL-50370 Wroclaw Poland

ISBN: (纸本)9783319054766;9783319054759

Hierarchical data structures are common in modern applications. Tree integration is one of the tools that is not fully researched in this scope. Therefore in this paper we define a complex tree to model common hierarchical structures. Complex tree integration aim is determined by specific integration criteria. In this paper we define and analyze a criterion measuring generalization of knowledge - upper semantic precision. We analyze the criterion in terms of simpler syntactic criteria and describe an extended example of an information retrieval system using this criterion.

关键词： knowledge generalization knowledge precission tree integration integration criteria integration algorithms

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Designing a Universal Suboptimal Tree integration Algorithm 7th

Designing a Universal Suboptimal Tree Integration Algorithm

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7th International Conference on Computational Collective Intelligence (ICCCI)

作者： Maleszka, Marcin Wroclaw Univ Technol PL-50370 Wroclaw Poland

ISBN: (纸本)9783319243061;9783319243054

Processing hierarchical data structures, due to their increasing popularity, becomes more and more important. In our previous works we have developed many exact integration algorithms for trees, but designing a new algorithm for each new integration aim is resource consuming. In this paper we propose a universal integration method based on genetic programming heuristic. Experimental evaluation shows that this approach is slightly slower than exact algorithms and sometimes provides worse solutions. One important advantage however is that it may be applied with no additional effort to any problem, without the need for a long design phase.

关键词： Tree integration integration algorithms Genetic programming Suboptimal integration

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