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Towards a Unified Single Analysis Framework Embedded with Multiple Spatial and Time Discretized Methods for Linear Structural Dynamics

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Computer Modeling in Engineering & Sciences 2023年第5期135卷 843-885页

作者： David Tae kumar k.tamma Department of Mechanical Engineering University of MinnesotaTwin CitiesMinneapolis55455USA

We propose a novel computational framework that is capable of employing different time integration algorithms and different space discretized methods such as the Finite Element Method,particle methods,and other spatial methods on a single body sub-dividedintomultiple *** is in conjunctionwithimplementing thewell known Generalized Single Step Single Solve(GS4)family of algorithms which encompass the entire scope of Linear Multistep algorithms that have been developed over the past 50 years or so and are second order accurate into the Differential Algebraic Equation *** the current state of technology,the coupling of altogether different time integration algorithms has been limited to the same family of algorithms such as theNewmarkmethods and the coupling of different algorithms usually has resulted in reduced accuracy in one or more variables including the Lagrange ***,the robustness and versatility of the GS4 with its ability to accurately account for the numerical shifts in various time schemes it encompasses,overcomes such barriers and allows a wide variety of arbitrary implicit-implicit,implicit-explicit,and explicit-explicit pairing of the various time schemes while maintaining the second order accuracy in time for not only all primary variables such as displacement,velocity and acceleration but also the Lagrange multipliers used for coupling the *** selecting an appropriate spatialmethod and time scheme on the area with localized phenomena contrary to utilizing a single process on the entire body,the proposed work has the potential to better capture the physics of a given *** method is validated by solving 2D problems for the linear second order systems with various combination of spatial methods and time schemes with great *** accuracy and efficacy of the present work have not yet been seen in the current field,and it has shown significant promise in its capabilities and effectiveness for ge

关键词： Time integration structural dynamics multiple scale and multiple methods ordinary differential equations differential algebraic equations

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A Consistent Time Level Implementation Preserving Second-Order Time Accuracy via a Framework of Unified Time Integrators in the Discrete Element Approach

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Computer Modeling in Engineering & Sciences 2023年第3期134卷 1469-1487页

作者： Tao Xue YazhouWang Masao Shimada David Tae kumar tamma Xiaobing Zhang School of Energy and Power Engineering Nanjing University of Science and TechnologyNanjing210094China'2Department of Mechanical EngineeringUniversity of Minnesota-Twin CitiesMinneapolis55455USA

In this work,a consistent and physically accurate implementation of the general framework of unified second-order time accurate integrators via the well-known GSSSS framework in the Discrete Element Method is *** improved tangential displacement evaluation in the present implementation of the discrete element method has been derived and implemented to preserve the consistency of the correct time level evaluation during the time integration process in calculating the algorithmic tangential *** numerical examples have been used to validate the proposed tangential displacement evaluation;this is in contrast to past practices which only seem to attain the first-order time accuracy due to inconsistent time level implementation with different algorithms for normal and tangential *** comparisons with the existing implementation and the superiority of the proposed implementation are given in terms of the convergence rate with improved numerical accuracy in ***,several schemes via the unified second-order time integrators within the framework of the GSSSS family have been carried out based on the proposed correct *** the numerical results demonstrate that using the existing state-of-the-art implementation reduces the time accuracy to be first-order accurate in time,while the proposed implementation preserves the correct time accuracy to yield second-order.

关键词： Computational dynamics time integration Discrete Element Method(DEM)

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