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A second-order accurate three sub-step composite algorithm for structural dynamics

APPLIED MATHEMATICAL MODELLING 2020年第Part2期77卷 1391-1412页

作者： Li, Jinze Yu, Kaiping He, Haonan Harbin Inst Technol Dept Astronaut Sci & Mech 92 West Dazhi St Harbin 150001 Heilongjiang Peoples R China

In this paper, a novel three sub-step composite algorithm with desired numerical properties is developed. The proposed method is a self-starting, unconditionally stable and second-order accurate implicit algorithm without overshoot. Particularly, the second-order accuracy in time is achieved in its final form, but it is not required in each sub-step. Its unique algorithmic parameter is analyzed to achieve the unconditional stability and it shares the identical effective stiffness matrix inside three sub-steps to save the computational cost in linear analyses. The same as the Bathe algorithm, the proposed algorithm is always L-stable, meaning that the spurious high-frequency modes can be effectively eliminated. Three numerical examples are simulated to illustrate the superiority of the proposed algorithm over some existing implicit algorithms. The first numerical simulation, solving a linear single-degree-of-freedom system, shows less period elongation errors and the second-order accuracy of the present scheme. The second one, a clamped-free bar excited by the end load, shows the ability of effectively damping out the unexpected high frequency modes. The last example solves the nonlinear mass-spring system with variable degree-of-freedoms and illustrates that the composite sub-step algorithm can save more computational cost than the traditional implicit algorithm when the integration step size is selected appropriately. (C) 2019 Elsevier Inc. All rights reserved.

关键词： Three sub-step algorithm Bathe algorithm Structural dynamics implicit integration algorithms

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An alternative to the Bathe algorithm

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APPLIED MATHEMATICAL MODELLING 2019年 69卷 255-272页

作者： Li, Jinze Yu, Kaiping Harbin Inst Technol Dept Astronaut Sci & Mech 92 West Dazhi St Harbin 150001 Heilongjiang Peoples R China

This paper presents a new composite sub-steps algorithm for solving reliable numerical responses in structural dynamics. The newly developed algorithm is a two sub-steps, second-order accurate and unconditionally stable implicit algorithm with the same numerical properties as the Bathe algorithm. The detailed analysis of the stability and numerical accuracy is presented for the new algorithm, which shows that its numerical characteristics are identical to those of the Bathe algorithm. Hence, the new sub-steps scheme could be considered as an alternative to the Bathe algorithm. Meanwhile, the new algorithm possesses the following properties: (a) it produces the same accurate solutions as the Bathe algorithm for solving linear and nonlinear problems;(b) it does not involve any artificial parameters and additional variables, such as the Lagrange multipliers;(c) The identical effective stiffness matrices can be obtained inside two sub-steps;(d) it is a self-starting algorithm. Some numerical experiments are given to show the superiority of the new algorithm and the Bathe algorithm over the dissipative CH-alpha algorithm and the non-dissipative trapezoidal rule. (C) 2018 Elsevier Inc. All rights reserved.

关键词： Sub-steps algorithm Bathe algorithm Structural dynamics implicit integration algorithms

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Stress resultant plasticity for shells revisited

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COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 2012年 247卷 146-165页

作者： Dujc, Jaka Brank, Bostjan Univ Ljubljana Fac Civil & Geodet Engn Ljubljana Slovenia

In this work, we revisit the stress resultant elastoplastic geometrically exact shell finite element formulation that is based on the Ilyushin-Shapiro two-surface yield function with isotropic and kinematic hardening. The main focus is on implicit projection algorithms for computation of updated values of internal variables for stress resultant shell elastoplasticity. Four different algorithms are derived and compared. Three of them yield practically identical final results, yet they differ considerably in computational efficiency and implementation complexity, since they solve different sets of equations and they use different procedures that choose active yield surfaces. One algorithm does not provide acceptable accuracy. It turns out that the most simple and straightforward algorithm performs surprisingly well and efficiently. Several numerical examples are presented to illustrate the Ilyushin-Shapiro stress resultant shell formulation and the numerical performance of the presented integration algorithms. (C) 2012 Elsevier B.V. All rights reserved.

关键词： Shell Geometrically exact model 4-node finite element Stress resultant plasticity Two-surface yield function implicit integration algorithms

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