潘天林, 吴斌. 基于桁架单元的能量一致积分方法[J]. 工程力学, 2018, 35(10): 1-9,36. DOI: 10.6052/j.issn.1000-4750.2017.06.0434
引用本文: 潘天林, 吴斌. 基于桁架单元的能量一致积分方法[J]. 工程力学, 2018, 35(10): 1-9,36. DOI: 10.6052/j.issn.1000-4750.2017.06.0434
PAN Tian-lin, WU Bin. AN ENERGY CONSISTENT INTEGRATION METHOD FOR TRUSS ELEMENTS[J]. Engineering Mechanics, 2018, 35(10): 1-9,36. DOI: 10.6052/j.issn.1000-4750.2017.06.0434
Citation: PAN Tian-lin, WU Bin. AN ENERGY CONSISTENT INTEGRATION METHOD FOR TRUSS ELEMENTS[J]. Engineering Mechanics, 2018, 35(10): 1-9,36. DOI: 10.6052/j.issn.1000-4750.2017.06.0434

基于桁架单元的能量一致积分方法

AN ENERGY CONSISTENT INTEGRATION METHOD FOR TRUSS ELEMENTS

  • 摘要: 基于能量平衡理论,提出针对桁架单元的能量一致积分方法。该方法具有非线性无条件稳定性,2阶精度。利用中值定理证明算法参数的存在性,并给出参数的求解形式。对离散后的动力方程线性化得到用于迭代的等效刚度矩阵。实现新算法在非线性有限元程序中的嵌入,并以此为基础完成单摆、输电塔体结构的非线性动力分析。数值结果表明,经典的平均加速度方法与隐式中点方法均会表现出能量不一致现象,甚至会产生发散结果;相比而言,该文方法在不同的时间步长情况下都表现出良好的数值稳定性。

     

    Abstract: Based on the energy equilibrium theory, an energy consistent integration method for truss elements is proposed in this paper. The method is unconditionally stable in nonlinear systems, and its accuracy is second order. The existence of algorithm parameters is proved by mean value theorem, and the solution form of the parameters is also provided. The discrete dynamic equations are linearized to obtain the equivalent stiffness matrices for iteration. The new algorithm is embedded in a nonlinear finite element program. On the basis of this program, the nonlinear dynamic analysis of a single pendulum and a transmission tower structure is completed. The numerical results show that the classic average acceleration method and implicit midpoint method are both energy inconsistent and may even produce divergent results. In contrast, the proposed method has good stability within different time steps.

     

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