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<p>For structural analysis considering large deformation, the quest for various equilibrium states, especially snap-through behavior, is challenging. This study introduces a sequential linear programming algorithm tailored for truss structures undergoing large deformation within the data-driven computational mechanics framework. The essential advantage lies in the capacity of this algorithm to capture geometric instabilities and obtain various equilibrium states in a stable and controllable way by manipulating the initial step size, such as snap-through and post-buckling. Furthermore, since data points represent the material constitutive model, the proposed algorithm can be applied to large deformation analysis of truss structures with linear and nonlinear material constitutive models. Numerical examples affirm that the results obtained by the proposed algorithm not only satisfy the calculation of strain measures but also yield a relative error in the external force on the order of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\({10}^{-4}\)</EquationSource> </InlineEquation>. For the classic two-bar truss example with snap-through, the load–displacement curve is consistent well with the theoretical solution. The load–displacement curve of a 25-bar truss with geometry instabilities obtained is very smooth, and the exact critical configuration at stationary points is captured. Finally, post-buckling configurations of an 1194-bar truss with both geometry and material nonlinearities are successfully obtained.</p>

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Data-driven based stable analysis algorithm for nonlinear truss structures with geometric instabilities

  • 期刊论文

  • 发表日期：

    2025年9月13日

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  • Mengcheng Huang,
  • Zongliang Du,
  • Tianchen Cui,
  • Chang Liu,
  • Xu Guo

摘要

For structural analysis considering large deformation, the quest for various equilibrium states, especially snap-through behavior, is challenging. This study introduces a sequential linear programming algorithm tailored for truss structures undergoing large deformation within the data-driven computational mechanics framework. The essential advantage lies in the capacity of this algorithm to capture geometric instabilities and obtain various equilibrium states in a stable and controllable way by manipulating the initial step size, such as snap-through and post-buckling. Furthermore, since data points represent the material constitutive model, the proposed algorithm can be applied to large deformation analysis of truss structures with linear and nonlinear material constitutive models. Numerical examples affirm that the results obtained by the proposed algorithm not only satisfy the calculation of strain measures but also yield a relative error in the external force on the order of \({10}^{-4}\) . For the classic two-bar truss example with snap-through, the load–displacement curve is consistent well with the theoretical solution. The load–displacement curve of a 25-bar truss with geometry instabilities obtained is very smooth, and the exact critical configuration at stationary points is captured. Finally, post-buckling configurations of an 1194-bar truss with both geometry and material nonlinearities are successfully obtained.