The nonlinear stochastic behavior of soft-core sandwich panels and the evolution of uncertainty along the nonlinear path are investigated. The paper focuses on the way the geometrically nonlinear and unstable behavior is affected by uncertainty and considers, for the first time, the evolution of uncertainty along the unstable structural response. The structural modeling relies on the EHSAPT and its integration into the geometrically nonlinear stochastic regime. A tailored nonlinear FE model that is based on a variational formulation and an arc-length solution scheme are developed. The stochastic analysis adopts the Perturbation-based SFEM and its generalization for the evolution of uncertainty along the process axis. A numerical study demonstrates the stochastic methodology and explores the impact of uncertainty on the nonlinear structural behavior. The evolution of the stochastic stress resultants at the displaced end is studied along the two axes of evolution. The differences between the two representations and their physical and engineering significance are highlighted revealing significant changes to the uncertainty evolution pattern with the shift from global buckling to localized wrinkling instabilities. The representation of the stochastic results along the process axis also quantifies the level of uncertainty near critical and singular points where conventional analyses diverge.

中文翻译：

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软芯夹芯板的非线性随机行为

研究了软芯夹芯板的非线性随机行为以及沿非线性路径的不确定性演化。本文重点关注几何非线性和不稳定行为受不确定性影响的方式，并首次考虑了不确定性沿不稳定结构响应的演变。结构建模依赖于 EHSAPT 及其与几何非线性随机体系的集成。开发了基于变分公式和弧长求解方案的定制非线性有限元模型。随机分析采用基于扰动的 SFEM 及其对沿过程轴的不确定性演化的推广。数值研究展示了随机方法并探讨了不确定性对非线性结构行为的影响。沿两个演化轴研究了位移端随机应力合力的演化。突出显示了两种表示形式及其物理和工程意义之间的差异，揭示了随着从整体屈曲到局部起皱不稳定性的转变，不确定性演化模式发生了重大变化。沿过程轴的随机结果的表示还量化了传统分析发散的临界点和奇异点附近的不确定性水平。