含软夹杂的非线性弹性梁的屈曲预测

中文摘要 AI 辅助

我们开发了一种高效且准确的多尺度计算框架，用于预测含周期性分布软夹杂的弹性梁的屈曲及后屈曲行为。该框架将我们此前针对线性弹性的多尺度补丁计算均匀化方法进行扩展，纳入了非线性效应，因此能够准确预测屈曲起始及后续的后屈曲响应。微观尺度计算仅在一组稀疏的小子域（补丁）内进行，而宏观尺度行为则通过经过验证的补丁耦合算法进行重构。我们对夹杂与基体杨氏模量之比介于0.001至1之间的梁，采用四分之一和半域补丁计算对该方案进行评估。结果表明，降低夹杂刚度会同时降低临界屈曲应变和临界屈曲应力，表明其不稳定性敏感性增加，同时产生更温和的后屈曲响应，横向挠度和应力降更小。雅可比矩阵的特征值分析可准确预测不稳定性的起始及对应的临界应变和应力。我们还给出了压缩载荷下非线性屈曲构型的分岔图，以及插值阶数对预测的屈曲和后屈曲响应影响的定量分析。与全域模拟的比较表明，所提出的框架在大幅降低计算成本的同时，能准确预测屈曲阈值和后屈曲行为。该方法可方便地扩展至异质梁、板、壳及其他工程结构。

英文摘要

We develop an efficient and accurate multiscale computational framework for predicting the buckling and post-buckling behaviour of elastic beams containing periodically distributed soft inclusions. The framework extends our previous multiscale, patch, computational homogenisation for linear elasticity by incorporating nonlinearity, and thus enables accurate prediction of both the buckling onset and the subsequent post-buckling response. Microscale computations are performed only within a sparse set of small subdomains (patches), while the macroscale behaviour is recovered through a proven patch-coupling algorithm. The scheme is assessed through quarter- and half-domain patch computations for beams with inclusion-to-matrix Young's modulus ratios ranging from 0.001 to 1. The results show that reducing the inclusion stiffness lowers both the critical buckling strain and the critical buckling stress, indicating an increased susceptibility to instability, while producing a milder post-buckling response with smaller transverse deflections and stress drops. Eigenvalue analysis of the Jacobian matrix accurately predicts the onset of instability and the corresponding critical strain and stress. Bifurcation diagrams of the nonlinear buckled configurations under compressive loading, and a quantitative analysis of the effect of the interpolation order on the predicted buckling and post-buckling responses, are also presented. Comparisons with full-domain simulations demonstrate that the proposed framework accurately predicts both the buckling threshold and the post-buckling behaviour while substantially reducing the computational cost. The methodology is readily extendable to heterogeneous beams, plates, shells, and other engineering structures.

发表机构

• Adelaide University（阿德莱德大学）

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