Abstract The focus of the present investigation is on the introduction of uncertainty directly in reduced order models of the nonlinear geometric response of structures following maximum entropy concepts. While the approach was formulated and preliminary validated in an earlier paper, its broad application to a variety of structures based on their finite element models from commercial software was impeded by two key challenges. The first of these involves an indeterminacy in the mapping of the nonlinear stiffness coefficients identified from the finite element model to those of the reduced order model form that is suitable for the uncertainty analysis. The second challenge is that a key matrix in the uncertainty modeling was expected to be positive definite but was numerically observed not to be. This latter issue is shown here to be rooted in differences in nonlinear finite element modeling between the commercial software and the theoretical developments. Both of these challenges are successfully resolved and applications examples are presented that confirm the broad applicability of the methodology.

中文翻译：

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使用非侵入式降阶模型对非线性几何响应进行结构不确定性建模

摘要 本研究的重点是在遵循最大熵概念的结构非线性几何响应的降阶模型中直接引入不确定性。虽然该方法在较早的一篇论文中得到了制定和初步验证，但它在基于商业软件有限元模型的各种结构中的广泛应用受到两个关键挑战的阻碍。第一个涉及从有限元模型确定的非线性刚度系数映射到适用于不确定性分析的降阶模型形式的那些的不确定性。第二个挑战是不确定性建模中的一个关键矩阵预计是正定的，但在数值上观察到不是。这里显示后一个问题的根源在于商业软件和理论发展之间非线性有限元建模的差异。这两个挑战都得到了成功解决，并提供了应用示例，证实了该方法的广泛适用性。