Nonintrusive parametric solutions in structural dynamics
Nonintrusive parametric solutions in structural dynamics
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DOI：
10.1016/j.cma.2021.114336
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发表时间：
2021-11
影响因子：
7.2
通讯作者：
F. Cavaliere;S. Zlotnik;R. Sevilla;X. Larráyoz;P. Díez
中科院分区：
文献类型：
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作者：
F. Cavaliere;S. Zlotnik;R. Sevilla;X. Larráyoz;P. Díez
本文提出了一种能够求解参数模态分析的非侵入式降阶方法。主要目标是能够有效地识别用户定义的参数的变化如何影响结构的基本固有频率和相应的模态振型的动态响应。利用适当的广义分解（PGD）原理，提出了一种参数化的逆幂法（IPM）。所提出的方法利用所谓的封装PGD工具箱，并包括一个新的算法计算的参数对象的平方根。只有一个离线计算，建议的PGD-IPM方法提供了一个解析的参数表达式的最小（幅度）的特征值（或自然频率）和相应的特征向量（模态），其中包含所有可能的解决方案，为每一个组合的参数在预定义的范围内。引入了一种拉格朗日乘子收缩技术来计算后续的特征对，该技术也可以有效地克服自由-自由结构的刚度矩阵奇异性。所提出的方法是非侵入性的，因此，它是可能的商业有限元（FE）包集成。两个数值例子强调的技术的属性。第一示例包括一个材料和一个几何参数。第二个例子显示了一个更现实的工业例子，其中的非侵入性的方法证明了采用商业FE包组装的FE矩阵。最后，一个多目标优化研究证明，开发的方法可以显着地帮助决策在一个新的设计过程的初步阶段。
A nonintrusive reduced order method able to solve a parametric modal analysis is proposed in this work. The main objective is being able to efficiently identify how a variation of user-defined parameters affects the dynamic response of the structure in terms of fundamental natural frequencies and corresponding mode shapes. A parametric version of the inverse power method (IPM) is presented by using the proper generalised decomposition (PGD) rationale. The proposed approach utilises the so-called encapsulated PGD toolbox and includes a new algorithm for computing the square root of a parametric object. With only one offline computation, the proposed PGD-IPM approach provides an analytical parametric expression of the smallest (in magnitude) eigenvalue (or natural frequency) and corresponding eigenvector (mode shape), which contains all the possible solutions for every combination of the parameters within pre-defined ranges. A Lagrange multiplier deflation technique is introduced in order to compute subsequent eigenpairs, which is also valid to overcome the stiffness matrix singularity in the case of a free-free structure. The proposed approach is nonintrusive and it is therefore possible to be integrated with commercial finite element (FE) packages. Two numerical examples are shown to underline the properties of the technique. The first example includes one material and one geometric parameter. The second example shows a more realistic industrial example, where the nonintrusivity of the approach is demonstrated by employing a commercial FE package for assembling the FE matrices. Finally, a multi-objective optimisation study is performed proving that the developed method could significantly assist the decision-making during the preliminary phase of a new design process.