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首页> 外文期刊>Computer Methods in Applied Mechanics and Engineering >Adaptive hpq finite element methods for the analysis of 3D-based models of complex structures. Part 1. Hierarchical modeling and approximations
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Adaptive hpq finite element methods for the analysis of 3D-based models of complex structures. Part 1. Hierarchical modeling and approximations

机译：自适应hpq有限元方法，用于分析基于3D的复杂结构模型。第1部分。层次建模和近似

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摘要

This is a paper out of a series of three papers devoted to model- and hpq-adaptive finite element methods assigned for modeling and analysis of complex structures. In this paper we focus our attention on hierarchical models and hierarchical approximations, while the issues of error estimation and adaptivity control will be presented in the next papers of the series. In all the papers we consider the elastic structures of complex mechanical description. We apply 3D or 3D-based mechanical models, hierarchical modeling, and hierarchical approximations within our finite element formulation. In the proposed approach, the mechanical model and discretization parameters, such as the size h of the element, and the longitudinal and transverse approximation orders, p and q, can vary locally, i.e. they can be different in each finite element. The a posteriori error estimation is based on the residual equilibration methods applied to the assessment of the modeling and approximation errors. The error-controlled adaptive procedures are derived from a four-step strategy, with possible iterations on h- and p-steps.
机译：这是一系列三篇论文中的一篇，专门针对模型和hpq自适应有限元方法，这些方法分配给复杂结构的建模和分析。在本文中，我们将注意力集中在层次模型和层次近似上，而错误估计和适应性控制的问题将在本系列的下一篇论文中介绍。在所有论文中，我们都考虑了复杂的机械描述的弹性结构。我们在有限元公式中应用基于3D或3D的机械模型，层次建模和层次近似。在提出的方法中，机械模型和离散化参数（例如元素的大小h）以及纵向和横向近似阶数p和q可以局部变化，即，在每个有限元中它们可以不同。后验误差估计基于残差平衡方法，该方法适用于建模误差和近似误差的评估。误差控制的自适应过程是从四步策略中得出的，可能在h步和p步上进行迭代。

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