An Anisotropic P-adaptive Method for Linear Elastostatic and Elastodynamic Analysis of Thin-walled and Massive Structures
An Anisotropic P-adaptive Method for Linear Elastostatic and Elastodynamic Analysis of Thin-walled and Massive Structures
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发表时间：
2007-03
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通讯作者：
D. Scholz
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作者：
D. Scholz
提出了一种求解线性弹性静力和动力问题的各向异性p-自适应方法，该方法基于高阶六面体单元，允许对不同的局部方向和不同的位移矢量分量独立调整多项式阶数。用于静态问题的p-自适应方法由各向异性分层误差指示器驱动，该指示器基于将解决方案从给定的Ancillary空间局部投影到减少的分层嵌套空间的想法，从而最小化应变能的差异。动态问题的p-自适应方法是基于调整多项式次数，以实现最佳的主特征频率的表示，从初始瞬态计算与粗离散化。为此目的所需的p-自适应特征值求解器是由一个类似的构造，本地计算，各向异性分层误差指标，从而最大限度地减少瑞利商。对于本文研究的所有数值例子，p-自适应离散显示出相当高的效率和更高的收敛速度相比，均匀p-细化。因此，这种方法可以被理解为一个统一的h-和p-版本的基本问题的补救措施，即可能较差的渐近行为，特别是在解决方案中存在任何不规则性。因此，它是可能的，以获得一个有效的，完全三维离散化的薄壁和紧凑的部分结构。
An anisotropic p-adaptive method for linear elastostatic and linear elastodynamic problems is proposed, based on a high-order hexahedral element formulation allowing for an independent adjustment of the polynomial degrees for different local directions and different components of the cartesian displacement vectors. The p-adaptive method for static problems is driven by an anisotropic hierarchic error indicator based on the idea of locally projecting the solution from a given Ansatz space to a reduced, hierarchically nested space, minimizing the difference in strain energy. The p-adaptive method for dynamic problems is based on adjusting the polynomial degrees to achieve an optimal representation of the dominant eigenfrequencies, obtained from an initial transient computation with a coarse discretization. The p-adaptive eigensolver required for this purpose is driven by an analogously constructed, locally computed, anisotropic hierarchic error indicator, thus minimizing the Rayleigh quotient. For all numerical examples investigated herein, the p-adaptive discretizations show a considerably higher efficiency and higher rates of convergence compared to uniform p-refinement. This method can accordingly be understood as a remedy for one basic problem of uniform h- and p-versions, i.e. the possibly poor asymptotic behavior, especially in presence of any irregularities in the solution. As a result, it is possible to obtain an efficient, fully three-dimensional discretization of both thin-walled and compact parts of structures.