The Numerical Method
The Numerical Method
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DOI：
10.1007/978-3-540-79111-9_4
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
M. Lucchesi;C. Padovani;G. Pasquinelli;N. Zani
中科院分区：
文献类型：
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作者：
M. Lucchesi;C. Padovani;G. Pasquinelli;N. Zani
在第三章中我们证明了，给定载荷（α u，α s，B），平衡问题的所有弱解的集合恰好是势能的所有极小元的集合（命题3.2，3.3和3.4）。我们还证明了每个强解都是余能的最小值（命题3.5）。从这样的结果，它遵循的数值解的平衡问题的砖石状固体可以通过不同的方法计算。最常见的方法是基于应用于平衡问题[1]，[68]，[70]，[76]，[96]的弱公式（3.21）的有限元法的位移公式。在[32]中，平衡问题通过最小化一组合适的应力场上的余能泛函来解决。另一种可能的方法是最小化所有运动学容许状态集合上的势能[2]。假设读者熟悉有限元法，否则可在[25]、[18]、[6]、[20]、[21]、[84]、[85]和[57]中找到详细说明。
In chapter 3 we proved that, given the load (̂u, ̂s, b), the set of all weak solutions to the equilibrium problem is exactly the set of all minimizers of the potential energy (propositions 3.2, 3.3 and 3.4). We moreover showed that each strong solution is a minimizer for the complementary energy (proposition 3.5). From such results, it follows that a numerical solution to the equilibrium problem of masonry-like solids can be calculated via different methods. The most common approach is based on a displacement formulation of the finite element method applied to the weak formulation (3.21) of the equilibrium problem [1],[68],[70],[76],[96]. In [32] the equilibrium problem is instead solved by minimizing the complementary energy functional on a suitable set of stress fields. Another possible approach is to minimize the potential energy on the set of all kinematically admissible states [2]. It is assumed that the reader is familiar with the finite element method, otherwise, detailed descriptions can be found in [25],[18],[6],[20],[21],[84],[85] and [57].