论文标题
关于建筑中最佳形状的存在
On the existence of optimal shapes in architecture
论文作者
论文摘要
我们考虑建筑中弹性系统的形状优化问题。在这种情况下，一个典型的问题是确定接近最初提出的最大稳定性结构。我们显示了在有限的Lipschitz域的类别中以及具有分形的边界的较宽类别的范围统一域中的类别中的存在。在第一种情况下，最佳形状意识到了整个类别中给定能量功能的最大功能，在第二种情况下，它意识到了最小值。作为一个具体的应用，我们讨论了在雪载下的最大稳定屋顶结构的存在。
We consider shape optimization problems for elasticity systems in architecture. A typical question in this context is to identify a structure of maximal stability close to an initially proposed one. We show the existence of such an optimally shaped structure within classes of bounded Lipschitz domains and within wider classes of bounded uniform domains with boundaries that may be fractal. In the first case the optimal shape realizes the infimum of a given energy functional over the class, in the second case it realizes the minimum. As a concrete application we discuss the existence of maximally stable roof structures under snow loads.
