Gajewski Tomasz, Staszak Natalia, Garbowski Tomasz
Institute of Structural Analysis, Poznan University of Technology, Piotrowo 5, 60-965 Poznan, Poland.
Doctoral School, Poznan University of Life Sciences, Wojska Polskiego 28, 60-637 Poznan, Poland.
Materials (Basel). 2023 Jul 8;16(14):4897. doi: 10.3390/ma16144897.
In engineering practice, one can often encounter issues related to optimization, where the goal is to minimize material consumption and minimize stresses or deflections of the structure. In most cases, these issues are addressed with finite element analysis software and simple optimization algorithms. However, in the case of optimization of certain structures, it is not so straightforward. An example of such constructions are bubble deck ceilings, where, in order to reduce the dead weight, air cavities are used, which are regularly arranged over the entire surface of the ceiling. In the case of these slabs, the flexural stiffness is not constant in all its cross-sections, which means that the use of structural finite elements (plate or shell) for static calculations is not possible, and therefore, the optimization process becomes more difficult. This paper presents a minimization procedure of the weight of bubble deck slabs using numerical homogenization and sequential quadratic programming with constraints. Homogenization allows for determining the effective stiffnesses of the floor, which in the next step are sequentially corrected by changing the geometrical parameters of the floor and voids in order to achieve the assumed deflection. The presented procedure allows for minimizing the use of material in a quick and effective way by automatically determining the optimal parameters describing the geometry of the bubble deck floor cross-section. For the optimal solution, the concrete weight of the bubble deck slab was reduced by about 23% in reference to the initial design, and the serviceability limit state was met.
在工程实践中，人们经常会遇到与优化相关的问题，其目标是使材料消耗最小化，并使结构的应力或挠度最小化。在大多数情况下，这些问题通过有限元分析软件和简单的优化算法来解决。然而，在某些结构的优化方面，情况并非如此简单。这种结构的一个例子是气泡夹层天花板，为了减轻自重，在天花板的整个表面上规则地布置了空气腔。对于这些楼板，其抗弯刚度在所有横截面上并非恒定不变，这意味着无法使用结构有限元（板或壳）进行静力计算，因此，优化过程变得更加困难。本文提出了一种使用数值均匀化和带约束的序列二次规划方法来使气泡夹层楼板重量最小化的程序。均匀化可以确定楼板的有效刚度，在下一步中，通过改变楼板和空洞的几何参数来依次校正有效刚度，以达到假定的挠度。所提出的程序能够通过自动确定描述气泡夹层楼板横截面几何形状的最优参数，快速有效地减少材料的使用。对于最优解，气泡夹层楼板的混凝土重量相对于初始设计减少了约23%，并且满足了正常使用极限状态。
