筏型地基加强梁的拓扑优化分析

Topology Optimization Analysis for Reinforced Beam of Raft Foundation

对筏型基础的加强梁分布进行拓扑优化分析,提出一种应力约束下的格栅结构的拓扑优化方法。采用正交异性增强复合材料模拟该类格栅连续体(或加肋板),该结构由无限细无限密的梁(或肋)构成。以梁在结点处的密度和方向作为设计变量,优化过程采用满应力准则法,利用有限元分析,经过少量迭代可以建立优化的材料连续分布场。借助程序自动生成的弯矩分布图,指导加强梁或加强筋的分布与走向,成为加肋板,显著地减小板的挠度,可以在原有基础上适当减小板的厚度,节省材料。

A method of topology optimization of grillage structure with stress constraints is presented and applied to analyze the reinforced beam of raft foundation. Fiber-reinforced orthotropic composite material is employed as the material model to simulate the constitutive relation of grillage-like continua/stiffened-raft. The structure contains infinite number of beams/ribs of infinitesimal spacing. The beams/ribs densities and orientations at the nodes are taken as the design variables. The optimization is accomplished by using finite element analysis and on the base of fully-stressed criterion and Grillage-like-continuum is achieved after several iterations. Finally the distribution and orientations of reinforced beam is determined according to the moment distribution produced by soft automatically. The stiffened-plate can obviously reduce the deflections of the plate, so the thickness of the plate could be reduced appropriately to save materials.