加勁板之彈性支承的剛度在均勻横向負載下的最佳化分析

Abstract

本研究的主要目的是將加勁板之彈性支承的剛度最佳化，使加勁板在均勻橫向力(uniform lateral load)作用時，其彈性支承有均勻的位移。 本研究將加勁板視為板與梁的組合，將彈性支承視為直線彈簧。本研究採用線性有限元素法分析邊界上具彈性支承的加勁板。 本研究採用平面三角殼元素與開口薄壁梁元素來模擬加勁板，在梁元素與板元素的結合處有共同節點及相同自由度，即梁元素的節點位於殼的中心而且有三個平移及三個旋轉自由度。 本研究中提出一個以彈性支承剛度為變數的目標函數及其拘束條件。本研究利用牛頓法提出一個數值程序以求得使目標函數有最小值且滿足拘束條件的彈性支承剛度，即求得最佳化的彈性支承剛度。本研究以數值例題探討不同加勁板之最佳化的彈性支承剛度，彈性支承變形的分佈及加勁板的最大撓度。

In order to unify deformation of the elastic restraints for stiffened plates with elastically restrained edges under uniform lateral load, the stiffness of the elastic restraints is chosen to be the design variables and an optimization method is proposed to find the optimal stiffness of elastic restraints. The stiffened plate is composed of a plate and stiffeners. The stiffeners and the elastic restraints are taken to be beams and linear spring, respectively. The finite element method is used here for the linear analysis of stiffened plate. The triangular flat shell element and the thin-walled beam element are used here. Because the nodes of the beam element must coincide with those of the shell element, the nodes of the beam element are shifted to the mid-plane of the plate. A numerical procedure based on the Newton method is proposed to find the optimal stiffness of the elastic restraints. Numerical examples are studied to demonstrate the accuracy of the proposed method and to investigate the distribution of the optimal stiffness of the elastic restraints, the deformation of the elastic restraints and deflection of the stiffened plate for stiffened plate with different number of stiffeners, different cross section of stiffeners and different thickness of plate.