船舶开孔梁局部屈曲的无网格MLPG分析方法

目的]针对船舶开孔梁板易产生局部屈曲效应、受到较高的集中载荷作用会产生明显的结构响应和屈曲破坏力的问题,提出采用无网格数值方法对该类问题进行数值分析。方法]首先,以问题域离散节点为基础建立其紧支函数,运用加权余量法建立系统位移场离散方程,并由移动最小二乘法构造离散节点的形函数,以获得位移函数的逼近函数;然后,结合经简化的屈曲评估法,将屈曲方程特征值求解进行降阶处理,得到更为精确的屈曲载荷因子;最后,进行算例演示,比较所提方法和传统计算方法并进行验证。结果]结果显示,所提方法有效,其结果与原结构有着更高的契合度。结论]针对开孔板梁的无网格法数值分析特性可为分析各种形状的蜂窝状板梁结构提供一种新的思路。

MLPG analysis method for local buckling of ship opening beams

Objectives]In order to solve the problems of the local buckling effect and obvious structural response and buckling failure force caused by high concentrated load,a meshless numerical method is proposed to simulate the problem.Methods]Based on discrete nodes in the problem domain,this method establishes a compact support function and uses the weighted residual method to establish a discrete equation of the system displacement field.Then uses the moving least square method to construct the shape function of the discrete nodes to finally obtain the approximation function of the displacement function.Finally,combined with the simplified buckling evaluation method,the eigenvalues of the buckling equation are effectively solved to reduce the order,and a more accurate buckling load factor is obtained.Results]The effectiveness of the proposed method is verified by the comparison between the proposed method and the traditional calculation method through the demonstration of an example.The calculation results of the proposed method also have a higher degree of agreement with the original structure.Conclusion]By analyzing the characteristics of meshless numerical analysis of perforated plate beam,a new method is provided for the analysis of various shapes of honeycomb plate beam structure.