矩形加肋板肋条布置的无网格优化
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摘要
为达到不同静荷载下加肋板中心点挠度值最小的目标,基于无网格法和约束随机方向法研究了肋条布置的优化.由于在优化过程中需要不断改变肋条位置,而无网格法利用一系列节点去离散结构,当肋条位置发生改变时并不需要重新布置节点,减少了计算量.利用无网格法计算加肋板挠度,并利用约束随机方向法对肋条位置进行优化,算例结果验证了该方法的有效性.
In order to minimize the central deflection of a stiffened plate under different static loads,rib layout optimization of the plate was studied based on a meshfree formulation incorporating the constrained random direction method. Because the rib position needed to be changed from time to time during the optimization process,in the proposed method,a series of nodes were used to discretize the structure; and the nodes did not need to be redistributed when the rib position changed. The deflection of the stiffened plate was calculated by the meshfree formulation,and the rib layout of the plate was optimized by the constrained random direction method. The validity of the proposed method was verified by several examples.
In order to minimize the central deflection of a stiffened plate under different static loads,rib layout optimization of the plate was studied based on a meshfree formulation incorporating the constrained random direction method. Because the rib position needed to be changed from time to time during the optimization process,in the proposed method,a series of nodes were used to discretize the structure; and the nodes did not need to be redistributed when the rib position changed. The deflection of the stiffened plate was calculated by the meshfree formulation,and the rib layout of the plate was optimized by the constrained random direction method. The validity of the proposed method was verified by several examples.
引文
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[4]彭林欣.矩形加肋板线性弯曲分析的移动最小二乘无网格法[J].计算力学学报,2012,29(2):210-216.
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[6]常利武.基于MLS近似的无单元/无网格方法及其在高阶连续结构数值模拟中的应用[D].郑州:郑州大学,2017.
[7] BELYTSCHKO T,LU Y Y,GU L. Element-free Galerkin methods[J]. International journal for numerical methods in engineering,1994,37(2):229-256.
[8] CHEN J S,PAN C H,WU C T,et al. Reproducing kernel particle methods for large deformation analysis of non-linear structures[J]. Computer methods in applied mechanics and engineering,1996,139(1):195-227.
[2] BRYAN G H. On the stability of a plane plate under thrust in its own plane,with applications to the"buckling"of the sides of a ship[J]. Proceedings of the London mathematical society,1890,22(1):54-67.
[3] JAMES M. Theory of elastic stability[M]. New York:McGraw-Hill,1961.
[4]彭林欣.矩形加肋板线性弯曲分析的移动最小二乘无网格法[J].计算力学学报,2012,29(2):210-216.
[5] CHENG K T,OLHOFF N. An investigation concerning optimal design of solid elastic plates[J]. International journal of solids and structures,1981,17(3):305-323.
[6]常利武.基于MLS近似的无单元/无网格方法及其在高阶连续结构数值模拟中的应用[D].郑州:郑州大学,2017.
[7] BELYTSCHKO T,LU Y Y,GU L. Element-free Galerkin methods[J]. International journal for numerical methods in engineering,1994,37(2):229-256.
[8] CHEN J S,PAN C H,WU C T,et al. Reproducing kernel particle methods for large deformation analysis of non-linear structures[J]. Computer methods in applied mechanics and engineering,1996,139(1):195-227.