无矩阵迭代法在膜结构风振耦合分析中的应用

提出在采用浸入物体法(IOM)对膜结构和空气流体建模时,可以采用带有预定条件的无矩阵Newton-Krylov迭代算法求解浸入物体法,并引入了预定条件矩阵。将提出的无矩阵迭代方法应用于一双坡型膜结构的风振耦合分析中,得出了结构的风压和风速分布,并对带有预定条件和不带预定条件的无矩阵迭代算法进行了对比。结果表明,将带有预定条件的无矩阵迭代算法应用于膜结构风振的耦合分析中,可以得到准确结果,并使计算效率大大提高。

Application of No-matrix Iteration Method in Coupling of Wind-induced Vibration of Membrane Structure

The application of no-matrix iteration method is studied to analyze the fluid-structure interaction in wind-induced vibration of membrane structure.Firstly,immersed object method (IOM) is employed to establish the finite element formula of membrane structures and the air flow.The weak form of the fluidstructure system is given using the IOM by introducing the fictitious domain.No-matrix Newton-Krylov iteration solution with pre-condition is proposed to solve the IOM established equations,with fluid velocity,fluid pressure,and solid pressure as the main unknowns.In the method,a pre-conditioning matrix rather than Jacobian matrix is needed for the calculation.Finite difference method is adopted to substitute the allowable velocity variance,which is a key step in the method.The presented method is then applied to analyze the fluid-structure interaction in wind-induced vibration of a double-sloped membrane structure.Wind pressure distribution and velocity vectors are obtained.Comparison is made between no-matrix iteration method with pre-condition and without pre-condition.And it is found that the one with pre-condition can greatly simplify the calculation.No-matrix iteration method applies well in studying fluid-structure interaction in wind-induced vibration of membrane structure,with accurate results,and with pre-condition,calculation efficiency is enormously improved.