大型圆形贮液池力学分析中的重心插值拟谱法

BARYCENTRIC INTERPOLATION PSEUDOSPECTRAL METHOD FOR ANALYZING CIRCULAR CONCRETE TANKS WITHOUT PRESTRESSING

  • 摘要: 针对传统大型圆形贮液池力学分析方法计算复杂、精度不高的问题,用拟谱法对圆形贮液池的线弹性静力问题进行了研究. 采用重心Lagrange插值多项式建立未知函数的微分矩阵,将池壁的控制方程表示为代数方程组. 通过求解代数方程组,求得池壁各个离散点挠度,进而采用微分矩阵直接求得池壁内力.算例表明,该方法原理简单,易于程序实现和数值计算精度高.

     

    Abstract: Traditional analyses of circular concrete tanks withoutprestressing suffer from some drawbacks, such as complicated computation andunsatisfactory accuracy. In this paper, a pseudospectralmethod based on barycentric Lagrange interpolation for linear elastic staticanalysis of tank is proposed. The differentiation matrix for the unknownfunction is constructed by using barycentric Lagrange interpolation. Thegoverning equations of equilibrium, in terms of stress resultants andcouples, are put into a generalized displacement form by the useof strain-displacement relationships and constitutive equations. Thegoverning equation of tank wall can be expressed as a set of algebraicequations by the pseudospectral method. With boundary conditions,the algebraic equation system is solved to obtained the deflections at discrete points. The principle of this method is simple and ease to program.The accuracy and the numerical stability are good.

     

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