子空间变分原理的修正及其应用于确定梁的剪切系数

REVISED SUBSPACE VARIATIONAL PRINCIPLE AND ITS APPLICATIONS TO DETERMINE SHEAR COEFFICIENTS OF BEAMS

首先简化子空间变分原理的数学结构，据此表明子空间变分原理存在一定的奇异性，并提出消除奇异性的修正子空间变分原理．作为应用，计算了单材料多种截面的剪切系数并与Ｃｏｗｐｅｒ解做了比较，结果表明修正后的子空间变分原理是正确的．我们还进一步计算了一个夹层梁在Ｃｏｗｐｅｒ意义下的剪切系数，说明了子空间变分原理处理复杂截面的能力．

in this paper, we arrive at the simplified mathematical structure of the subspace variational functional, where a singularity is found. To remove this singularity, a revised subspace variational principle is proposed. As applications, the shear coefficients of single material beams with various shapes of cross-section are calculated, which agree well with Cowper's analytical solutions of shear coefficients for some simple cross-section problems. We have further calculated the shear coefficient of a sandwiched beam based on the Gordaninejad's model, in order to exhibit the capability of the revised subspace variational principle in estimating the shear coefficients of beams with multiply materials.