用切比雪夫多项式计算薄板的弯曲变形和临界压力

CALCULATION OF THIN PLATES BENDING EEFORMATION AND CRITICAL PRESSURE BY THE TCHEBYCHEV'S POLYNOMIALS

本文利用第二类切比雪夫多项式作为试函数,并结合康脱洛维奇变分解法,用于薄板的能量泛函来求解矩形板在各种支承条件下承受均布载荷或集中力时的弯曲变形和矩形板屈曲时的临界压力。虽然采用的是一级近似计算,但计算结果表明,这种方法简单易行,在工程实用中是足够精确的。

In this paper trial functions of the second Tchebychev's polynomials is used with Cantorovich variational method in energy functional of thin plate. Bending deformaion of rectangle plate under even loads or concentrate force with several bearing and critical pressure in buckling is resolved. Though the first similar is used but calculations indicate that this method is simple and exact in engineering.