Reissner模型中厚板边界元法的进一步应用

FURTHER APPLICATIONS OF BEM FOR MODERATELY THICK PLATES OF REISSNER’S MODEL

利用边界单元法求解Reissner模型中厚板弯曲问题以及对解的精度和收敛性的研究已在文献中作了详细的研究.在文献中主要求解了矩形板、菱形板和斜板的弯曲问题.本文主要研究悬臂板、中心穿孔、偏心穿孔的简支方板的弯曲问题并与文献的薄板边界元结果及其它已有文献的结果相对照.

In this paper, the BEM of Reissner's model plates is further applied to bending porblemsof cantilevered plates, simply-supported square plates with perforated eccentric and centric ho-les, cantileveral rhombic plates and arbitrary quadrilateral plates. Double nodes or partly dis-continuous elements are employed at corners and edge points, and modified Bessel func-tions are approximated by polynomial expressions, singular integrations are calculated usingcubic nonlinear polynomial transformations at singular points and the unified standard Gau-ssian integral scheme. Results obtained show that both thin and thick plates with arbitrary geometric shapes andboundary conditions can be analysed after the above treatments, and the computational accuracyis higher, input data fewer, and computer time less.