弹性薄板弯曲问题的边界轮廓法

导出了弹性薄板弯曲问题边界积分方程的另一种形式，基于这种方程，提出了平板弯曲问题的边界轮廓法，讨论了三次边界单元边界轮廓法的计算列式，并给出了计算内力的边界轮廓法方程。该法无需进行数值积分计算，完全避免了角点问题和奇异积分计算。给出的算例，与解析解相比较，证实该方法的有效性。

A BOUNDARY CONTOUR METHOD FOR THENUMERICAL SOLUTION OF ELASTIC THIN PLATEBENDING PROBLEMS

A variant of the usual boundary element method, called the boundarycontour method, has been presented for elasticity in the literature inrecent years. The new method requires no numerical integrals at all fortwo-dimensional problems and numerical evaluation of the line integralsonly for three-dimensional problems. 　　A boundary contour method for elastic thin plate bending problems hasbeen presented first in this paper. By defining new boundary variables anew type of the boundary integral equation from the Betti's formulationhas been derived. It is shown that the integrand vector of the boundaryintegral equation has the property of divergence free everywhere exceptat the point of singularity if the field variables correspond to a forcefree elastic plate with the same elastic constants as the fundamentalsolution. Therefore, the line integral on the usual boundary elements istransformed into the evaluation of potential functions at points on theboundary of a plate. The cubic shape function is chosen according to thecomplex expression of deflection solutions and the configuration ofcorrespondent boundary elements is given. The numerical implementationwith cubic boundary elements is carried out. This approach avoidscompletely numerical integration and the modeling of corners. 　　The formulation of the boundary contour method is presented forevaluating moments. This formulation is regular at the points of theboundary except the ends of boundary elements such that the effect ofthe boundary layer is removed. 　　To verify the effectiveness of the present method, some plate bendingexamples are solved by the present method. Comparison between theresults of the boundary contour method and the analytical results showswell agreement.