A new analytical approach is presented for gravity-induced stresses in elastic half plane with a slope. The half plane is mapped onto the unit circle in ζ plane by conformal transformations. The mapping function proposed by Schwarz-Christoffel is irrational and difficult to be applied to the problem in the paper. Therefore, the explicit expression of the mapping function, which is easy to use and has high precision, is proposed through power series approximation. Based on the complex potentials with body force, a simple method for solving gravity-induced stresses which do not involve analytic continuation and Cauchy integral is established. The analytic functions are expressed as power series. Through the stress boundary condition on the ground surface, a set of linear equations with the coefficients of the power series can be directly constructed and solved. The stress results obtained by the presented analytical method agree well with the numerical solution. The stress distributions under different Poisson’s ratio and slope angle are studied.

提出了一种新的分析方法，用于分析具有斜率的弹性半平面中的重力引起的应力。半平面映射到ζ 中的单位圆上平面通过保形变换。Schwarz-Christoffel 提出的映射函数是不合理的，难以应用于论文中的问题。因此，通过幂级数近似提出了使用方便、精度高的映射函数的显式表达式。基于具有体力的复势，建立了一种不涉及解析延拓和柯西积分的简单求解重力应力的方法。解析函数表示为幂级数。通过地表应力边界条件，可以直接构造和求解一组具有幂级数系数的线性方程组。通过所提出的分析方法获得的应力结果与数值解非常吻合。