等厚度楔形杆的应力分析

本文将应力场分为基本应力场和修正应力场两个部分。基本应力场的应力σ_x用勒让德级数展开,级数的前两项系数用截面法确定;其他应力τ_(xy),σ_y由平衡方程和侧表面边界条件确定;再用余能原理确定其余各项系数。由于该级数收敛很快,故可得到封闭解并能给出该解的应用范围,为精确满足自由端的静力边界条件,又引入一个从自由端到固定端迅速衰减的修正应力场,该应力场的应力在自由端等于已知外力与基本应力解之差。其确定方法与基本应力场相同,它也有一个封闭解。将以上两应力场相加卽可得到满足全部边界条件的解。

STRESS ANALYSIS OF TAPERED BARS WITH UNIFORM THICKNESS

In this paper,the stress field is divided into two parts:the basic stress field and the modified stress field.In the basic stress field,the stress component x is expanded into legendre series.The first two terms of this series are determined by the sectional method.The stress components txy and ay are expressed by the equations of equilibrium and boundary conditions of forces on lateral surfaces.All of the other coefficients are defermined by the princple of minimum complementary energy.Due to the rapid conver-gency of the above series,a closed form solution and its range of availability can be obtained.To satisfy the boundary condition of force at free end exactly,it is necessary to introduce a modified stress field,in which,stress at free end is equal to the differences of bnundary surface tractions and basic stress field and damped out rapidly from the free end to the fixed end.This stress field is determined by the equations of equilibrium,boundary conditions of forces and principle of minimum complementary energy and also has a closed form solution.Finally,a complete stress solution can be obtained by the superposition of the above two fields.