Mechanics of Solids ( IF 0.7 ) Pub Date : 2021-02-26 , DOI: 10.3103/s0025654420080269 N. N. Shavlakadze , O. M. Jokhadze , S. S. Kharibegashvili
Abstract
The problem to determine the mechanical field in a homogeneous half-plane supported by a finite homogeneous stringer, material of which obeys the nonlinear Hooke’s law, is considered. The contact between the plate and stringer is realized by a thin glue layer. The posed problem is reduced to a nonlinear singular integrodifferential equation. Using the Schauder fixed-point principle, we prove the existence of a solution to this equation. The uniqueness of the solution of the problem is proved. Using the small-parameter method, we obtain a system of recurrence linear singular integral equations of the first kind.
中文翻译:
有限长度非线性变形纵梁粘在边界上的弹性板的接触问题
摘要
考虑了确定由有限均质纵梁支撑的均质半平面中的机械场的问题,该有限均质纵梁的材料服从非线性胡克定律。板和纵梁之间的接触是通过薄胶层实现的。提出的问题简化为非线性奇异积分微分方程。使用Schauder定点原理,我们证明了该方程的解。证明了问题解决方案的唯一性。使用小参数方法,我们获得了第一类递归线性奇异积分方程组。