Tokovyy Yuriy V, Yasinskyy Anatoliy V, Lubowicki Sebastian, Perkowski Dariusz M
Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, National Academy of Sciences of Ukraine, 79060 Lviv, Ukraine.
Department of Applied Mathematics, Institute of Applied Mathematics and Fundamental Sciences, National University Lviv Polytechnic, 79013 Lviv, Ukraine.
Materials (Basel). 2021 Dec 31;15(1):297. doi: 10.3390/ma15010297.
A unified approach is presented for constructing explicit solutions to the plane elasticity and thermoelasticity problems for orthotropic half-planes. The solutions are constructed in forms which decrease the distance from the loaded segments of the boundary for any feasible relationship between the elastic moduli of orthotropic materials. For the construction, the direct integration method was employed to reduce the formulated problems to a governing equation for a key function. In turn, the governing equation was reduced to an integral equation of the second kind, whose explicit analytical solution was constructed by using the resolvent-kernel algorithm.
本文提出了一种统一的方法，用于构建正交各向异性半平面的平面弹性和热弹性问题的显式解。对于正交各向异性材料弹性模量之间的任何可行关系，这些解以减少与边界加载段距离的形式构建。在构建过程中，采用直接积分法将所提出的问题简化为一个关键函数的控制方程。反过来，控制方程又被简化为第二类积分方程，其显式解析解通过使用预解核算法构建。
