Axial Force of the Member due to the Temperature Change in Winkler Model

Winkler 모델에서 온도변화에 의한 부재의 축력

In the axial Winkler model, the axial strain increased by the temperature change T is ${\alpha}T$, where ${\alpha}$ is the coefficient of thermal expansion. When a point thermal load T is applied x=a, the thermal strain can not be expressed in the form of continuous function in the given range. But using the generalized function, the thermal strain can be expressed like ${\alpha}T{\delta}_0$(x-a), which is differentiable. And that, with the aid of characteristics of generalized functions the particular solution of the governing differential equation is also easily obtained. When the solution of the point thermal loaded case is known, then the solution of the partial or whole loaded cases can be obtained by the proper integration over the given range. This study shows that how the displacement u(x) and axial force N(x) can be obtained, depending on the ends conditions and boundary conditions, when thermal loads are applied. Moreover, when the axial spring constant k changes, the trend of N(x) and u(x) can be known by the nondimensionalized N(x) and u(x).