The boundary conditions are idealized in mechanics of materials. However, small imperfections may exist which deviate the conditions from being ideal. The non-ideal boundary conditions are modeled using perturbations and applied to buckling problems of columns. A linear and a nonlinear model are treated separately. The effect of such conditions on the critical loads and buckling shapes are analytically calculated using the strained parameter perturbation method. Depending on the mode numbers and the physical parameters, the critical loads may either decrease or increase. The mode shapes of the buckling are also distorted by the imperfections in the support conditions.

Buckling is one of the most complicated concepts in mechanical engineering. Buckling often happens by compressive loads on thin structures. Thermal gradient between two ends of a column may cause a deflection in it. This will add an extra deformation to the one provided by compressive loads on the column. This phenomenon occurs when two ends of the column are at different temperatures, which can be seen at various structures. Because of the considered temperature gradients, the critical load of the column will decrease. In the current paper, various columns are modeled and the effect of thermal gradient and compressive load and other parameters on the Bi-material columns are studied. In other words, influences of compressive load and temperature gradient on critical load of Bi-material columns with interface crack are investigated. Effect of change in each parameter on critical load of column and crack opening was investigated. First, the thermal gradient was only applied to the model and in the next step; only the effect of mechanical loading was studied. Furthermore, artificial neural network (ANN) was used to extend the results to a bigger range of temperature conditions through the columns. Based on the results, ANN and finite element results are in a good agreement and the thermal effects may have a significant role in buckling of the column.