The general approximate solutions for the two-dimensional thermoelastic problems with a nearly circular hole are provided in this study. Based on Stroh formalism and the method of conformal mapping, the boundary perturbation analysis is applied to solve the problems of a hole with arbitrary shape. The radius of the hole considered here is represented as a sum of a reference constant and a perturbation magnitude that is expanded into a Fourier series. In order to illustrate the applicability and efficiency of the present approach, special examples associated with polygonal hole problems are solved explicitly and discussed in detail. Since the general solutions have not been found in the literature, comparison is made with some special cases for which the analytical solutions exist, which shows that our proposed method is effective and general.

The effect of stress distribution due to the changes of the distal screw alignment in relation to the Gamma nail and the femoral shaft is thoroughly studied in this paper. Failure of the Gamma nail composite occurs through the cranial aperture of the distal screws and the insertion hole for the lag screw due to nonunion, delayed-union and continued weight-bearing. A three-dimensional finite element model was used to study the fractured femur, the Gamma nail, the lag screw and the distal locking screws. The first and the second distal screws were inserted into the Gamma nail in four different configurations. We found that the stress of the Gamma nail composite was substantially reduced with the two screws configured in the anterior to posterior direction. This alignment can bear greater loading in the more demanding fracture types. In the subtrochanteric fracture or the comminuted fractures at the proximal femur, the optimal alignment of the two distal screws was in the anterior to posterior direction.

The thermoelastic problem associated with a point heat source embedded in an anisotropic body containing an elliptic hole or a rigid inclusion is considered in this paper. By using the formalism of Stroh [1], the approach of analytic function continuation and the technique of conformal mapping, the expression for the temperature, displacements and stress functions is expressed in explicit matrix form. The present derived solutions are also valid for some special problems such as a crack or a rigid line inclusion if one lets the minor axis of the ellipse approach to zero. The stress intensity factors induced by a point heat source are also obtained.