Optimized design of thermo-mechanically loaded non-uniform bars by using a variational method

Abstract

The present paper evaluates the axial strain and stress of a thermo-mechanically loaded non-uniform bar by using a numerical method based on a variational principle. The solutions are obtained up to the elastic limit of the material based on the assumptions that material properties are independent of temperature variation and plane cross-sections remain plane maintaining axisymmetry. This approximation is carried out by Galerkin's principle, using a linear combination of sets of orthogonal co-ordinate functions which satisfy prescribed boundary conditions. The solution algorithm is implemented with the help of MATLAB® computational simulation software. Some numerical results of thermoelastic field are presented and discussed for different bar materials such as mild steel, copper, aluminium alloy 6061 (Al alloy 6061), aluminium alloy 7075 (Al alloy 7075) and diamond. The effect of geometry parameters like aspect ratio, slenderness ratio and the type of taperness is investigated and the relevant results are obtained in dimensional form. The term bar used in this paper is in generic sense and hence the formulation is applicable for all one dimensional elements, e.g., rods, pipes, truss members, etc.