A thermal stress finite element analysis of isotropic and laminated beams via unified formulation

In this work the mechanical and thermal behaviour of three-dimensional isotropic and laminated beams is investigated. The beam-like three dimensional structure is modelled through refined 1D finite elements obtained via hierarchical expansion of the displacement field over the cross-section coordinates. The approximation order of the displacements is a free parameter that leads to the formulation of a family of several beam elements. Linear, quadratic and cubic one-dimensional finite elements are considered. The governing algebraic equations are obtained via the Principle of Virtual Displacements.The temperature field is obtained by exactly solving Fourier's heat conduction equation and it is treated as an external load within the mechanical analysis. Results in terms of displacements and stresses are validated towards three-dimensional FEM results as well as analytical solutions. Numerical investigations show that the proposed finite elements yield accurate yet computationally efficient solutions for the three-dimensional stress state generated by the thermal load.