A hygro-thermal stress finite element analysis of laminated beam structures by hierarchical one-dimensional modelling

A hygro-thermal stress finite element analysis of laminated beam structures by hierarchical one-dimensional modelling Composite structure operating under severe temperature conditions and/or wet environments are very common is several engineering fields such as aeronautics, space and transportation. Hygro-thermal solicitation of beam-like structures results in a three- dimensional response that classical one-dimensional models are not always capable of describe effectively. An accurate prediction calls, then, for refined higher-order theories making this subject of research relevant and up-to-date. In this work, laminated composite Several beam models are hierarchically derived by means of a unified formulation [1, 2] that allows for atheoretical derivation of the finite elements independent from the displacements polynomial approximation order over the cross-section as well as the number of nodes per element. Elements stiffness matrix are derived in a compact form (“fundamental nucleus”) via the Principle of Virtual Displacements. As a result, a family of several one-dimensional finite elements accounting for transverse shear deformations and cross section in- and out-of-plane warping can be obtained. Temperature and humid-ity profiles are obtained by directly solving the corresponding diffusion equation(Fourier’s heat conduction equation for temperature and Fick’s law for moisture). These fields are, then, accounted as sources terms in the elastic analysis through Hooke’s law. Simply supported and cantilever configurations are considered. Numerical results in terms of temperature, moisture, displacement and stress distributions are provided for different beam slenderness ratios. Three-dimensional finite element solutions developed within the commercial code Ansys are presented for validation. The numerical investigations show that the hygro-thermo-elastic problem presents a complex three-dimensional stress state that can be efficiently obtained by a suitable choice of approximation order over the cross section: the accuracy is comparable to the reference solutions whereas the computational costs can beconsiderably reduced