A variational asymptotic approach for hygrothermal analysis of composite laminates

A hygrothermal model for analyzing composite laminates under both mechanical and hygrothermal loadings is constructed by the variational asymptotic method (VAM). The original 3-D nonlinear, one-way coupled, hygrothermoelasticity problem is formulated based on a set of intrinsic variables defined on the reference plane and for arbitrary deformation of the normal line. Then the VAM is used to rigorously split the 3-D problem into two problems: a nonlinear, 2-D, plate analysis over the reference plane to obtain the global deformation and a linear analysis through the thickness to provide the 2-D generalized constitutive law and the recovering relations to approximate the original 3-D results. The nonuniqueness of asymptotic theory correct up to a certain order is used to cast the obtained asymptotically correct second-order free energy into a Reissner–Mindlin type model to account for transverse shear deformation. The present theory is implemented into the computer program, Variational Asymptotic Plate and Shell Analysis (VAPAS). Results from VAPAS for several cases have been compared with the exact hygrothermal solutions, classical lamination theory and first-order shear-deformation theory to demonstrate the accuracy and power of the proposed theory and use of VAPAS. The proposed theory can achieve an accuracy comparable to high-order layerwise theories with many more degrees of freedom at the cost of a first-order shear-deformation theory.

► A hygrothermoelastic model is constructed by variational-asymptotic method.
► Dimensional reduction is carried out systematically without kinematical assumptions.
► A general 2D constitutive law is obtained by the 1D through-the-thickness analysis.
► Hygrothermal distribution is approximated by a layerwise fourth-degree polynomial.
► Original 3D results are accurately reproduced from a Reissner–Mindlin plate analysis.