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Abstract
Quasi-static linear behavior of composite laminates is formulated by an
anisotropic hygrothermal-viscoelastic constitutive model. Based on the variational
principle of linear viscoelasticity, a specially developed numerical model (direct
time integrations) has been introduced for the solution of hygrothermal-viscoelastic
boundary value problems in anisotropic laminates. The proposed model exploits a
recursive approach to save both the computational time and storage. Throughout the
present study, the material is assumed to be non-aging and thermorheologically
simple. 2-D theories (Mindlin alld higher-order shear) and 3-D elements are
employed in the framework of viscoelastic analysis of composite structures
subjected to mechanical and hygrothermal loads. The comparative studies show
good agreement with the previous analytical and computational models. The
viscoelastic displacement fields in the transverse direction of the cross-ply and
angle ply laminates are calculated, and the stacking sequence of the laminates, the
skew angle, temperature and moisture effects are discussed in detail.
Zocher’s recursive formula is limited only to the quasi-static analysis,
therefore the proposed model exploits the aforementioned formula for analyzing
dynamic responses of composite structures with time taking into account the
temperature and moisture-dependent linear viscoelastic damping. Variational
principles, the Newmark average acceleration method and 2-D theories (Mindlin
and higher-order shear only) are used. Recursion formulas have been introduced in
order to reduce computer storage where only the previous time state is required to
compute the next time state. Verification studies were conducted to evaluate the
accuracy and convergence of the present numerical algorithm, and they show that
the numerical solutions of the proposed model are in favorable agreement with the
analytical solutions developed for special cases. Also, the comparative study shows
that the present elastic response of cross ply unsymmetric laminates agrees well
with the closed form solution of Reddy. Numerical results for displacement fields
are presented showing the effects of plate side-to-thickness ratio, stacking sequence,
skew angle, the environment, etc. on the dynamic response. Moreover, transient
displacement fields for rectangular laminates as well as skew ones aloe introduced to
show the influence of load release and pulse length on the response.