Abstract
A novel Normal and Shear Deformation Theory (NSDT) for analysis of laminated composite and sandwich beams, taking into account shear deformation as well as normal deformation, is developed. The paper investigates flexural behaviors of thick laminated and sandwich beams under plane stress conditions using NSDT. A generalized displacement-based refined formulation is elucidated with inclusion of various warping functions in terms of thickness coordinates to represent shear and normal deformation effects. These effects become pronounced in thick laminated beams and particularly in sandwich beams with transversely flexible core. Present formulation satisfies the shear stress free surface conditions at the top and bottom surfaces of the beam with realistic through-the-thickness variation of transverse shear stresses. The results obtained are compared with higher order theories available in literature. It is observed that NSDT predicts displacement and stresses accurately compared to other higher order theories.
Highlights
Laminated composite structures are used in many engineering applications such as aerospace, automotive, and marine engineering
In early 18th century Euler and Bernoulli presented Elementary Beam Theory (EBT), which disregard the effect of shear deformation and under predicts deflections and over predicts natural frequencies and buckling load
In case of the present Normal and Shear Deformation Theory (NSDT), it is noteworthy that coefficient of (x) is a derivative of coefficients of shear slopes and its inclusion leads to non-trivial solution of traction-free boundaries
Summary
Laminated composite structures are used in many engineering applications such as aerospace, automotive, and marine engineering. Equivalent single layer, displacement based, strain consistent higher-order shear deformation theory for analysis of symmetric and unsymmetric laminated beams has been used by Zenkour (1999). The classical theories assume that the cross-section normal to the neutral axis remain plane after deformation It leads to gross error in predicting displacements and stresses in thick beams and laminated composites and become significantly pronounced in case of sandwich beams with transversely flexible core; especially in vicinity of singular conditions like supports and concentrated loads. It has been observed from the available open literature that many researchers have not incorporated the normal deformability in their formulations. Numerical examples are presented for validation and efficacy of the present theory
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