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Variable-stiffness shells are curved composite structures in which the fibre-reinforcement follow curvilinear paths in space.
With the advancement of fiber placement technology, it is possible to manufacture fibers even with curvilinear paths or so-called variable stiffness (VS) composites.
A transverse stress recovery procedure taking into account the variability of the structural properties due to the fibers' curvilinear paths is also presented.
A composite laminate may be designed as a permutation of several straight-fiber layers or as a matrix embracing fibers positioned in curvilinear paths.
Variable stiffness composites, where fibre angles are spatially varied by steering the tows in curvilinear paths to optimise the structural response, have been a subject of intensive study.
Spatial variation of stiffness can be induced by steering composite fibers in curvilinear paths to give beneficial load and stiffness distribution patterns.
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The curvilinear path defined in the previous subsection is the trajectory of the particle.
It is pointed out that the curvilinear path is caused by heterogeneity.
(Curvilinear path) A set of maps γ such that γ : T → Γ ⊂ M : t ∈ [ t 1, t 2 ] ↦ γ ( t ) = γ 0 ( t ) = t, γ 1 ( t ), γ 2 ( t ), …, γ n ( t ), γ i : R → R : t ↦ γ i ( t ), γ i ∈ C ∞, is called a curvilinear path (or simply "path"), and a set of paths, Γ, is called a curvilinear-path space.
This paper investigates the problem of spatial curvilinear path following control of underactuated autonomous underwater vehicles (AUVs) with multiple uncertainties.
(Variational vector) A variational vector is defined as a cotangent vector at γ ( t ) ∈ M on the curvilinear path δ γ ( t ).
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