Abstract
Abstract An analytical solution is presented for the determination of deformation of curved composite beams. Each cross-section is assumed to be symmetrical and the applied loads are acted in the plane of symmetry of curved beam. In-plane deformations are considered of composite curved beams. Assumed form of the displacement field assures the fulfillment of the classical Bernoulli-Euler beam theory. The curvature of beam is constant and the internal forces in a cross-section is replaced by an equivalent forcecouple system at the origin of the cylindrical coordinate system used. The internal forces are expressed in terms of two kinematical variables, which are the radial displacement and the rotation of the cross-sections. The determination of the analytical solutions of the considered static problems are based on the fundamental solutions. Linear combination of the fundamental solutions which are filling to the given loading and boundary conditions, gives the total solution. Closed form formulae are derived for the radial displacement, cross-sectional rotation, nomral and shear forces and bending moments. The circumferential and radial normal stresses and shear stresses are obtained by the integration of equilibrium equations. Examples illustrate the developed method.
Highlights
The analysis of curved beam has been a topic of interest to research workers for over a century, it is a standard chapter in the most text-books of mechanics of solids [1,2,3,4,5,6,7]
An analytical solution is presented for the determination of deformation of curved composite beams
The internal forces are expressed in terms of two kinematical variables, which are the radial displacement and the rotation of the cross-sections
Summary
The analysis of curved beam has been a topic of interest to research workers for over a century, it is a standard chapter in the most text-books of mechanics of solids [1,2,3,4,5,6,7]. J. Lengyel on the cross-sectional coordinates (r, z), the curved beam in circumferential direction is homogeneous. Lengyel on the cross-sectional coordinates (r, z), the curved beam in circumferential direction is homogeneous This type of non-homogeneous curved beam is called φ-homogeneous curved beam [16]. The definition of φ-homogeneity includes those cases when the curved beam is a composite of different materials, so that moduli of elasticity are piecewise constants. Type of these beams are laminated and fibre reinforced beams. It must be mentioned that papers by Ecsedi and Lengyel [17, 18] provide analytical solution for layered curved composite beams with interlayer slip. According to the simplified form of Hooke’s law and Eq (4) we can write
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