Abstract
New analytical solutions for the static deflection of anisotropic composite beams resting on variable stiffness elastic foundations are obtained by the means of the Homotopy Analysis Method (HAM). The method provides a closed-form series solution for the problem described by a non-homogeneous system of coupled ordinary differential equations with constant coefficients and one variable coefficient reflecting variable stiffness elastic foundation. Analytical solutions are obtained based on two different algorithms, namely conventional HAM and iterative HAM (iHAM). To investigate the computational efficiency and convergence of HAM solutions, the preliminary studies are performed for a composite beam without elastic foundation under the action of transverse uniformly distributed loads considering three different types of stacking sequence which provide different levels and types of anisotropy. It is shown that applying the iterative approach results in better convergence of the solution compared with conventional HAM for the same level of accuracy. Then, analytical solutions are developed for composite beams on elastic foundations. New analytical results based on HAM are presented for the static deflection of composite beams resting on variable stiffness elastic foundations. Results are compared to those reported in the literature and those obtained by the Chebyshev Collocation Method in order to verify the validity and accuracy of the method. Numerical experiments reveal the accuracy and efficiency of the Homotopy Analysis Method in static beam problems.
Highlights
Laminated composite structures resting on elastic foundations are increasingly used in aerospace, marine, civil, biomedical, and other engineering applications due to their high strength-to-weight ratio, improved damage tolerance nature, and corrosion resistance
An explicit analysis of the static deflection of composite beams resting on variable stiffness elastic foundations subject to uniformly distributed loads described by a non-homogeneous system of coupled differential equations with the combination of constant and variable coefficients has been performed by means of the Homotopy Analysis Method
The main difference between the two algorithms is in the method of achieving more accurate results: in conventional Homotopy Analysis Method (HAM) the order of deformation equation increases for this purpose, while in iterative HAM (iHAM) the initial guess is updated at each iteration
Summary
Laminated composite structures resting on elastic foundations are increasingly used in aerospace, marine, civil, biomedical, and other engineering applications due to their high strength-to-weight ratio, improved damage tolerance nature, and corrosion resistance. Composite beams are fundamental structural elements, and understanding of their static deflection behaviour is essential for engineering design and modelling purposes. Different analytical approaches have been applied to analyse static and dynamic structural behaviour of beams resting on elastic foundations, for example, solutions such as that following Navier [1,2,3,4,5,6,7], Fourier series [8,9,10,11,12], Power series [13,14,15], Variational Iteration Method [16,17,18,19,20], and Homotopy.
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