Static analysis of composite beams on variable stiffness elastic foundations by the Homotopy Analysis Method

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.

Analytical and computational analysis of vibrational behavior of axially loaded beams placed on elastic foundations

“…In Ref. [23], the static study of composite beams over elastic foundations with varying stiffness has been performed out using the homotopy approach. A Pasternak‐type elastic foundation was used to support FG beams with changing cross‐sections and provided an analytical solution for investigating their vibrations [24].…”

Effects of shear deformation and rotary inertia on elastically constrained beam resting on pasternak foundation

“…Asif et al [23] explored the dispersion of elastic waves in an inhomogeneous multilayered plate over a Winkler elastic foundation with imperfect interfacial conditions. Doeve et al [24] to statistically analyze composite beams on elastic foundations with variable stiffness. Doyle and Pavlovic [25] performed dynamic analysis of beams on partial elastic foundations.…”

Analyzing the Effect of Rotary Inertia and Elastic Constraints on a Beam Supported by a Wrinkle Elastic Foundation: A Numerical Investigation

“…The dynamic characteristics and dispersion properties of an elastic five-layered plate subjected to anti-plane shear vibrations, using an asymptotic approach and considering interfacial imperfections were detailed in [23,24]. The homotopy analysis method to accomplish static analysis of composite beams on elastic foundations with variable stiffness was employed in [25]. The analytical solution to study the vibrations of functionally graded beams with varying cross-sections supported by elastic foundations of the Pasternak type was provided in [26].…”