Closed form solutions for an anisotropic composite beam on a two-parameter elastic foundation

Doeva, Olga; Masjedi, Pedram Khaneh

doi:10.1016/j.euromechsol.2021.104245

Cited by 17 publications

(18 citation statements)

References 32 publications

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“…Since numerical results for bending of fully coupled composite beams on variable elastic foundations are not available in the literature, static deflection analysis of homogeneous isotropic and composite beams on constant stiffness elastic foundations considered in several well-known studies is performed, and the results are compared with analytical and numerical results existing in the literature. First, values of mid-span deflection of a uniformly loaded isotropic beam with clamped-clamped and simply supported-simply supported boundary conditions obtained from the present HAM and iHAM solutions, exact analytical solution [61], analytical solution based on Green's functions [68], and the DQM solution [69] are presented in Table 3. For convenience, the mid-span transverse deflection and Winkler elastic foundation parameter are normalised as follows:…”

Section: Verification Studiesmentioning

confidence: 99%

“…In both approaches,h = −1 was assumed. [61] are given in Table 4 for normalised Winkler elastic foundation parameter k w taking values 0, 10, and 100. It is noted thath i = −1, i = u, ϕ, w, v, was used for both HAM approaches.…”

Section: Verification Studiesmentioning

confidence: 99%

“…Mathematically, the coupled deflection of composite beams is a boundary value problem presented by a linear system of four coupled governing differential equations, reflecting four degrees of freedom, namely bending in two principal directions, axial elongation and twist [57][58][59][60]. In [61], this model was extended to composite beams resting on constant stiffness elastic foundations. A corresponding exact analytical solution was provided.…”

Section: Introductionmentioning

confidence: 99%

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

Doeva

Masjedi

2021

Acta Mech

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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.

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Section: Verification Studiesmentioning

confidence: 99%

Section: Verification Studiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Doeva

Masjedi

2021

Acta Mech

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“…Olga et al 14 analyze the behavior of composite beams on two-parameter elastic foundations with coupling between stretching, shearing, bending, and twisting. The beam on elastic foundation theory is reviewed by Lamprea-Pineda et al 15 for railway engineering applications.…”

Section: Introductionmentioning

confidence: 99%

Modified harmonic balance method for forced nonlinear vibration of beam on an elastic foundation

Rahman

Trishna

2023

Noise & Vibration Worldwide

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A modified harmonic balance method has been presented and adopted for the nonlinear vibration problem of beams on an elastic foundation. By this method, a nonlinear algebraic equation along with a set of linear algebraic equations are required to be solved, which reduces computation effort. The results determined by the present method are compared with the corresponding results obtained by the existing method. Besides, the effect of various parameters on nonlinear vibrational behavior is examined.

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“…Due to these advances, it was possible to investigate the static behaviour of more and more complex structures such as: the composite beam resting on a two-parameter elastic foundation (cf. Doeva et al [1]), the infinite beam resting on a deformable foundation with a local subsidence (cf. Liang et al [2]) or on tensionless foundation (cf.…”

Section: Introductionmentioning

confidence: 99%

The Stability Analysis of Periodic Beams Interacting with Periodic Elastic Foundation with the Use of the Tolerance Averaging Technique

Marczak

Jędrysiak

2021

Materials

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In this paper a stability analysis of microperiodic beams resting on the periodic inhomogeneous foundation is carried out. The main issue of this considerations, which is the analytical solution to the governing equations characterised by periodic, highly oscillating and non-continuous coefficients, is overwhelmed by the application of the tolerance averaging technique. As a result of such application, the governing equation is transformed into a form with constant coefficients which can be solved using well-known mathematical methods. In several calculation examples, the convergence of the results of two derived averaged models is examined, as well as the convergence of the lowest value of the critical force parameter derived from the averaged models with the FEM model. The results prove the superiority of the presented analytical solution over the FEM analysis in the optimisation process.

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Closed form solutions for an anisotropic composite beam on a two-parameter elastic foundation

Cited by 17 publications

References 32 publications

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

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

Modified harmonic balance method for forced nonlinear vibration of beam on an elastic foundation

The Stability Analysis of Periodic Beams Interacting with Periodic Elastic Foundation with the Use of the Tolerance Averaging Technique

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