Buckling Of Beams On Elastic Foundations

Hassan, M

doi:10.33899/rengj.2008.44659

Cited by 2 publications

(2 citation statements)

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“…This explains the necessity for numerical methods that could achieve approximate, yet accurate solutions. Hassan (2008) used the exact methods for solving ordinary differential equations to obtain solutions for buckling of EBBoEF for different types of supported ends. Aristizabal-Ochoa (2013) investigated the stability problems of EBBoEFs for various cases of end supports using approximate methods for solving ordinary differential equations.…”

Section: Literature Reviewmentioning

confidence: 99%

Ritz Variational Method for Buckling Analysis of Euler-Bernoulli Beams Resting on Two-Parameter Foundations

Ike

2024

IJCE

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Section: Literature Reviewmentioning

confidence: 99%

Ritz Variational Method for Buckling Analysis of Euler-Bernoulli Beams Resting on Two-Parameter Foundations

Ike

2024

IJCE

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“…Soltani [32] solved the GDES for BoEF using the numerical approach of finite element analysis. Hassan [33] and Aristizabal-Ochoa [34] presented solutions for BoEF under different end supports. Anghel and Mares [35] solved the GDES for BoEF by using collocation techniques to solve the resulting integral formulation of the GDES.…”

Section: Introductionmentioning

confidence: 99%

Fourier series method for the stability solution of simply supported thin beams on two-parameter elastic foundations of the Pasternak, Filonenko-Borodich, Hetenyi or Vlasov models

Ike

2024

J., eng., them. sci.

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The analysis of stability problems of beams on two-parameter foundations (Bo2PFs) is an important part of their design for compressive loads. This work presents novel first principles derivation of the governing differential equations of elastic stability (GDES) of thin beams resting on two-parameter elastic foundations of the Pasternak, Filonenko-Borodich, Hetenyi or Vlasov models. The requirements of translational and rotational equilibrium of all the applied, reactive and internal forces on an infinitesimal segment of the Bo2PF and the laws of infinitesimal calculus were used to formulate the GDES as a fourth order ordinary differential equation (ODE) in terms of the transverse displacement function ux. The GDES is non-homogeneous in the presence of applied transverse load qx but homogeneous when qx vanishes. This study presents the Fourier series method (FSM) for solving the governing differential equation of stability (GDES) for the case of Dirichlet boundary conditions. The FSM has the advantage of amenability to differentiation, and integration due to the orthogonality properties of the sinusoidal functions. Implementation of the FSM by assuming the unknown function in the GDES as a Fourier series of infinite terms and the exploitation of orthogonalization simplifies the problem to an algebraic eigenvalue problem which is the characteristic buckling equation. The exact eigenvalues are found by algebraic solution of the buckling equation. The exact eigenvalues were used to find the exact buckling loads and the exact buckling load coefficients. The critical buckling load was found to correspond to the first buckling mode (n= 1), and is identical with previous solutions in the literature. Numerical calculations for the critical buckling load parameters Kcr were presented for the Bo2PF problem for values of the dimensionless foundation parameters k-1= 0, k-2= 0; k-1= 100, k-2= 0; k-1= 0, k-2= 1; k-1= 100, k-2= 100; k-1= 0, k-2= 2.5; k-1= 100, k-2= 2.5. The present solutions were compared with previous solutions for Kcr in the literature. The comparison shows that the present FSM results are identical with previous results obtained using various other methods such as Recursive Differentiation Method, Finite Element Method, Generalized Integral Transform Method (GITM) and Stodola-Vianello Iteration Method. The study has illustrated the effectiveness of the FSM for solving Bo2PFs.

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Buckling Of Beams On Elastic Foundations

Cited by 2 publications

References 3 publications

Ritz Variational Method for Buckling Analysis of Euler-Bernoulli Beams Resting on Two-Parameter Foundations

Ritz Variational Method for Buckling Analysis of Euler-Bernoulli Beams Resting on Two-Parameter Foundations

Fourier series method for the stability solution of simply supported thin beams on two-parameter elastic foundations of the Pasternak, Filonenko-Borodich, Hetenyi or Vlasov models

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