A Quasi 3D Modified Strain Gradient Formulation for Static Bending of Functionally Graded Micro beams Resting on Winkler-Pasternak Elastic Foundation

Gholami, Mohammad; Alizadeh, Mansour

doi:10.24200/sci.2021.55000.4019

Cited by 4 publications

(3 citation statements)

References 55 publications

(58 reference statements)

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“…(i) The methods of the mathematical theory of elasticity were used for BoEF problems by Gholami and Alizadeh (2022), Anyaegbunam (2014), andThanh andLinh (2021), but failed to investigate stability problems.…”

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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“…In addition to investigating the small deflection of beams with different beam theories [5,7,8,11,[27][28][29], generally, two different types of theory may be used to analyze the large deflection of beams [6,9,10,22,24,26], it has detailed by Taghipour and Darfarin [30]. There are two types of people: the first ignores the shear deformation effect, while the second considers it.…”

Section: Sharabiani and Yazdimentioning

confidence: 99%

Functionally graded nanobeams subjected to large deflection by considering surface effects

Taghipour,

Zeinali

2023

Scientia Iranica

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In the current study, structurally graded nanobeams with distributed load are subjected to a large deflection analysis that takes surface effects into account. The nanobeams Young's elasticity modulus changes with thickness under a power-law function. The displacement elements are presented, generalization of the Young-Laplace formula is employed to account for the surface effects, and the total Lagrangian finite element formulation is utilized to get the outcomes by cracking the system of nonlinear differential equations founded on the Timoshenko beams theory. The reliability and correctness of the findings are confirmed by comparison with previously published publications. The investigation is done into how various characteristics, including length-to-thickness ratio, material gradient index, boundary conditions, and surface effects, affect the outcomes. The findings demonstrate that, in the presence of surface effects, residual surface tension plays a significant influence on the deflection of nanobeams. Additionally, a comparison of the power-law and exponential kinds of FG distribution is conducted in this study, and it is discovered that the FG materials with the power-law distribution are more applicable since they are less susceptible to surface effects than the exponential type.

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“…Finite element methods were used in the studies of beam on elastic foundation by Alzubaidi et al [47], Wieckowski and Swiatkiewiez [48], and Worku and Habte [49]. Theory of elasticity methods were also studied by Gholami and Alizadeh [50], Anyaegbunam [51] and Thanh and Linh [52]; but none studied buckling problems.…”

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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A Quasi 3D Modified Strain Gradient Formulation for Static Bending of Functionally Graded Micro beams Resting on Winkler-Pasternak Elastic Foundation

Cited by 4 publications

References 55 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

Functionally graded nanobeams subjected to large deflection by considering surface effects

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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