A nonlinear thick plate formulation based on the modified strain gradient theory

Ashoori, A.R.; Mahmoodi, Mohammad Javad

doi:10.1080/15376494.2017.1308588

Cited by 20 publications

(4 citation statements)

References 27 publications

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“…Such approach, known as strain gradient theory, has been utilized also by others in other contexts in solid mechanics [38][39][40]. Strain gradient theory [41] has been demonstrated to be a constrained version of other higher-order unconstrained versions available in the literature such as couple stress [42][43][44] as well as micropolar theories [45][46][47].…”

Section: Introductionmentioning

confidence: 99%

Meshless Computational Strategy for Higher Order Strain Gradient Plate Models

Fabbrocino

Saitta

Vescovini

et al. 2022

MCA

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The present research focuses on the use of a meshless method for the solution of nanoplates by considering strain gradient thin plate theory. Unlike the most common finite element method, meshless methods do not rely on a domain decomposition. In the present approach approximating functions at collocation nodes are obtained by using radial basis functions which depend on shape parameters. The selection of such parameters can strongly influences the accuracy of the numerical technique. Therefore the authors are presenting some numerical benchmarks which involve the solution of nanoplates by employing an optimization approach for the evaluation of the undetermined shape parameters. Stability is discussed as well as numerical reliability against solutions taken for the existing literature.

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Section: Introductionmentioning

confidence: 99%

Meshless Computational Strategy for Higher Order Strain Gradient Plate Models

Fabbrocino

Saitta

Vescovini

et al. 2022

MCA

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“…In general, different nonlocal theoretical frameworks can be developed. Examples of nonlocal approaches that should be mentioned for completeness purposes are the strain and stress gradient theories [ 58 , 59 , 60 ], the modified couple stress theory [ 61 , 62 , 63 , 64 ], and the ones based on micropolar formulations [ 65 , 66 , 67 ]. A comprehensive literature review concerning nonlocal elasticity can be found in the paper by Zhao et al [ 68 ] for completeness purposes.…”

Section: Introductionmentioning

confidence: 99%

Third-Order Theory for the Bending Analysis of Laminated Thin and Thick Plates Including the Strain Gradient Effect

Bacciocchi

Tarantino

2021

Materials

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The aim of the paper is the development of a third-order theory for laminated composite plates that is able to accurately investigate their bending behavior in terms of displacements and stresses. The starting point is given by the corresponding Reddy’s Third-order Shear Deformation Theory (TSDT). This model is then generalized to consider simultaneously the Classical Laminated Plate Theory (CLPT), as well as the First-order Shear Deformation Theory (FSDT). The constitutive laws are modified according to the principles of the nonlocal strain gradient approach. The fundamental equations are solved analytically by means of the Navier methodology taking into account cross-ply and angle-ply lamination schemes. The numerical applications are presented to highlight the nonlocal effects on static behavior.

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“…By using the FSDT, Jiang and Wang [12] investigated the natural frequencies of the FG microplates. This theory was employed by Ashoori and Mahmoodi [13] to reveal a nonlinear strain gradient isotropic plate formulation. Mohammadimehr et al [14] employed generalized differential quadrature technique to investigate the dynamic stability of the annular carbon nanotube reinforced composite facesheets sandwich plates.…”

Section: Introductionmentioning

confidence: 99%