Isogeometric Analysis of FGM Plates

Auad, Samir P.; Praciano, Jamires Sousa Cordeiro; Barroso, Elias Saraiva; Sousa, João Batista M.; Parente, Evandro

doi:10.1016/j.matpr.2019.02.015

Cited by 9 publications

(4 citation statements)

References 18 publications

(18 reference statements)

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“…assumed. The buckling for the plate with nonsymmetric pore distribution under SSSS and SCSC boundary conditions is not possible, because by applying the small axial load, these plates undergo lateral deformation [92][93][94][95].…”

Section: Resultsmentioning

confidence: 99%

Parametric study for modified couple stress theory on postbuckling of size-dependent FG saturated porous mindlin microplates

et al. 2023

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Using modified couple stress plate and Mindlin theories, the present study is a parametric study for revealing the effect of length scale parameter on postbuckling of saturated poroelastic rectangular microplates with pore distribution being functionally graded across thickness. The microplate postbuckling is a nonlinear eigenvalue problem with coupled partial differential equations of equilibrium. In order to find the mode shapes, the eigenfunctions have been approximated by some complete polynomial series expansions in accordance with the conventional Ritz approximation technique. After discretizing the governing equations throughout the microplate grid points, the assembled difference equations construct a nonlinear eigenvalue problem with coupled algebraic equations. The nontrivial coefficients of the expansions were calculated such that the eigenfunctions extremize the microplate potential energy for satisfying the equilibrium homogeneous equations. Variation of the potential energy have been derived with respect to the expansions coefficients from the vantage of using Maple software. By gradual reduction in the initial end shortening of the movable supports and solving the assembled difference equations via Newton-Raphson iterations, the critical postbuckling displacement imposed to the movable supports are found along with the nontrivial coefficients regarding eigenfunctions. The results of the parametric study have revealed how geometric parameters, pore distribution, the Skempton coefficient, porosity, and different boundary conditions modify the influence of length scale parameter on the microplate postbuckling.

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Section: Resultsmentioning

confidence: 99%

Parametric study for modified couple stress theory on postbuckling of size-dependent FG saturated porous mindlin microplates

et al. 2023

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“…According to the Reissner-Mindlin theory, also known as the Firstorder Shear Deformation Theory (FSDT), the displacements of the plate, at any point, can be written in matrix form as [44][45][46]:…”

Section: Governing Equationsmentioning

confidence: 99%

“…The first example corresponds to the computation of the critical load of a clamped square plate with a=h ¼ 100, where a is the plate length. The boundary conditions were used as specified in Auad et al [46] and a 8 Â 8 cubic NURBS mesh is used for structural analysis. The material properties are E m ¼ 207:79 GPa, v m ¼ 0:28; E c ¼ 322:27 GPa, and v c ¼ 0:28.…”

Section: Analysis Validationmentioning

confidence: 99%

Surrogate based optimization of functionally graded plates using radial basis functions

Ribeiro

Maia

Parente

et al. 2020

Composite Structures

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“…Due to the complex behavior of structures made of FGM, numerical methods such as finite element analysis (FEA) and isogeometric analysis (IGA) are widely used to evaluate their structural responses. IGA has been used in association with various plate theories for composite plates analysis, such as the first-order shear deformation theory (FSDT) Auad et al 2019;Wang et al 2019) and higher-order shear deformation theory (HSDT) (Lieu et al 2018;Shi et al 2018;Do et al 2018).…”

Section: Introductionmentioning

confidence: 99%

Kriging-based optimization of functionally graded structures

Maia

Parente

Melo

2021

Struct Multidisc Optim

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This work presents an efficient methodology for the optimum design of functionally graded structures using a Krigingbased approach. The method combines an adaptive Kriging framework with a hybrid particle swarm optimization (PSO) algorithm to improve the computational efficiency of the optimization process. In this approach, the surrogate model is used to replace the high-fidelity structural responses obtained by a NURBS-based isogeometric analysis. In addition, the impact of key factors on surrogate modelling, as the correlation function, the infill criterion used to update the surrogate model, and the constraint handling is assessed for accuracy, efficiency, and robustness. The design variables are related to the volume fraction distribution and the thickness. Displacement, fundamental frequency, buckling load, mass, and ceramic volume fraction are used as objective functions or constraints. The effectiveness and accuracy of the proposed algorithm are illustrated through a set of numerical examples. Results show a significant reduction in the computational effort over the conventional approach.

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Isogeometric Analysis of FGM Plates

Cited by 9 publications

References 18 publications

Parametric study for modified couple stress theory on postbuckling of size-dependent FG saturated porous mindlin microplates

Parametric study for modified couple stress theory on postbuckling of size-dependent FG saturated porous mindlin microplates

Surrogate based optimization of functionally graded plates using radial basis functions

Kriging-based optimization of functionally graded structures

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