The weak patch test for nonhomogeneous materials modeled with graded finite elements

Paulino, Gláucio H.; Kim, Jeong-Ho

doi:10.1590/s1678-58782007000100010

Cited by 17 publications

(6 citation statements)

References 60 publications

(49 reference statements)

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“…The quadrilateral elements, like the linear Q4 and quadratic Q8 types, perform more than the classical elements and provide a good argument with analytical solutions. Paulino and Kim [19] used finite elements with graded properties to analyse the consistency and stability of FGM by weak patch test and using graded quadrature elements Q4, Q8, and Q9 for axisymmetric problems. The previous study discussed the effect of these elements on the analysis.…”

Section: Formulation Of Rmq-7 Elementmentioning

confidence: 99%

Innovative mixed finite element method for bending analysis of functionally graded beams: modelling, validation, and applications

Benmalek,

Bouziane,

Bouzerd

et al. 2024

Eng. Res. Express

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In this research, we consider solutions for the Euler-Bernoulli theory (CBT) and the theory of Timoshenko (TBT). It presents an innovative mixed finite element method tailored for analysing beams with functionally graded properties, focusing on their behaviour under bending loads. The method employs an isoparametric formulation in natural coordinates, enabling precise modelling of complex geometries common in structural engineering and materials science. A significant contribution is extending the mixed finite element approach to assess the bending behaviour of functionally graded beams. Hence, it is vital to understand material responses to external forces. To illustrate its effectiveness and versatility, we provide two numerical examples involving cantilever and simply-supported isotropic beams with property variations along the material's thickness, following power-law distributions.Additionally, a third example features a cantilever made from isotropic functionally graded material with quadratic property changes through the thickness. The method's robustness and credibility are established through rigorous validation against numerical and analytical solutions found in existing literature. This validation confirms the accuracy and reliability of the mixed finite element method for assessing functionally graded materials under bending conditions, enhancing its utility in structural analysis. This research introduces a potent numerical tool for investigating the behaviour of functionally graded materials subjected to bending, providing valuable implications for engineering and materials science applications.

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Section: Formulation Of Rmq-7 Elementmentioning

confidence: 99%

Innovative mixed finite element method for bending analysis of functionally graded beams: modelling, validation, and applications

Benmalek,

Bouziane,

Bouzerd

et al. 2024

Eng. Res. Express

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“…Values of the FGM properties at each Gaussian integration point can be defined by interpolation from the element nodal values. Therefore, the Young's modulus E(G)(y) and Poisson's ratio ν(G)(y) at Gaussian integration points are, respectively given by 59 where NIP is the number of Gaussian integration points, Ni E and Ni ν are appropriate element isoparametric shape functions corresponding to Ei and νi, which may be different from each other. Ei and νi are, respectively the values of Young's modulus and Poisson's ratio corresponding to nodal point i .…”

Section: The Fgm Model and Isoparametric Graded Finite Element Formulmentioning

confidence: 99%

“…This technique leads to a highly accurate results and is widely employed to model the behavior of FGMs. 39,[57][58][59][60][61] The second technique is the CHFE formulation, in which the material properties are specified at the centroid of each finite element. This implies that the material property distribution is constant over a given finite element and, consequently, this approach may lead to distinct discontinuities in the material properties.…”

Section: The Fgm Model and Isoparametric Graded Finite Element Formulmentioning

confidence: 99%

Modeling and analysis of the nonlinear indentation problems of functionally graded elastic layered solids

Attia

El-Shafei

2019

Proceedings of the Institution of Mechanical Engineers, Part J:

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In tribological and thermo-electro-mechanical applications with an appropriate gradation of properties, functionally graded materials provide superior performance for damage and wear resistance of contact systems and thermal and mechanical responses for other mechanical devices. This paper presents a nonlinear mixed variational-based computational model for the analysis of nonlinear plane indentation problems of elastic functionally graded layered elastic solids. The functionally graded elastic layer is perfectly bonded to the elastic substrate and is normally loaded by a cylindrical rigid punch. In addition to nonlinearity inherent to the contact problem, the developed model accounts for the geometric nonlinearity in the sense of larger displacements and rotations, but smaller strains. The modulus of elasticity as well as Poisson's ratio of the graded layer are varying along the thickness of the layer according to both exponential and power laws. On the contrary, in the conventional homogeneous finite element formulation the isoparametric graded finite element formulation is adopted on the level of Gaussian integration points to realize the gradation in material properties. The friction at the contact interface is modeled using Coulomb's friction law. Moreover, the inequality contact constraints are exactly satisfied throughout the contact interface by employing the Lagrange multiplier method, where the indentation force and the displacement fields are treated as independent variables. The obtained results of contact pressure, tangential contact stress, stress distribution, and indentation force show a significant influence of the material distribution, gradation law, gradient index, and thickness of the functionally graded layer.

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“…Young's modulus) change in each finite element, greatly impacts the accuracy of FEA solutions [45]. A material threshold is proposed to evaluate the validity of meshes of heterogeneous materials.…”

Section: General Adaptive Meshing Schemementioning

confidence: 99%

Adaptive meshing for finite element analysis of heterogeneous materials

You

Kou

Tan

2015

Computer-Aided Design

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Adaptive meshing of 2D planar regions, curved surfaces as well as 3D volumes has been extensively studied in Finite Element Analysis (FEA) in the past few decades. Despite the maturity of these adaptive meshing approaches, most of the existing schemes assume the domain or sub-domain of interest is homogeneous. In the context of FEA of heterogeneous objects, traditional adaptive mesh generation strategies become inadequate as they fail to take into account the material heterogeneities. This paper is motivated to tackle such problems and propose an adaptive mesh generation scheme for FEA of versatile heterogeneous materials. The proposed approach takes full advantages of the material heterogeneity information, and the mesh density is formulated with a specific function of the material variations. Dual triangulation of centroidal Voronoi tessellation is then constructed and necessary mesh subdivision is applied with respect to a predefined material threshold. Experiments show that the proposed approach distributes the material composition variation over mesh elements as equally as possible and thus minimizes the number of elements in terms of the given material threshold. FEA results show that the proposed method can significantly decrease the mesh complexities as well as computational resources in FEA of heterogeneous objects and compared with existing approaches, significant mesh reduction can be achieved without sacrifice in FEA qualities.

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The weak patch test for nonhomogeneous materials modeled with graded finite elements

Cited by 17 publications

References 60 publications

Innovative mixed finite element method for bending analysis of functionally graded beams: modelling, validation, and applications

Innovative mixed finite element method for bending analysis of functionally graded beams: modelling, validation, and applications

Modeling and analysis of the nonlinear indentation problems of functionally graded elastic layered solids

Adaptive meshing for finite element analysis of heterogeneous materials

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