Coupling effects in elastic analysis of FGM composite plates by mesh-free methods

Sator, L.; Sládek, V.; Sládek, J.

doi:10.1016/j.compstruct.2014.04.016

Cited by 42 publications

(12 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…THIN ELASTIC PLATES The bending of elastic plates can be described in a unique way [7] by including the assumptions of three plate bending theories, such as the Kirchhoff-Love theory (KLT), shear deformation plate bending theories of the 1st and 3rd order (FSDPT and TSDPT). Considering the thin elastic, homogeneous plates, the tensor of bending moments is expressed in terms of derivatives of dimensionless deflections ( )…”

Section: Formulation Of Boundary Value Problems Formentioning

confidence: 99%

Mesh-Free Analysis of Plate Bending Problems by Moving Finite Element Approximation

Sládek

Repka

2019

Boundary Elements and Other Mesh Reduction Methods XLII

Self Cite

View full text Add to dashboard Cite

The governing equations for plate bending problems are given by the partial differential equations of the 4th order. Therefore C 1 continuous elements are required for approximation and discretization with using the standard finite element method (FEM). A novel discretization method is proposed and developed for numerical solution of plate bending boundary value problems. In contrast to the standard FEM, the analysed domain is not covered by a mesh of fixed non-overlapping finite elements, but only a net of nodes is used for discretization. Around each node, there is properly created a Lagrange finite element and the spatial variation of field variables is interpolated within this element in terms of nodal values and polynomial shape functions defined in the intrinsic coordinate space of the finite element. Thus, the Lagrange finite element associated with a node is moving within the analysed domain from node to node. Since there are no element interfaces known in standard FEM with a fixed finite element mesh, the difficulties with continuity of derivatives of field variables on such interfaces are avoided and higher order derivatives are available within the moving finite element. This makes the moving finite element (MFE) approximation to be applicable also to the development of the strong formulation of a boundary value problem with collocation of both the governing equations and boundary conditions at interior and boundary nodes, respectively. To decrease the order of the polynomial interpolation, the original set of the governing PDE is decomposed into a system of 2nd order PDEs by introducing a new field variable. Then, the boundary conditions are to be modified and the bi-quadratic Lagrange finite element is sufficient for approximation. Both the strong and the local weak formulations are derived and employed in the numerical test examples with focusing on verification of the reliability (accuracy and stability) and efficiency of the new method.

show abstract

Section: Formulation Of Boundary Value Problems Formentioning

confidence: 99%

Mesh-Free Analysis of Plate Bending Problems by Moving Finite Element Approximation

Sládek

Repka

2019

Boundary Elements and Other Mesh Reduction Methods XLII

Self Cite

View full text Add to dashboard Cite

show abstract

“…But the change of the bending stiffness is not the only modification required to obtain correct behaviour of the FGM (Functionally Graded Material) plate as compared with the homogeneous one. The transversal gradation of Young's modulus yields coupling between the bending and in-plane deformation modes [2,3]. Therefore it is insufficient to change only the coefficients in the governing equations corresponding to homogeneous plate, but it is necessary to modify also the set of governing equations, in order to get the response of the FGM plate to applied loading.…”

Section: Introductionmentioning

confidence: 99%

Multiple gradations coupling effects in the bending of thin elastic FGM plates

Sládek¹,

Sator²,

Sládek³

2015

WIT Transactions on Modelling and Simulation

View full text Add to dashboard Cite

In this paper we present the derivation of the governing equations and boundary conditions for thin elastic plates with functionally graded Young's modulus and thickness of the plate. The derivation is based on the assumptions of the Kirchhoff-Love theory for bending of thin elastic plates. The combination of the transversal gradation of Young's modulus with in-plane gradations of Young's modulus and/or thickness of the plate yields the multiple gradations coupling effects. The main manifestation of these effects is a finite deflection of the plate even if it is subjected only to in-plane loading on the boundary edge. Of course the response of the plate is affected by coupling between the in-plane deformation and bending modes. In numerical simulations of the multiple gradations coupling effects, the meshless strong formulation with MLS (Moving Least Squares) approximation of field variables are employed for solution of formulated boundary value problems. Several numerical results are presented for illustration of the multiple gradations coupling effects in bending of thin elastic FGM (Functionally Graded Material) plates.

show abstract

“…This work followed by Fantuzzi et al [25,26], where they researches deals with Radial Basis Function method for laminated composite arbitrarily shaped plates. Recently few researcher shows significant interest in applying mesh free methods in their research [27][28][29][30]. Sahu [31] have done some work on static and free vibration analysis of laminated composited skew plate with and without cutout using finite element method.…”

Section: Introductionmentioning

confidence: 99%

Free Vibration Study of Anti-Symmetric Angle-Ply Laminated Plates under Clamped Boundary Conditions

Viswanathan

Karthik

Sanyasiraju

et al. 2016

Curved and Layered Structures

View full text Add to dashboard Cite

Two type of numerical approach namely, Radial Basis Function and Spline approximation, used to analyse the free vibration of anti-symmetric angle-ply laminated plates under clamped boundary conditions. The equations of motion are derived using YNS theory under first order shear deformation. By assuming the solution in separable form, coupled differential equations obtained in term of mid-plane displacement and rotational functions. The coupled differential is then approximated using Spline function and radial basis function to obtain the generalize eigenvalue problem and parametric studies are made to investigate the effect of aspect ratio, length-to-thickness ratio, number of layers, fibre orientation and material properties with respect to the frequency parameter. Some results are compared with the existing literature and other new results are given in tables and graphs.

show abstract

Coupling effects in elastic analysis of FGM composite plates by mesh-free methods

Cited by 42 publications

References 15 publications

Mesh-Free Analysis of Plate Bending Problems by Moving Finite Element Approximation

Mesh-Free Analysis of Plate Bending Problems by Moving Finite Element Approximation

Multiple gradations coupling effects in the bending of thin elastic FGM plates

Free Vibration Study of Anti-Symmetric Angle-Ply Laminated Plates under Clamped Boundary Conditions

Contact Info

Product

Resources

About