Analysis of Laminated Shells by Murakami’s Zig-Zag Theory and Radial Basis Functions Collocation

Maturi, Dalal Adnan; Ferreira, A.J.M.; Zenkour, Ashraf M.; Mashat, Daoud S.

doi:10.1155/2013/123465

Cited by 18 publications

(8 citation statements)

References 51 publications

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“…Different basis functions known as Gaussian, Multiquadrics and Inverse Multiquadrics are generally used [28]. In problems related to structural analysis, also Cubic, Thin plate splines and Wendland functions are used [10,26]. These basis functions are continuously differentiable and integrable, this is useful for the approximation of the derivatives.…”

Section: Radial Basis Function Networkmentioning

confidence: 99%

A study on the stress gradient reconstruction in finite elements problems with application of radial basis function networks

2019

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The recovery of the stress gradient in finite elements problems is a widely discussed topic with many applications in the design process. The stress gradient is related to the second derivative (Hessian) of the nodal displacements and numerical techniques are required for its calculation. Particular difficulties are encountered in the reconstruction of the stress gradient in the boundary regions of the domain. This is of particular concern in most applications, especially in mechanical components, where the maximum values of stresses are often located in these regions and the stress gradient has a strong influence on the fatigue life of the component.This paper presents a comparison between some already published, partially modified, recovery techniques and a different approach based on radial basis function networks. The aim of the paper is to compare the performances of the different approaches for a number of element types with particular focus on the boundary regions. Some examples of mechanical interest are considered.

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Section: Radial Basis Function Networkmentioning

confidence: 99%

A study on the stress gradient reconstruction in finite elements problems with application of radial basis function networks

2019

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“…This outcome is known as zig-zag effect. As specified in [97,98,99], this effect is well-captured by Layer-Wise (LW) models, in which the degrees of freedom are assumed as independent parameters along each layer. Nevertheless, this approach is quite onerous in terms of computational resources.…”

Section: Introductionmentioning

confidence: 99%

Free Vibrations of Sandwich Plates with Damaged Soft-Core and Non-Uniform Mechanical Properties: Modeling and Finite Element Analysis

2019

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The paper aims to investigate the natural frequencies of sandwich plates by means of a Finite Element (FE) formulation based on the Reissner-Mindlin Zig-zag (RMZ) theory. The structures are made of a damaged isotropic soft-core and two external stiffer orthotropic face-sheets. These skins are strengthened at the nanoscale level by randomly oriented Carbon nanotubes (CNTs) and are reinforced at the microscale stage by oriented straight fibers. These reinforcing phases are included in a polymer matrix and a three-phase approach based on the Eshelby-Mori-Tanaka scheme and on the Halpin-Tsai approach, which is developed to compute the overall mechanical properties of the composite material. A non-uniform distribution of the reinforcing fibers is assumed along the thickness of the skin and is modeled analytically by means of peculiar expressions given as a function of the thickness coordinate. Several parametric analyses are carried out to investigate the mechanical behavior of these multi-layered structures depending on the damage features, through-the-thickness distribution of the straight fibers, stacking sequence, and mass fraction of the constituents. Some final remarks are presented to provide useful observations and design criteria.

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“…However, accurate results have been obtained in these cases introducing peculiar functions to the kinematic model, such as the Murakami's function, which are able to capture the so-called zig-zag effect. This aspect is investigated in depth in the works by Maturi et al [31] and Carrera [32,33]. Recently, the well-known and hugely exploited fiber-reinforced layers, commonly used in the stacking sequence of laminated composite structures, have been subjected to such an innovative development that has led to a new class of composite materials.…”

Section: Introductionmentioning

confidence: 99%

Foam core composite sandwich plates and shells with variable stiffness: Effect of the curvilinear fiber path on the modal response

Tornabene

Fantuzzi

Bacciocchi

2017

Jnl of Sandwich Structures & Materials

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This paper presents the free vibration analysis of composite sandwich plates and doubly curved shells with variable stiffness. The reinforcing fibers are located in the external skins of the sandwich structures according to curved paths. These curvilinear paths are described by a general expression that combines power-law, sinusoidal, exponential, Gaussian and ellipse-shaped functions. As a consequence, the reinforcing fibers are placed in these orthotropic layers in an arbitrary manner, in order to achieve the desired mechanical properties. The effect of this variable fiber orientation on the natural frequencies is investigated by means of several parametric studies. As far as the structural theory is concerned, an equivalent single layer approach based on the well-known Carrera Unified Formulation is employed. The Murakami's function is added to the kinematic model to capture the zigzag effect, when the soft-core effect is significant. Thus, several higher order shear deformation theories are taken into account in a unified manner. The differential geometry is employed to describe the reference surface of doubly curved shells and panels, which are characterized by variable radii of curvature. The numerical solution is obtained using the generalized differential quadrature method, due to its accuracy and stability features. The present solution is compared with the results available in the literature or obtained by finite element commercial codes.

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Analysis of Laminated Shells by Murakami’s Zig-Zag Theory and Radial Basis Functions Collocation

Cited by 18 publications

References 51 publications

A study on the stress gradient reconstruction in finite elements problems with application of radial basis function networks

A study on the stress gradient reconstruction in finite elements problems with application of radial basis function networks

Free Vibrations of Sandwich Plates with Damaged Soft-Core and Non-Uniform Mechanical Properties: Modeling and Finite Element Analysis

Foam core composite sandwich plates and shells with variable stiffness: Effect of the curvilinear fiber path on the modal response

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