The effect of orthotropic material gradation on the plane sliding frictional contact mechanics problem

2019 ◽  
Vol 54 (4) ◽  
pp. 254-275
Author(s):  
Korhan Babacan Yilmaz ◽  
Isa Comez ◽  
Mehmet Ali Güler ◽  
Bora Yildirim
Keyword(s):  
Finite Element Analysis ◽  
Integral Equation ◽  
Finite Element ◽  
Singular Integral Equation ◽  
Singular Integral ◽  
Functionally Graded ◽  
Orthotropic Materials ◽  
Contact Method ◽  
Element Analysis ◽  
Cylindrical Punch

With the advent of new functional and intelligent non-conventional materials, understanding the behavior of these materials in different contact conditions over the conventional materials is one of the most crucial aspects in early design process for coated systems. Therefore, the sliding contact problem for a functionally graded orthotropic coating–substrate system and a rigid cylindrical punch is considered in this article to study the aforementioned aspects. The functionally graded orthotropic coating is modeled to be bonded to an isotropic substrate of finite thickness and is loaded by a sliding rigid cylindrical punch under plane strain conditions. For the material orthotropy, five different real orthotropic materials are utilized and the stiffness coefficients of each principal direction are graded separately. Navier’s equations are converted to ordinary differential equations using the Fourier integral transformation technique. Then, the algebraic equations are solved and the problem is cast into a singular integral equation. A parametric finite element analysis based on augmented contact method is also conducted. The normalized surface stress distributions and the normalized contact boundaries obtained from finite element analysis are validated with the results obtained from singular integral equation approach. The results of this study may be helpful for engineers in design and optimization of the characteristics of non-conventional coatings that are used as thermal or structural barriers and wear-resistant surfaces in engineering applications.

Natural frequency analysis of a functionally graded rotor-bearing system with a slant crack subjected to thermal gradients

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Arnab Bose ◽  
Prabhakar Sathujoda ◽  
Giacomo Canale
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Power Law ◽  
Beam Theory ◽  
Functionally Graded ◽  
Thermal Gradients ◽  
Element Analysis ◽  
Rotor Bearing ◽  
Natural Frequency Analysis ◽  
Bearing System

Abstract The present work aims to analyze the natural and whirl frequencies of a slant-cracked functionally graded rotor-bearing system using finite element analysis for the flexural vibrations. The functionally graded shaft is modelled using two nodded beam elements formulated using the Timoshenko beam theory. The flexibility matrix of a slant-cracked functionally graded shaft element has been derived using fracture mechanics concepts, which is further used to develop the stiffness matrix of a cracked element. Material properties are temperature and position-dependent and graded in a radial direction following power-law gradation. A Python code has been developed to carry out the complete finite element analysis to determine the Eigenvalues and Eigenvectors of a slant-cracked rotor subjected to different thermal gradients. The analysis investigates and further reveals significant effect of the power-law index and thermal gradients on the local flexibility coefficients of slant-cracked element and whirl natural frequencies of the cracked functionally graded rotor system.

A semianalytical and finite-element solution to the unbonded contact between a frictionless layer and an FGM-coated half-plane

2017 ◽  
Vol 24 (2) ◽  
pp. 448-464 ◽  
Author(s):  
Jie Yan ◽  
Changwen Mi ◽  
Zhixin Liu
Keyword(s):  
Integral Equation ◽  
Finite Element ◽  
Singular Integral Equation ◽  
Contact Problem ◽  
Singular Integral ◽  
Material Properties ◽  
Elastic Layer ◽  
Coated Substrate ◽  
Receding Contact ◽  
Contact Size

In this work, we examine the receding contact between a homogeneous elastic layer and a half-plane substrate reinforced by a functionally graded coating. The material properties of the coating are allowed to vary exponentially along its thickness. A distributed traction load applied over a finite segment of the layer surface presses the layer and the coated substrate against each other. It is further assumed that the receding contact between the layer and the coated substrate is frictionless. In the absence of body forces, Fourier integral transforms are used to convert the governing equations and boundary conditions of the plane receding contact problem into a singular integral equation with the contact pressure and contact size as unknowns. Gauss–Chebyshev quadrature is subsequently employed to discretize both the singular integral equation and the force equilibrium condition at the contact interface. An iterative algorithm based on the method of steepest descent has been proposed to numerically solve the system of algebraic equations, which is linear for the contact pressure but nonlinear for the contact size. Extensive case studies are performed with respect to the coating inhomogeneity parameter, geometric parameters, material properties, and the extent of the indentation load. As a result of the indentation, the elastic layer remains in contact with the coated substrate over only a finite interval. Exterior to this region, the layer and the coated substrate lose contact. Nonetheless, the receding contact size is always larger than that of the indentation traction. To validate the theoretical solution, we have also developed a finite-element model to solve the same receding contact problem. Numerical results of finite-element modeling and theoretical development are compared in detail for a number of parametric studies and are found to agree very well with each other.

Finite element analysis of flexible functionally graded beams with variable Poisson’s ratio

2016 ◽  
Vol 33 (8) ◽  
pp. 2421-2447 ◽  
Author(s):  
João Paulo Pascon
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Poisson’S Ratio ◽  
Scientific Literature ◽  
Functionally Graded ◽  
Poisson's Ratio ◽  
Transverse Strain ◽  
Thickness Direction ◽  
Element Analysis ◽  
Content Type

Purpose The purpose of this paper is to deal with large deformation analysis of plane beams composed of functionally graded (FG) elastic material with a variable Poisson’s ratio. Design/methodology/approach The material is assumed to be linear elastic, with a Poisson’s ratio varying according to a power law along the thickness direction. The finite element used is a plane beam of any-order of approximation along the axis, and with four transverse enrichment schemes, which can describe constant, linear, quadratic and cubic variation of the strain along the thickness direction. Regarding the constitutive law, five materials are adopted: two homogeneous limiting cases, and three intermediate FG cases. The effect of both finite element kinematics and distribution of Poisson’s ratio on the mechanical response of a cantilever is investigated. Findings In accordance with the scientific literature, the second scheme, in which the transverse strain is linearly variable, is sufficient for homogeneous long (or thin) beams under bending. However, for FG short (or moderate thick) beams, the third scheme, in which the transverse strain variation is quadratic, is needed for a reliable strain or stress distribution. Originality/value In the scientific literature, there are several studies regarding nonlinear analysis of functionally graded materials (FGMs) via finite elements, analysis of FGMs with constant Poisson’s ratio, and geometrically linear problems with gradually variable Poisson’s ratio. However, very few deal with finite element analysis of flexible beams with gradually variable Poisson’s ratio. In the present study, a reliable formulation for such beams is presented.

scholarly journals A Centrifuge Modelling and Finite Element Analysis of Laterally Loaded Single Piles in Sand with Focus on P–Y Curves

2020 ◽  
Author(s):  
Hocine Haouari ◽  
Ali Bouafia
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Hyperbolic Function ◽  
Contact Method ◽  
Centrifuge Modelling ◽  
Element Analysis ◽  
Soil Response ◽  
Dense Sand ◽  
Centrifuge Tests ◽  
Abaqus Software

Centrifuge modelling and finite element analysis are powerful tools of research on the lateral pile/soil interaction. This paper aims at presenting the main results of experimental and numerical analysis of the pile response under monotonic lateral loading in sand. After description of the experimental devices, it focuses on the determination of the load-transfer P-Y curves for rigid and semi-rigid piles embedded in dry dense sand by using the experimental bending moment profiles obtained in centrifuge tests, as well as by a three-dimensional finite element models using ABAQUS Software. The elastic perfectly plastic Mohr-Coulomb constitutive model has been used to describe the soil response, and the surface-to-surface contact method of ABAQUS software has been used to take into account the nonlinear response at soil/pile interface. The analysis methodology has allowed to propose a hyperbolic function as a model to construct P-Y curves for rigid and semi-rigid piles embedded in dry dense sand, this model is governed by two main parameters, which are the initial subgrade reaction modulus, and the lateral soil resistance, the latter has been formulated in terms of Rankine’s passive earth pressure coefficient, the sand dry unit weight, and the pile diameter.

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