Bending analysis of thin FGM skew plate resting on Winkler elastic foundation using multi-term extended Kantorovich method

Hassan, Ahmed Hassan Ahmed; Kurgan, Naci

doi:10.1016/j.jestch.2020.03.009

Cited by 8 publications

(9 citation statements)

References 30 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…EW technique is also applicable through sections of the sectional elements, e.g., layers of shell, and cells of beam elements. Continuous variation of properties can be approximated using the EW technique by increasing the number of elements/layers/cells in the direction of variation [8,10].…”

Section: Element/layer-wise Materials Assignment (Ew)mentioning

confidence: 99%

Modeling Functionally Graded Materials in ANSYS APDL

Hassan

Kurgan

2022

Preprint

Self Cite

View full text Add to dashboard Cite

Since its first implementation in the mid-eighties of the past century, Functionally Graded Materials (FGM) have been under heavy research in many directions including manufacturing techniques, modeling, and exploring possible applications. Numerous FGM models and analysis methods are continuously appended to the literature. Just like in the rest of the mechanical design field, the Finite Element Method (FEM) has been extensively used in the analysis of FGM, in addition to being a main validation tool for the other proposed methods. ANSYS has been one of the main general-purpose FEM packages that facilitate the use of FEM. However, no single publication is found exploring the modeling of FGM in ANSYS. This work does just that. It explores and compares the various techniques of modeling FGM in ANSYS using Mechanical APDL. The techniques explored here should be applicable in any other FEM package. APDL codes are provided for the various considered cases. Three main techniques of modeling FGM in ANSYS are presented, namely imposing fictive thermal load, stacking elements/layers, and using user-defined fields. Other advanced methods, that require recompiling the executable ANSYS.exe, are briefly mentioned. Various modeling techniques are implemented on a relatively long cuboid FGM part which is assumed under lateral load and supported at its far edge/s. The configuration of cuboid geometry and lateral load is intentionally considered to allow volume-, area-, and line-finite elements to be implemented. One dimensional continuous and discrete properties variation is considered. The presented modeling techniques of FGM are found equivalent in accuracy.

show abstract

Section: Element/layer-wise Materials Assignment (Ew)mentioning

confidence: 99%

Modeling Functionally Graded Materials in ANSYS APDL

Hassan

Kurgan

2022

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…There is a minor deviation between the physical neutral surface and the mid-plane while appraising the FGMs due to the distribution of mechanical properties. The physical neutral plan's position can be described by [76,78,79],…”

Section: Mathematical Modelingmentioning

confidence: 99%

Thermal buckling of functionally graded piezomagnetic micro- and nanobeams presenting the flexomagnetic effect

Malikan

Wiczenbach

Eremeyev

2021

Continuum Mech. Thermodyn.

View full text Add to dashboard Cite

Galerkin weighted residual method (GWRM) is applied and implemented to address the axial stability and bifurcation point of a functionally graded piezomagnetic structure containing flexomagneticity in a thermal environment. The continuum specimen involves an exponential mass distributed in a heterogeneous media with a constant square cross section. The physical neutral plane is investigated to postulate functionally graded material (FGM) close to reality. Mathematical formulations concern the Timoshenko shear deformation theory. Small scale and atomic interactions are shaped as maintained by the nonlocal strain gradient elasticity approach. Since there is no bifurcation point for FGMs, whenever both boundary conditions are rotational and the neutral surface does not match the mid-plane, the clamp configuration is examined only. The fourth-order ordinary differential stability equations will be converted into the sets of algebraic ones utilizing the GWRM whose accuracy was proved before. After that, by simply solving the achieved polynomial constitutive relation, the parametric study can be started due to various predominant and overriding factors. It was found that the flexomagneticity is further visible if the ferric nanobeam is constructed by FGM technology. In addition to this, shear deformations are also efficacious to make the FM detectable.

show abstract

“…With mathematical operations and concerning the transform equations of coordinates (8), the following transform equations are obtained for the Laplacian operators true∇¯2 and true∇¯4 in skew coordinates ( x , y , z ) 13,15,16,37,38,56 …”

Section: Derivation Of the Equation Governing The Bending Deflection ...mentioning

confidence: 99%

“…Briefly, the EKM method can be employed to rewrite and discretize the transformed equation (equation (11)) in oblique coordinate systems of x and y using the separation of variables and a mapping procedure from the orthogonal to the oblique coordinate system. 15,16,37,38 Now to start the iterative procedure, we consider a proper arbitrary initial guess for the function g j (y) as…”

Section: Introductionmentioning

confidence: 99%

“…The buckling analysis of thin skew plate made of isotropic material on elastic-Pasternak foundation has been performed using extended Kantorovich method in Ahmed Hassan and Kurgan. 37 In Ahmed Hassan and Kurgan, 38 the bending analysis of the skew plate made of functionally graded material on Winkler foundation, and with various boundary conditions under lateral loads has been conducted using the extended Kantorovich method, and the results have been compared with those obtained from finite element method. Thermal buckling analysis of general quadrilateral orthotropic auxetic FGM plates on elastic foundations has been studied in Mansouri and Shariyat 39 using differential quadrature method.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Bending deflection and stress analyses in a thin functionally graded material skew plate with different boundary conditions on the Winkler–Pasternak elastic foundation and under combined in-plane and uniform lateral loads using the extended Kantorovich method

Mamandi

2021

Proceedings of the Institution of Mechanical Engineers, Part C:

View full text Add to dashboard Cite

In this study, bending deflection and stress analyses have been conducted for a thin skew plate made of functionally graded material (FGM) with different boundary conditions on the Winkler–Pasternak elastic foundation and under combined loads including uniform transverse load, normal and shear in-plane forces, and planar body forces. The Cartesian partial differential equation governing the bending deflection of the skew plate has been converted into a partial differential equation in oblique coordinates using the conversion relations. Then, by employing the variational principle and residual weighted Galerkin method and using the Extended Kantorovich Method (EKM), the equation has been converted to a set of linear differential equations in terms of two functions in the longitudinal and transverse directions of the oblique plate, and afterward, the equation has been solved using the iterative solution method. Different boundary conditions in a combined form of simply and clamped supports have been investigated and their effects on bending deflection and generated in-plane normal and shear stresses are discussed.

show abstract

Bending analysis of thin FGM skew plate resting on Winkler elastic foundation using multi-term extended Kantorovich method

Cited by 8 publications

References 30 publications

Modeling Functionally Graded Materials in ANSYS APDL

Modeling Functionally Graded Materials in ANSYS APDL

Thermal buckling of functionally graded piezomagnetic micro- and nanobeams presenting the flexomagnetic effect

Bending deflection and stress analyses in a thin functionally graded material skew plate with different boundary conditions on the Winkler–Pasternak elastic foundation and under combined in-plane and uniform lateral loads using the extended Kantorovich method

Contact Info

Product

Resources

About