• Steel and Composite Structures
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• v.51 no.3
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• pp.261-270
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• 2024

This paper proposes an effective method for optimizing the structure of functionally graded isotropic and incompressible linear elastic materials. The main emphasis is on utilizing a specialized polytopal composite finite element (PCE) technique capable of handling a broad range of materials, addressing common volumetric locking issues found in nearly incompressible substances. Additionally, it employs a continuum model for bi-directional functionally graded (BFG) material properties, amalgamating these aspects into a unified property function. This study thus provides an innovative approach that tackles diverse material challenges, accommodating various elemental shapes like triangles, quadrilaterals, and polygons across compressible and nearly incompressible material properties. The paper thoroughly details the mathematical formulations for optimizing the topology of BFG structures with various materials. Finally, it showcases the effectiveness and efficiency of the proposed method through numerous numerical examples.

• Advances in aircraft and spacecraft science
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• v.5 no.3
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• pp.295-318
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• 2018

This research studies thermo-elastic behavior of rotating micro discs that are employed in various micro devices such as micro gas turbines. It is assumed that material is functionally graded with a variable profile thickness, density, shear modulus and thermal expansion in terms of radius of micro disc and as a power law function. Boundary condition is considered fixed-free with uniform thermal loading and elastic field is symmetric. Using incompressible material's constitutive equation, we extract governing differential equation of four orders; to solution this equation, we utilize general differential quadrature (GDQ) method and the results are schematically pictured. The obtained result in a particular case is compared with another work and coincidence of results is shown. We will find out that surface effect tends to split micro disc's area to compressive and tensile while nonlocal parameter tries to converge different behaviors with each other; this convergence feature make FGIMs capable to resist in high temperature and so in terms of thermo-elastic behavior we can suggest, using FGIMs in micro devices such as micro turbines (under glass transition temperature).

• Structural Engineering and Mechanics
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• v.50 no.1
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• pp.53-71
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• 2014

A semi-analytical method is developed to consider free vibrations of a functionally graded elastic plate resting on Winkler elastic foundation and in contact with a quiescent fluid. Material properties are assumed to be graded distribution along the thickness direction according to a power-law in terms of the volume fractions of the constituents. The fluid is considered to be incompressible and inviscid. In the analysis, the effect of an in-plane force in the plate due to the weight of the fluid is taken into account. By satisfying the compatibility conditions along the interface of fluid and plate, the fluid-structure interaction is taken into account and natural frequencies and mode shapes of the coupled system are acquired by employing energy methods. The results obtained from the present approach are verified by those from a finite element analysis. Besides, the effects of volume fractions of functionally graded materials, Winkler foundation stiffness and in-plane forces on the dynamic of plate are elucidated.

• Steel and Composite Structures
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• v.45 no.1
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• pp.39-49
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• 2022

This research investigates a rotary disk with variable cross-section and incompressible hyperelastic material with functionally graded properties in large hyperelastic deformations. For this purpose, a power relation has been used to express the changes in cross-section and properties of hyperelastic material. So that (m) represents the changes in cross-section and (n) represents the manner of changes in material properties. The constants used for hyperelastic material have been obtained from experimental data. The obtained equations have been solved for different m, n, and (angular velocity) values, and the values of radial stresses, tangential stresses, and elongation have been compared. The results show that m and n have a significant impact on disk behavior, so the expected behavior of the disk can be obtained by an optimal selection of these two parameters.