Bending and free vibrations of functionally graded annular and circular micro-plates under thermal loading

2016-03-01
Eshraghi, Iman
Dağ, Serkan
Soltani, Nasser
We introduce solution methods capable of treating static bending and free vibration problems involving thermally loaded functionally graded annular and circular micro-plates. Formulation is based on modified couple stress theory; and related governing partial differential equations and boundary conditions are derived by means of Hamilton's principle. Displacement field is expressed in a unified way so as to produce numerical results in accordance with Kirchhoff, Mindlin, and third-order shear deformation theories. All material properties, including the length scale parameter, are assumed to be functions of the thickness coordinate. The static and dynamic problems are solved by means of differential quadrature method. Proposed procedures are verified through comparisons made to the findings available in the technical literature on thermally stressed axisymmetric plates. Detailed numerical results are presented in order to demonstrate the influences of thermal loading magnitude, and material and geometric parameters upon static deformation profiles, stresses, and natural vibration frequencies.
COMPOSITE STRUCTURES

Suggestions

Modelling of graded rectangular micro-plates with variable length scale parameters
Aghazadeh, Reza; Dağ, Serkan; Ciğeroğlu, Ender (2018-03-10)
This article presents strain gradient elasticity-based procedures for static bending, free vibration and buckling analyses of functionally graded rectangular micro-plates. The developed method allows consideration of smooth spatial variations of length scale parameters of strain gradient elasticity. Governing partial differential equations and boundary conditions are derived by following the variational approach and applying Hamilton's principle. Displacement field is expressed in a unified way to produce n...
Thermal fracture analysis of orthotropic functionally graded materials using an equivalent domain integral approach
Dağ, Serkan (2006-12-01)
A new computational method based on the equivalent domain integral (EDI) is developed for mode I fracture analysis of orthotropic functionally graded materials (FGMs) subjected to thermal stresses. By using the constitutive relations of plane orthotropic thermoelasticity, generalized definition of the J-integral is converted to an equivalent domain integral to calculate the thermal stress intensity factor. In the formulation of the EDI approach, all the required thermomechanical properties are assumed to ha...
Free vibration analysis of functionally graded rectangular nanoplates considering spatial variation of the nonlocal parameter
Ghassabı, A. Alipour; Dağ, Serkan; Ciğeroğlu, Ender (2017-01-01)
WE PRESENT A NEW NONLOCAL ELASTICITY-BASED ANALYSIS METHOD for free vibrations of functionally graded rectangular nanoplates. The introduced method allows taking into account spatial variation of the nonlocal parameter. Governing partial differential equations and associated boundary conditions are derived by employing the variational approach and applying Hamilton's principle. Displacement field is expressed in a unified way to be able to produce numerical results pertaining to three different plate theori...
Consideration of spatial variation of the length scale parameter in static and dynamic analyses of functionally graded annular and circular micro-plates
Eshraghi, Iman; Dağ, Serkan; Soltani, Nasser (2015-09-01)
This article introduces new methods for static and free vibration analyses of functionally graded annular and circular micro-plates, which can take into account spatial variation of the length scale parameter. The underlying higher order continuum theory behind the proposed approaches is the modified couple stress theory. A unified way of expressing the displacement field is adopted so as to produce numerical results for three different plate theories, which are Kirchhoff plate theory (KPT), Mindlin plate t...
Contact mechanics of graded materials: Analyses using singular integral equations
Dağ, Serkan (2006-10-18)
Contact stress distribution at an FGM surface is evaluated using an analytical technique based on the singular integral equations. An FGM half-plane is assumed to be in sliding contact with a rigid stamp of an arbitrary profile. The functionally graded medium is assumed to possess two-dimensional material property variations. Two independent nonhomogeneity constants are used to derive the governing partial differential equations. By using the integral transform techniques, all boundary conditions are satisf...
Citation Formats
I. Eshraghi, S. Dağ, and N. Soltani, “Bending and free vibrations of functionally graded annular and circular micro-plates under thermal loading,” COMPOSITE STRUCTURES, pp. 196–207, 2016, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/46745.