Semi-Analytical Solution for the Static Analysis of 2D Functionally Graded Solid and Annular Circular Plates Resting on Elastic Foundation

2013 ◽  
Vol 20 (7) ◽  
pp. 515-528 ◽  
Author(s):  
A. Behravan Rad ◽  
A. Alibeigloo
Keyword(s):  
Analytical Solution ◽  
Static Analysis ◽  
Elastic Foundation ◽  
Functionally Graded ◽  
Circular Plates

Semi-Analytical Solution for Functionally Graded Solid Circular and Annular Plates Resting on Elastic Foundations Subjected to Axisymmetric Transverse Loading

2012 ◽  
Vol 4 (2) ◽  
pp. 205-222 ◽  
Author(s):  
A. Behravan Rad
Keyword(s):  
Elastic Foundation ◽  
Differential Quadrature Method ◽  
Three Dimensional ◽  
Theory Of Elasticity ◽  
Functionally Graded ◽  
Circular Plates ◽  
Linear Elastic ◽  
Edge Conditions ◽  
The One ◽  
Foundation Plate

AbstractIn this paper, the static analysis of functionally graded (FG) circular plates resting on linear elastic foundation with various edge conditions is carried out by using a semi-analytical approach. The governing differential equations are derived based on the three dimensional theory of elasticity and assuming that the mechanical properties of the material vary exponentially along the thickness direction and Poisson’s ratio remains constant. The solution is obtained by employing the state space method (SSM) to express exactly the plate behavior along the graded direction and the one dimensional differential quadrature method (DQM) to approximate the radial variations of the parameters. The effects of different parameters (e.g., material property gradient index, elastic foundation coefficients, the surfaces conditions (hard or soft surface of the plate on foundation), plate geometric parameters and edges condition) on the deformation and stress distributions of the FG circular plates are investigated.

scholarly journals Bending analysis of functionally graded beam with porosities resting on elastic foundation based on neutral surface position

2019 ◽  
Vol 13 (1) ◽  
pp. 33-45 ◽  
Author(s):  
Nguyen Thi Bich Phuong ◽  
Tran Minh Tu ◽  
Hoang Thu Phuong ◽  
Nguyen Van Long
Keyword(s):  
Analytical Solution ◽  
Elastic Foundation ◽  
Power Law ◽  
Coupling Effect ◽  
Functionally Graded ◽  
Transverse Load ◽  
Neutral Surface ◽  
Equilibrium Equations ◽  
Functionally Graded Beam ◽  
Bending Analysis

In this paper, the Timoshenko beam theory is developed for bending analysis of functionally graded beams having porosities. Material properties are assumed to vary through the height of the beam according to a power law. Due to unsymmetrical material variation along the height of functionally graded beam, the neutral surface concept is proposed to remove the stretching and bending coupling effect to obtain an analytical solution. The equilibrium equations are derived using the principle of minimum total potential energy and the physical neutral surface concept. Navier-type analytical solution is obtained for functionally graded beam subjected to transverse load for simply supported boundary conditions. The accuracy of the present solutions is verified by comparing the obtained results with the existing solutions. The influences of material parameters (porosity distributions, porosity coefficient, and power-law index), span-to-depth ratio and foundation parameter are investigated through numerical results. Keywords: functionally graded beam; bending analysis; porosity; elastic foundation; bending; neutral surface. Received 10 December 2018, Revised 28 December 2018, Accepted 24 January 2019

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