Thermal stress analysis of in-plane two-directional functionally graded plates subjected to in-plane edge heat fluxes

2016 ◽  
Vol 232 (8) ◽  
pp. 693-716
Author(s):  
MK Apalak ◽  
MD Demirbas
Keyword(s):  
Mechanical Properties ◽  
Thermal Stress ◽  
Functionally Graded ◽  
Heat Fluxes ◽  
Material Composition ◽  
Stress Distributions ◽  
Thermal And Mechanical Properties ◽  
Functionally Graded Plates ◽  
Spatial Derivatives ◽  
Derivatives Of

This study investigates the thermal stress and deformation states of bi-directional functionally graded clamped plates subjected to constant in-plane heat fluxes along two ceramic edges. The material properties of the functionally graded plates were assumed to vary with a power law along two in-plane directions not through the plate thickness direction. The spatial derivatives of thermal and mechanical properties of the material composition were considered, and the effects of the bi-directional composition variations and spatial derivative terms on the displacement, strain and stress distributions were also investigated. The heat conduction and Navier equations describing the two-dimensional thermo-elastic problem were discretized using finite-difference method, and the set of linear equations were solved using the pseudo singular value method. The compositional gradient exponents and the spatial derivatives of thermal and mechanical properties of the material composition were observed to play an important role especially on the heat transfer durations, the displacement and strain distributions, but had a minor effect on the temperature and stress distributions.

Thermal stress analysis of one- and two-dimensional functionally graded plates subjected to in-plane heat fluxes

2017 ◽  
Vol 233 (4) ◽  
pp. 546-562 ◽  
Author(s):  
M Didem Demirbas ◽  
M Kemal Apalak
Keyword(s):  
Heat Flux ◽  
Thermal Stress ◽  
Functionally Graded ◽  
Heat Fluxes ◽  
Gradient Material ◽  
Two Dimensional ◽  
Functionally Graded Plates ◽  
Functionally Gradient Material ◽  
Functionally Gradient ◽  
Composition Variation

This study addresses the thermal stress analysis of one- and two-dimensional functionally graded plates subjected to in-plane heat fluxes. The material composition variation is assumed in-plane, not through the plate thickness according to a power-law distribution in terms of the volume fraction of the constituents. The mathematical model considers the spatial derivatives of local mechanical and thermal properties. The heat transfer and Navier equations of the two-dimensional thermo-elastic model were discretized using the finite difference method, and the set of linear equations were solved using the pseudo singular value method. The performance of both one- and two-dimensional functionally gradient material plates was investigated under two types of in-plane fluxes: one-edge and two-edges. For each type of heat fluxes, one- and two-dimensional functionally gradient material plates exhibited different displacement, stress and strain distributions. The temperature levels and distributions were affected with increasing ceramic constituent in the composition variation of the plate. One-dimensional functionally gradient material plate was more suitable for an one-edge heat flux along the direction of material composition variation, whereas two-dimensional functionally gradient material plate was more effective on the relieving the thermal stresses for a two-edges heat flux.

scholarly journals A Novel MDD-Based BEM Model for Transient 3T Nonlinear Thermal Stresses in FGA Smart Structures

2020 ◽  
Author(s):  
Mohamed Abdelsabour Fahmy
Keyword(s):  
Thermal Stress ◽  
Boundary Element ◽  
Thermal Stresses ◽  
Smart Structures ◽  
Industrial Applications ◽  
Functionally Graded ◽  
Numerical Results ◽  
Stress Distributions ◽  
Proposed Model ◽  
Further Development

The main objective of this chapter is to introduce a novel memory-dependent derivative (MDD) model based on the boundary element method (BEM) for solving transient three-temperature (3T) nonlinear thermal stress problems in functionally graded anisotropic (FGA) smart structures. The governing equations of the considered study are nonlinear and very difficult if not impossible to solve analytically. Therefore, we develop a new boundary element scheme for solving such equations. The numerical results are presented highlighting the effects of the MDD on the temperatures and nonlinear thermal stress distributions and also the effect of anisotropy on the nonlinear thermal stress distributions in FGA smart structures. The numerical results also verify the validity and accuracy of the proposed methodology. The computing performance of the proposed model has been performed using communication-avoiding Arnoldi procedure. We can conclude that the results of this chapter contribute to increase our understanding on the FGA smart structures. Consequently, the results also contribute to the further development of technological and industrial applications of FGA smart structures of various characteristics.

Improved Mathematical Models of Thermal Residual Stresses in Functionally Graded Adhesively Bonded Joints: A Critical Review

2019 ◽  
Vol 7 (4) ◽  
pp. 367-416 ◽  
Author(s):  
M. Kemal Apalak ◽  
M. Didem Demirbas
Keyword(s):  
Residual Stresses ◽  
Mathematical Models ◽  
Adhesive Layer ◽  
Adhesive Joints ◽  
Functionally Graded ◽  
Stress And Strain ◽  
Stress Distributions ◽  
Adhesively Bonded ◽  
Thermal Residual Stresses ◽  
Derivatives Of

Functionally graded material (FGM) concept has been applied successfully in order to improve/design heat transfer, electric and electronic conductivity, static and dynamic strengths of adhesive joints by reliving stress distributions in both adhesive and adherend materials. This new approach relies on tailoring material composition of adhesive and adherends along one or more coordinate directions. Thermal residual stresses in adhesive joints are a vital issue in terms of the joint strength. FGM concept also allows to relieve/control thermal residual stresses encountered in adhesive joints due to mismatches between coefficients of thermal expansion of adhesive and adherend materials. Mathematical models and solutions on the thermal residual stress analysis have been continuously improved. This paper reviews the current status of mathematical models, and offers an improved mathematical model and numerical solution method by considering two-dimensional thermal stress and deformation states of adhesively bonded bi-directional functionally graded clamped plates subjected to an in-plane heat flux along one of the ceramic edges. This mathematical model assumes the material properties of the functionally graded plates to vary with a power law along two in-plane directions and not through the plate thickness direction, in particular, considers the spatial derivatives of thermal and mechanical properties of the material, and enables the investigation of the effects of the bi-directional composition variations and spatial derivative terms on the displacement, strain and stress distributions. The heat conduction and Navier equations describing the twodimensional thermo-elastic problem are discretized using finite-difference method, and the set of linear equations are solved using the pseudo singular value method. The functionally graded plates relieve both stress and strain distributions and levels in the adhesive layer and in the plates even though the adhesive layer is still ungraded. The spatial derivatives of mechanical and thermal properties of the local material become more effective on the strain and stress distributions of the plates and adhesive layer. The model, disregarding these derivative terms, exhibits sensitivity to small changes in the compositional gradients (n, m) by adjusting the variations of ceramic volume fraction along the x - and y-directions, respectively, and instability in the calculation of stress and strain distributions and levels. However, the improved model with material derivatives, which considers the effects of these derivative terms, predicts stress and strain distributions and levels complying with changes in the compositional gradient exponents.

scholarly journals Experimental Investigation of Stress Distributions in 3D Printed Graded Plates with a Circular Hole

Materials ◽  
2021 ◽  
Vol 14 (24) ◽  
pp. 7845
Author(s):  
Quanquan Yang ◽  
He Cao ◽  
Youcheng Tang ◽  
Yun Li ◽  
Xiaogang Chen
Keyword(s):  
Experimental Investigation ◽  
Stress Concentration ◽  
Young’S Modulus ◽  
Circular Hole ◽  
Young's Modulus ◽  
Theoretical Models ◽  
Research Field ◽  
Functionally Graded ◽  
Stress Distributions ◽  
Functionally Graded Plates

An experimental investigation is presented for the stress distributions in functionally graded plates containing a circular hole. On the basis of the authors’ previously constructed theoretical model, two kinds of graded plates made of discrete rings with increasing or decreasing Young’s modulus were designed and fabricated in virtue of multi-material 3D printing. The printed graded plates had accurate size, smooth surface, and good interface. The strains of two graded plates under uniaxial tension were measured experimentally using strain gages. The stresses were calculated within the range of linear elastic from the measured strains and compared with analytical theory. It is found that the experimental results are consistent with the theoretical results, and both of them indicate that the stress concentration around the hole reduces obviously in graded plates with radially increasing Young’s modulus, in comparison with that of perforated homogenous plates. The successful experiment in the paper provides a good basis and support for the establishment of theoretical models and promotes the in-depth development of the research field of stress concentration in functionally graded plates.

Sign in / Sign up

Export Citation Format

Share Document