Transient analysis of FGM plates bending under thermal loading: comparative study within classical and generalized thermoelasticity

Ladislav Sator,Jan Sladek,Vladimir Sladek,I Malujda,Ł Warguła,D Wojtkowiak,P Krawiec,M Dudziak,D Wilczyński,J Górecki,M Berdychowski,K Talaśka

doi:10.1051/matecconf/201925406004

Abstract

In the classical thermoelasticty, there is coupling between thermal and elastic fields, in general, but the elastic and thermal excitations spread according to physically different laws. In classical thermodynamics, the temperature change propagates according to diffusion law. However, the heat pulses at low temperature propagate evidently with a finite velocity in view of waves similar to spreading of elastic excitations. A great effort has been spent in this matter and there are two main non-classical theories: Lord-Shulman theory and Green-Lindsay theory. In this paper, we compare the response of thin FGM plates under thermal load within the classical and non-classical theories of thermoelasticity. The variable material properties of plate (such as the Young’s modulus, thermal expansion coefficient, etc.) are allowed to be continuous functions of the position. The strong form meshless formulations for solution of considered initial-boundary value problems is developed in combination with Moving Least Squares (MLS) approximation scheme. The response of FGM plates on thermal loading is studied via numerical simulations with focusing on comparison of results obtained within the classical and generalized thermoelasticity. The numerical results concern also the parametric study of influence of gradation of material coefficients on bending of FGM plates

Highlights

Thermal stresses, especially at the interface between two different materials, often represent a significant factor in the failure of laminated composite structures
The temperature field is coupled with the elastic fields, in general, but the temperature change does not propagate in a wave form [1]
The strong form meshless formulations for solution of thin plate bending problem is developed in combination with Moving Least Squares (MLS) approximation scheme [2]

Summary

Introduction

Thermal stresses, especially at the interface between two different materials, often represent a significant factor in the failure of laminated composite structures. There is a need to accurately predict thermal stresses in composite structures [9]. This is a strong motivation to replace laminated plate structures by FGM ones if possible. The heat pulses at low temperature propagate with a finite velocity like waves. Such a behaviour is described within Lord-Shulman theory of generalized thermoelasticity [10]. The bending of thin FGM plates under thermal load is considered within the classical and generalized theory of thermoelasticity. The attention is paid to the numerical investigation of the influence of several parameters of gradations of material coefficients on the deflection of the plate

Governing equations

Numerical experiments

Conclusion