Abstract

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.

Highlights

  • Smart materials, which are called intelligent materials, are engineered materials that have the ability to respond to the changes that occur around them in a controlled fashion by external stimuli, such as stress, heat, light, ultraviolet, moisture, chemical compounds, mechanical strength, and electric and magnetic fields

  • The main aim of this chapter is to introduce a new memory-dependent derivative (MDD) model based on boundary element method (BEM) for obtaining the transient three-temperature nonlinear thermal stresses in functionally graded anisotropic (FGA) smart structures

  • We propose a new boundary element formulation for solving such equations

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Summary

Introduction

Smart materials, which are called intelligent materials, are engineered materials that have the ability to respond to the changes that occur around them in a controlled fashion by external stimuli, such as stress, heat, light, ultraviolet, moisture, chemical compounds, mechanical strength, and electric and magnetic fields. In the BEM, only the boundary of the domain needs to be discretized, so it has a major advantage over other methods requiring full domain discretization [81–87] such as finite difference method (FDM), finite element method (FEM), and finite volume method (FVM) in engineering applications This advantage of BEM over domain methods has significant importance for modeling of nonlinear generalized thermoelastic problems which can be implemented using BEM with little cost and less input data. The main objective of this chapter is to introduce a novel memory-dependent derivative model for solving transient three-temperature nonlinear thermal stress problems in functionally graded anisotropic (FGA) smart structures.

Formulation of the problem
BEM solution of temperature field
BEM solution of displacement field
Computational performance of the problem
Methods
Numerical results and discussion
Conclusion
Full Text
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