A new boundary element formulation for modeling and simulation of three‐temperature distributions in carbon nanotube fiber reinforced composites with inclusions

Abstract

A new boundary element method (BEM) formulation is developed in this paper for modeling and simulation of nonlinear three‐temperature (3T) distributions in carbon nanotube (CNT) fiber‐reinforced composites embedded with many rigid‐line inclusions that can be treated as having constant temperature distributions. The fast multipole method (FMM) has been applied to accelerate the proposed BEM solution of the considered problem of a large number of nano‐inclusions, and therefore, the computational complexity and computational time are reduced. The CPU time and memory requirement are also reduced by implementing generalized modified shift‐splitting (GMSS) iteration method which does not require the entire matrix to be stored in the memory. Then, we introduced a new formula which can play an important role in solving thermal problems arising in CNT nanotechnology. Effective thermal conductivity of fiber‐reinforced composites can be evaluated using the computed temperature and heat flux fields. The fast multipole BEM results are depicted graphically to show the effects of CNT manufacturing methods and thermal conductivities of different CNT composites on the temperature and heat flux distributions. The computational performance of the proposed methodology has been demonstrated. The fast multipole BEM results are compared graphically with the finite element method (FEM) results and with the experimental results reported in the literature. Excellent agreements are found in both cases, which clearly demonstrate the validity, accuracy, and efficiency of our proposed algorithm and modeling and simulation technique. The findings and solutions of this study contribute to the further development of CNT nanotechnology applications and devices.

Boundary Element and Sensitivity Analysis of Anisotropic Thermoelastic Metal and Alloy Discs with Holes

“…It can be seen from these figures that our BEM results are in excellent agreement with the FEM results and experimental (Exp) results of Wang et al [14]. We refer the interested readers to [15][16][17][18][19][20][21][22] for further references. The advantages of spark plasma sintering (SPS) over conventional hot pressing (HP) or hot isostatic pressing (HIP), such as reduced sintering time and temperatures, minimize grain growth and frequently result in improved mechanical, physical, or optical properties.…”

“…It can be seen from these figures that our BEM results are in excellent agreement with the FEM results and experimental (Exp) results of Wang et al [14]. We refer the interested readers to [15][16][17][18][19][20][21][22] for further references. Table 1 shows a comparison of the computer resources needed in the analysis of anisotropic thermoelastic metal and alloy discs, for BEM with additional line integrals (Case 1) versus BEM without additional line integrals (Case 2).…”

“…It can be seen from these figures that our BEM results are in excellent agreement with the FEM results and experimental (Exp) results of Wang et al [ 14 ]. We refer the interested readers to [ 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 ] for further references.…”

RETRACTED ARTICLE: Fractional boundary element solution of three-temperature thermoelectric problems

“…Numerical methods, including the BEM, should be used to solve such problems. Different three-temperature theories have been investigated in the context of micropolar-thermoelasticity 40 , carbon nanotube fiber reinforced composites 41 , micropolar piezothermoelasticity 42 , Micropolar Magneto-thermoviscoelasticity 43 and Magneto-thermooviscoelasticity 44 Also, Fahmy introduced new boundary element models for bioheat problems 45 , micropolar composites with temperature-dependent problems 46 , Generalized Porothermoelastic Problems 47 and Size-Dependent thermopiezoelectric Problems 48…”

Acoustic radiation performance investigation of a double-walled cylindrical shell equipped with annular plates and porous foam media

“…Besides, the BEM impose restrictions on the ability of handling the exterior acoustic problem in nonisotropic and nonhomogeneous media. In these cases, a novel singular boundary method (SBM) 25,26 was proposed to handle the acoustic problems while Fahmy et al [27][28][29][30][31][32][33][34][35] optimized the algorithm to reduce the computational complexity and computational time and to overcome some nonlinear problems. These methods contribute to solving singular or hypersingular integrals, but much of the research is focused on future-proofing the method and higher resolutions of elements is continually desired, particularly as this is necessary for modeling high frequency problems.…”