scholarly journals Three-Dimensional Volume Integral Equation Method for Solving Isotropic/Anisotropic Inhomogeneity Problems

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1866
Author(s):  
Jungki Lee ◽  
Mingu Han
Keyword(s):  
Integral Equation ◽  
Three Dimensional ◽  
Practical Interest ◽  
Integral Equation Method ◽  
Equation Method ◽  
Volume Integral ◽  
Volume Integral Equation ◽  
Isotropic Solid ◽  
Anisotropic Inhomogeneity ◽  
Volume Integral Equation Method

In this paper, the volume integral equation method (VIEM) is introduced for the analysis of an unbounded isotropic solid composed of multiple isotropic/anisotropic inhomogeneities. A comprehensive examination of a three-dimensional elastostatic VIEM is introduced for the analysis of an unbounded isotropic solid composed of isotropic/anisotropic inhomogeneity of arbitrary shape. The authors hope that the volume integral equation method can be used to compute critical values of practical interest in realistic models of composites composed of strong anisotropic and/or heterogeneous inhomogeneities of arbitrary shapes.

Parallel Volume Integral Equation Method for Two-Dimensional Elastodynamic Analysis

2019 ◽  
Vol 16 (06) ◽  
pp. 1840025
Author(s):  
Jungki Lee ◽  
Hogwan Jeong
Keyword(s):  
Integral Equation ◽  
Wave Scattering ◽  
Integral Equation Method ◽  
Equation Method ◽  
Two Dimensional ◽  
Volume Integral ◽  
Scattering Problems ◽  
Volume Integral Equation ◽  
Parallel Volume ◽  
Volume Integral Equation Method

The parallel volume integral equation method (PVIEM) is applied for the analysis of two-dimensional elastic wave scattering problems in an unbounded isotropic solid containing various types of multiple multilayered anisotropic inclusions. It should be noted that the volume integral equation method (VIEM) does not require the use of the Green’s function for the anisotropic inclusion — only the Green’s function for the unbounded isotropic matrix is needed. A detailed analysis of the SH wave scattering problem is presented for various types of multiple multilayered orthotropic inclusions. Numerical results are presented for the elastic fields at the interfaces for square and hexagonal packing arrays of various types of multilayered orthotropic inclusions in a broad frequency range of practical interest. Standard parallel programming was used to speed up computation in the VIEM. The PVIEM enables us to investigate the effects of single/multiple scattering, fiber packing type, fiber volume fraction, single/multiple layer(s), multilayer’s shapes and geometry, isotropy/anisotropy, and softness/hardness of various types of multiple multilayered anisotropic inclusions on displacements and stresses at the interfaces of the inclusions and far-field scattering patterns. Also, powerful capabilities of the PVIEM for the analysis of general two-dimensional multiple scattering problems are investigated.

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