APPLICATION OF SPHERICAL HARMONICS FOR COMPUTING FUNDAMENTAL SOLUTIONS OF 3D STATIC THERMOELASTIC PROBLEMS IN QUASICRYSTALS

Abstract

This paper explores the use of spherical harmonics for computing fundamental solutions of three-dimensional static thermoelastic problems in quasicrystals. Quasicrystals are complex anisotropic materials with unique thermo-mechanical behavior, requiring advanced modeling approaches. The fundamental solution serves as a key component in solving boundary value problems for such media. The Radon transform is employed to reduce the governing equations to a more manageable form. Its inverse, expressed as an integral over a hemisphere, is efficiently evaluated by expanding the integrand in spherical harmonics. The first harmonic represents the isotropic response, while higher-order terms capture anisotropic effects. This approach ensures fast convergence and enables semi-analytical representation of solutions. The proposed method enhances both the accuracy and computational efficiency of modeling thermoelastic behavior in quasicrystalline materials.