A general solution for three-dimensional problems of anisotropic elasticity

Abstract eng:
Clifford algebra and Clifford analysis, which are the m-dimensional extensions of complex algebra and complex analysis are applied to solve three-dimensional problems of anisotropic elasticity. Using the coordinate transformation as what is done in the Lekhnitskii formalism or the Stroh formalism for two-dimensional problems, we convert the governing equations of three-dimensional elasticity of anisotropic materials into eigenvalue problems taking values of Clifford numbers. After solving the eigenvalue problems with the aid of Clifford analysis, we obtain a truly three-dimensional general solution of anisotropic elasticity.

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