Regular Quaternionic Functions and their Applications in Three- dimensional Elasticity

Abstract eng:
In the plane elasticity an effective method of using the holomorphic complex function theory is based on Kolosov-Muskhelishvili formulae. For three–dimensional problems monogenic Clifford functions or regular quaternionic functions of a reduced quaternion variable are used. We present some variants of three–dimensional Kolosov-Muskhelishvili formulae where elastic displacements and stresses are expressed in terms of two arbitrary regular quaternionic functions. It is shown that in particular cases of plane and axially symmetric deformations these representations go into the Kolosov–Muskhelishvili and Solov’ev formulae expressed in terms of two complex functions. Some applications of quaternionic representations for elastic equilibrium problems are shown.

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