The use of quaternions to generalize the Kolosov-Muskhelishvili method to three-dimensional problems of the theory of elasticity

Abstract A boundary equation is obtained for the first fundamental problem of the theory of elasticity using the Kolosov-Muskhelishvili method, by replacing the field of complex numbers by the field of Hamiltonian quaternions. A specific solution is given for the space with an elliptical cavity, subjected to a uniform tensile force at infinity.