One representation of the conditions of the compatibility of deformations
It is shown that the conditions of the compatibility of deformations can be represented in the form of three equations in the region occupied by the deformed body, and three boundary conditions on its surface. A combination of the requirements of the conditions of equilibrium and compatibility leads to a unique formulation of the problem in terms of the stresses for the deformed body in the form of a system of six equations for the six unknown components of the stress tensor, and of a set of boundary conditions corresponding to the ninth order of the system of equations. The classical formulation of the problem in terms of the stresses for a deformed rigid body leads to the need to solve a system containing its three equations of equilibrium and six compatability equations for six unknown components of the stress tensor. It can therefore be expected that some of the demands imposed by the formulation of the problem may be redundant. After all, such reasoning has been used systematically in similar situations in the scientific literature when formulating new problems, and was found to be effective.
scientific article; zbMATH DE number 4018480