A detailed variational formulation is provided for a simplified strain gradient elasticity theory
by using the principle of minimum total potential energy. This leads to the simultaneous …

This article is devoted to the formulation and numerical solution of boundary-value problems
in the theory of elasticity with respect to deformations. Similar to the well-known Beltrami …

The main parameters characterizing the process of deformation of solids are displacements,
strain and stress tensors. From the point of view of the strength and reliability of the structure …

Usually, the boundary value problems of the theory of elasticity are formulated with respect
to displacements, and are reduced to the well-known Lame equations. Strains and stresses …

The dual conservation laws of elasticity are systematically re-examined by using both
Noether's variational approach and Coleman–Noll–Gurtin's thermodynamics approach …

This review is devoted to various formulations of problems in stresses in the linear theory of
elasticity, taking into account the compatibility conditions in various ways. This paper is …

It is known that the plane problems of the theory of elasticity and thermoelasticity are usually
reduced to solving the biharmonic equation with respect to the Airy stress function. Solutions …

We consider arbitrary preexisting residual stress states in arbitrarily shaped, unloaded
bodies. These stresses must be self-equilibrating and traction free. Common treatments of …

The problem of finding the number of independent compatibility equations in strains in n-
dimensional Euclidean space is discussed. The number in question coincides with the …

In this work the continuum theory of defects has been revised through the development of
kinematic defect potentials. These defect potentials and their corresponding variational …