Dorin Iesan

This paper is concerned with the deformation of beams in the framework of the linear theory of micromorphic elastic solids. First, the plane strain of anisotropic and homogeneous elastic cylinders is investigated. Existence and uniqueness results are presented. Then, Saint-Venant’s problem for micromorphic beams is formulated. A method is established to reduce the extension, bending and torsion to the study of some plane problems. Finally, the deformation of beams loaded on the lateral surface is investigated. As a special case, the solution of the flexure problem is obtained. The method is used to study the deformation of a micromorphic rod subjected to a uniform pressure on the lateral surface.

The interest in the gradient theory of elasticity is stimulated by the fact that this theory is adequate to investigate important problems related to size effects and nanotechnology. In this paper, we use the theory of microstretch solids and the Green-Naghdi theory of thermomechanics of continua to derive a linear strain gradient theory of porous thermoelastic bodies, which is capable of predicting a finite speed of heat propagation and leads to a symmetric conductivity tensor. A uniqueness theorem for the mixed problem is presented. In the case of isotropic solids we establish the continuous dependence of solutions upon initial data and body supplies. The problem of a concentrated heat source is also investigated.

This paper is concerned with a theory of elastic materials with voids where the second gradient of deformation and the second gradient of volume fraction field are added to the set of independent constitutive variables. First, we establish the nonlinear theory and study the continuous dependence of solutions upon initial state and body loads. Then, we derive the linear theory and establish a uniqueness theorem with no definiteness assumption on the constitutive coefficients. We present the equations for homogeneous and isotropic solids and establish a counterpart of the Boussinesq‐Somigliana‐Galerkin solution in the classical elastostatics. The effects of concentrated body loads acting in an infinite space are investigated.