Sergei Khakalo

TL;DR: In this paper, a generalized Bernoulli-Euler and Timoshenko sandwich beam models are derived by means of a computational homogenization technique and two additional length scale parameters involved in the models are validated by matching the lattice response in benchmark problems for static bending and free vibrations calibrating the strain energy and inertia gradient parameters, respectively.

TL;DR: In this paper, the authors formulated the fourth-order boundary value problems of one parameter gradient-elastic bar and plane strain/stress models in a variational form within an H 2 Sobolev space setting.

TL;DR: In this article, the fundamental equations for Form II of Mindlin's second strain gradient elasticity theory for isotropic materials are derived and a corresponding simplified formulation is then proposed, with six and two higher-order material parameters for the strain and kinetic energy, respectively.

TL;DR: In isogeometric analysis of higher-order strain gradient elasticity by user element implementations within a commercial finite element software Abaqus, the convergence properties of the method in the energy norm are shown to be optimal with respect to the NURBS order of the discretizations.

TL;DR: In this paper, the authors developed a pair of two-scale plate models relying on the anisotropic form of Mindlin's strain gradient thermoelasticity theory for three-dimensional cellular plate-like structures with a triangular microarchitecture.