For linear partial differential equations, there exist well-developed classical methods of their analytical solution, which, in particular, includes the separation of variables, different integral transforms, Fourier series and their generalizations. At the same time, the study of symmetry properties of such equations is important, first of all, for the development of methods of symmetry analys...

Athermal random fiber networks are usually modeled by representing each fiber as a truss, a Euler-Bernoulli or a Timoshenko beam, and, in the case of cross-linked networks, each cross-link as a pinned, rotating, or welded joint. In this work we study the effect of these various modeling options on the dependence of the overall network stiffness on system parameters. We conclude that Timoshenko ...

A complex network of Euler-Bernoulli beams is studied in this paper. As for this network, the boundary vertices are clamped, the displacements of the structure are continuous but the rotations of different beams are not continuous at the interior vertices. The feedback controller are designed at the interior nodes to stabilize the elastic system. The well-posed-ness of the closed loop system is...

In the present study, nonlinear free vibration behavior of nanobeam subjected to magnetic field is investigated based on Eringen’s nonlocal elasticity and Euler–Bernoulli beam theory. The Hamilton’s principal is adopted to derive the governing equations together with Euler–Bernoulli beam theory and the von-Kármán’s nonlinear strain–displacement relationships. An approximate analytical solution ...

In this paper, we use Hermite cubic finite elements to approximate the solutions of a nonlinear Euler– Bernoulli beam equation. The equation is derived from Hollomon’s generalized Hooke’s law for work hardening materials with the assumptions of the Euler–Bernoulli beam theory. The Ritz–Galerkin finite element procedure is used to form a finite dimensional nonlinear program problem, and a nonlin...