In this paper, we give the first a priori error analysis of the hybridizable discontinuous Galerkin (HDG) methods for Timoshenko beams. The analysis is based on the use of a projection especially designed to fit the structure of the numerical traces of the HDG method. This property allows to prove in a very concise manner that the projection of the errors is bounded in terms of the distance bet...

The dynamical stability of planar networks of non-uniform Timoshenko beams system is considered. Suppose that the displacement and rotational angle is continuous at the common vertex of this network and the bending moment and shear force satisfies Kirchhoff’s laws, respectively. Timedelay terms exist in control inputs at exterior vertices. The feedback control laws are designed to stabilize thi...

The numerical solution of boundary value problems in solid mechanics is dominated by the Finite Element Method (FEM). present study provides an alternative approach using Theory Functional Connections (TFC) for solving this type. Here TFC used to solve multiple beam Timoshenko–Ehrenfest theory which accounts transverse shear strain. results obtained are then compared those with both FEM and ana...

In this paper, surface effects including surface elasticity, surface stress and surface density, on the free vibration analysis of Euler-Bernoulli and Timoshenko nanobeams are considered using nonlocal elasticity theory. To this end, the balance conditions between nanobeam bulk and its surfaces are considered to be satisfied assuming a linear variation for the component of the normal stress thr...

in this paper, surface and piezoelectric effects on the vibration behavior of nanowires (nws) are investigated by using a timoshenko beam model. the electric field equations and the governing equations of motion for the piezoelectric nws are derived with the consideration of surface effects. by the exact solution of the governing equations, an expression for the natural frequencies of nws with ...