S. Papargyri-Beskou

Bio: S. Papargyri-Beskou is an academic researcher from Aristotle University of Thessaloniki. The author has contributed to research in topics: Boundary value problem & Equations of motion. The author has an hindex of 13, co-authored 26 publications receiving 1045 citations.

Static, stability and dynamic analysis of gradient elastic flexural Kirchhoff plates

Abstract: The governing equation of motion of gradient elastic flexural Kirchhoff plates, including the effect of in-plane constant forces on bending, is explicitly derived. This is accomplished by appropriately combining the equations of flexural motion in terms of moments, shear and in-plane forces, the moment–stress relations and the stress–strain equations of a simple strain gradient elastic theory with just one constant (the internal length squared), in addition to the two classical elastic moduli. The resulting partial differential equation in terms of the lateral deflection of the plate is of the sixth order instead of the fourth, which is the case for the classical elastic case. Three boundary value problems dealing with static, stability and dynamic analysis of a rectangular simply supported all-around gradient elastic flexural plate are solved analytically. Non-classical boundary conditions, in additional to the classical ones, have to be utilized. An assessment of the effect of the gradient coefficient on the static or dynamic response of the plate, its buckling load and natural frequencies is also made by comparing the gradient type of solutions against the classical ones.

Static and dynamic analysis of a gradient-elastic bar in tension.

Abstract: The problem of a bar under a static or dynamic uniaxial tension is studied analytically on the basis of a simple linear theory of gradient elasticity with surface energy. The dynamic case includes both wave propagation analysis and forced longitudinal vibrations. The governing equations of equilibrium and motion are obtained by a combination of the basic equations and a variational statement. The additional boundary conditions of the static and dynamic cases are obtained by both variational and weighted residuals approaches. Various boundary value problems under both static and dynamic loading conditions are solved, and the gradient-elasticity effect on the solutions is identified and assessed.

A microstructure-dependent Timoshenko beam model based on a modified couple stress theory

Abstract: A microstructure-dependent Timoshenko beam model is developed using a variational formulation. It is based on a modified couple stress theory and Hamilton's principle. The new model contains a material length scale parameter and can capture the size effect, unlike the classical Timoshenko beam theory. Moreover, both bending and axial deformations are considered, and the Poisson effect is incorporated in the current model, which differ from existing Timoshenko beam models. The newly developed non-classical beam model recovers the classical Timoshenko beam model when the material length scale parameter and Poisson's ratio are both set to be zero. In addition, the current Timoshenko beam model reduces to a microstructure-dependent Bernoulli–Euler beam model when the normality assumption is reinstated, which also incorporates the Poisson effect and can be further reduced to the classical Bernoulli–Euler beam model. To illustrate the new Timoshenko beam model, the static bending and free vibration problems of a simply supported beam are solved by directly applying the formulas derived. The numerical results for the static bending problem reveal that both the deflection and rotation of the simply supported beam predicted by the new model are smaller than those predicted by the classical Timoshenko beam model. Also, the differences in both the deflection and rotation predicted by the two models are very large when the beam thickness is small, but they are diminishing with the increase of the beam thickness. Similar trends are observed for the free vibration problem, where it is shown that the natural frequency predicted by the new model is higher than that by the classical model, with the difference between them being significantly large only for very thin beams. These predicted trends of the size effect in beam bending at the micron scale agree with those observed experimentally. Finally, the Poisson effect on the beam deflection, rotation and natural frequency is found to be significant, which is especially true when the classical Timoshenko beam model is used. This indicates that the assumption of Poisson's effect being negligible, which is commonly used in existing beam theories, is inadequate and should be individually verified or simply abandoned in order to obtain more accurate and reliable results.

Bernoulli–Euler beam model based on a modified couple stress theory

Abstract: A new model for the bending of a Bernoulli–Euler beam is developed using a modified couple stress theory. A variational formulation based on the principle of minimum total potential energy is employed. The new model contains an internal material length scale parameter and can capture the size effect, unlike the classical Bernoulli–Euler beam model. The former reduces to the latter in the absence of the material length scale parameter. As a direct application of the new model, a cantilever beam problem is solved. It is found that the bending rigidity of the cantilever beam predicted by the newly developed model is larger than that predicted by the classical beam model. The difference between the deflections predicted by the two models is very significant when the beam thickness is small, but is diminishing with the increase of the beam thickness. A comparison shows that the predicted size effect agrees fairly well with that observed experimentally.

Surface tension effect on the mechanical properties of nanomaterials measured by atomic force microscopy

Abstract: The effect of reduced size on the elastic properties measured on silver and lead nanowires and on polypyrrole nanotubes with an outer diameter ranging between 30 and 250 nm is presented and discussed. Resonant-contact atomic force microscopy (AFM) is used to measure their apparent elastic modulus. The measured modulus of the nanomaterials with smaller diameters is significantly higher than that of the larger ones. The latter is comparable to the macroscopic modulus of the materials. The increase of the apparent elastic modulus for the smaller diameters is attributed to surface tension effects. The surface tension of the probed material may be experimentally determined from these AFM measurements.

Microstructure-dependent couple stress theories of functionally graded beams

Abstract: A microstructure-dependent nonlinear Euler–Bernoulli and Timoshenko beam theories which account for through-thickness power-law variation of a two-constituent material are developed using the principle of virtual displacements. The formulation is based on a modified couple stress theory, power-law variation of the material, and the von Karman geometric nonlinearity. The model contains a material length scale parameter that can capture the size effect in a functionally graded material, unlike the classical Euler–Bernoulli and Timoshenko beam theories. The influence of the parameter on static bending, vibration and buckling is investigated. The theoretical developments presented herein also serve to develop finite element models and determine the effect of the geometric nonlinearity and microstructure-dependent constitutive relations on post-buckling response.