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A.K. Lazopoulos

Bio: A.K. Lazopoulos is an academic researcher from Army and Navy Academy. The author has contributed to research in topics: Fractional calculus & Bending stiffness. The author has an hindex of 10, co-authored 30 publications receiving 337 citations. Previous affiliations of A.K. Lazopoulos include Hellenic Military Academy & National Technical University of Athens.

Papers
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Journal ArticleDOI
TL;DR: In this paper, a simple linear strain gradient elastic theory with surface energy is employed for the bending of thin beams, and the governing beam equations with its boundary conditions are derived through a variational method.
Abstract: Bending of strain gradient elastic thin beams is studied adopting Bernoulli-Euler principle. Simple linear strain gradient elastic theory with surface energy is employed. The governing beam equations with its boundary conditions are derived through a variational method. It turns out that new terms are introduced, indicating the importance of the cross-section area in bending of thin beams. Those terms are missing from the existing strain gradient beam theories. Those terms increase highly the stiffness of the thin beam. The buckling problem of the thin beams is also discussed.

137 citations

Journal ArticleDOI
TL;DR: In this paper, the governing equilibrium equations for strain gradient elastic thin shallow shells are derived, considering nonlinear strains and linear constitutive strain-gradient elastic relations, and the equilibrium equations along with the boundary conditions are formulated through a variational procedure.
Abstract: The governing equilibrium equations for strain gradient elastic thin shallow shells are derived, considering nonlinear strains and linear constitutive strain gradient elastic relations. Adopting Kirchhoff’s theory of thin shallow structures, the equilibrium equations, along with the boundary conditions, are formulated through a variational procedure. It turns out that new terms are introduced, indicating the importance of the cross-section area in bending of thin plates. Those terms are missing from the existing strain gradient shallow thin shell theories. Those terms highly increase the stiffness of the structures. When the curvature of the shallow shell becomes zero, the governing equilibrium for the plates is derived.

27 citations

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TL;DR: In this paper, the governing equation of motion of thin flexural beams is studied in the context of strain gradient elasticity, and the results of the analysis are compared with the existing theories.

26 citations

Journal ArticleDOI
TL;DR: In this article, the basic fluid mechanics equations are studied and revised under the prism of fractional continuum mechanics (FCM), a very promising research field that satisfies both experimental and theoretical demands.
Abstract: Abstract Basic fluid mechanics equations are studied and revised under the prism of fractional continuum mechanics (FCM), a very promising research field that satisfies both experimental and theoretical demands. The geometry of the fractional differential has been clarified corrected and the geometry of the fractional tangent spaces of a manifold has been studied in Lazopoulos and Lazopoulos (Lazopoulos KA, Lazopoulos AK. Progr. Fract. Differ. Appl. 2016, 2, 85–104), providing the bases of the missing fractional differential geometry. Therefore, a lot can be contributed to fractional hydrodynamics: the basic fractional fluid equations (Navier Stokes, Euler and Bernoulli) are derived and fractional Darcy’s flow in porous media is studied.

24 citations

Journal ArticleDOI
TL;DR: In this article, a fractional bending of a beam is introduced, applying Euler-Bernoulli bending principle, implemented to the bending deformation of a cantilever beam under continuously distributed loading.
Abstract: Clarifying the geometry of the fractional tangent space of a curve, fractional differential geometry of curves has already been revisited, Lazopoulos and Lazopoulos (2015), defining also the curvature vector. Fractional bending of a beam is introduced, applying Euler–Bernoulli bending principle. The proposed theory is implemented to the bending deformation of a cantilever beam under continuously distributed loading.

23 citations


Cited by
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Book ChapterDOI
01 Jan 2015

3,828 citations

Journal ArticleDOI
TL;DR: In this article, the stability problem of nano-sized beam based on the strain gradient elasticity and couple stress theories is addressed, and the size effect on the critical buckling load is investigated.

436 citations

Journal ArticleDOI
TL;DR: In this paper, a review of geometrically non-linear free and forced vibrations of shells made of traditional and advanced materials is presented, including closed shells and curved panels made of isotropic, laminated composite, piezoelectric, functionally graded and hyperelastic materials.
Abstract: The present literature review focuses on geometrically non-linear free and forced vibrations of shells made of traditional and advanced materials. Flat and imperfect plates and membranes are excluded. Closed shells and curved panels made of isotropic, laminated composite, piezoelectric, functionally graded and hyperelastic materials are reviewed and great attention is given to non-linear vibrations of shells subjected to normal and in-plane excitations. Theoretical, numerical and experimental studies dealing with particular dynamical problems involving parametric vibrations, stability, dynamic buckling, non-stationary vibrations and chaotic vibrations are also addressed. Moreover, several original aspects of non-linear vibrations of shells and panels, including (i) fluid–structure interactions, (ii) geometric imperfections, (iii) effect of geometry and boundary conditions, (iv) thermal loads, (v) electrical loads and (vi) reduced-order models and their accuracy including perturbation techniques, proper orthogonal decomposition, non-linear normal modes and meshless methods are reviewed in depth.

203 citations

Journal ArticleDOI
TL;DR: In this paper, a bending analysis of micro-sized beams based on the Bernoulli-Euler beam theory is presented within the modified strain gradient elasticity and modified couple stress theories.
Abstract: Bending analysis of micro-sized beams based on the Bernoulli-Euler beam theory is presented within the modified strain gradient elasticity and modified couple stress theories. The governing equations and the related boundary conditions are derived from the variational principles. These equations are solved analytically for deflection, bending, and rotation responses of micro-sized beams. Propped cantilever, both ends clamped, both ends simply supported, and cantilever cases are taken into consideration as boundary conditions. The influence of size effect and additional material parameters on the static response of micro-sized beams in bending is examined. The effect of Poisson’s ratio is also investigated in detail. It is concluded from the results that the bending values obtained by these higher-order elasticity theories have a significant difference with those calculated by the classical elasticity theory.

194 citations

Journal ArticleDOI
TL;DR: In this paper, size-dependent equations of motion for functionally graded cylindrical shell were developed using shear deformation model and rotation inertia, where material properties of the shell were assumed as continuously variable along thickness, consistent with the variation in the component's volume fraction based on power law distribution.

191 citations