Search results for "Virtual work"
showing 10 items of 18 documents
The role of virtual work in Levi-Civita's parallel transport
2015
The current literature on history of science reports that Levi-Civita’s parallel transport was motivated by his attempt to provide the covariant derivative of the absolute differential calculus with a geometrical interpretation (For instance, see Scholz in The intersection of history and mathematics, Birkhauser, Basel, pp 203–230, 1994, Sect. 4). Levi-Civita’s memoir on the subject was explicitly aimed at simplifying the geometrical computation of the curvature of a Riemannian manifold. In the present paper, we wish to point out the possible role implicitly played by the principle of virtual work in Levi-Civita’s conceptual reasoning to formulate parallel transport.
A gradient elasticity theory for second-grade materials and higher order inertia
2012
Abstract Second-grade elastic materials featured by a free energy depending on the strain and the strain gradient, and a kinetic energy depending on the velocity and the velocity gradient, are addressed. An inertial energy balance principle and a virtual work principle for inertial actions are envisioned to enrich the set of traditional theoretical tools of thermodynamics and continuum mechanics. The state variables include the body momentum and the surface momentum, related to the velocity in a nonstandard way, as well as the concomitant mass-accelerations and inertial forces, which do intervene into the motion equations and into the force boundary conditions. The boundary traction is the …
The mechanically-based approach to 3D non-local linear elasticity theory: Long-range central interactions
2010
Abstract This paper presents the generalization to a three-dimensional (3D) case of a mechanically-based approach to non-local elasticity theory, recently proposed by the authors in a one-dimensional (1D) case. The proposed model assumes that the equilibrium of a volume element is attained by contact forces between adjacent elements and by long-range forces exerted by non-adjacent elements. Specifically, the long-range forces are modelled as central body forces depending on the relative displacement between the centroids of the volume elements, measured along the line connecting the centroids. Further, the long-range forces are assumed to be proportional to a proper, material-dependent, dis…
Mechanically-based approach to non-local elasticity: Variational principles
2010
Abstract The mechanically-based approach to non-local elastic continuum, will be captured through variational calculus, based on the assumptions that non-adjacent elements of the solid may exchange central body forces, monotonically decreasing with their interdistance, depending on the relative displacement, and on the volume products. Such a mechanical model is investigated introducing primarily the dual state variables by means of the virtual work principle. The constitutive relations between dual variables are introduced defining a proper, convex, potential energy. It is proved that the solution of the elastic problem corresponds to a global minimum of the potential energy functional. Mo…
Variational approach to the mechanics of metal V-belt systems
2005
The mechanical behaviour of metal V-belt drives is strongly dependent on the elastic properties of both the belt and the pulley, which influence the belt penetration into the groove and the sliding on the pulley wall. The distribution of tension and penetration is quite different from the rubber belts, which may be dealt with in the assumption of perfectly rigid pulleys. The restoring effect of the centrifugal forces of the plate elements has also to be taken into account. The present analysis considers the combination of all those effects, choosing a three parameter deformation function to describe the plate bending and applying the principle of virtual work for the calculation of the unkn…
International Transport Corridors Functioning Efficiency in the Digital Economy Conditions
2019
The problem that is taken under consideration in the following article concerns the implementation, use and effectiveness of virtual work in the supply chain in e-economy. Any solution concern employee mobility or the use of mobile technology are due to growing market competition and constant search for new solutions that may enable the companies in the supply chain to be more efficient than the competition. In the supply chain the E-business creates for the companies new challenges they have to face. One of the possibilities to improve your business in the supply chain is to use virtual work. The new challenge facing the e-economy needs to be met. The aim of the article is to refer the vir…
Fractional visco-elastic Euler–Bernoulli beam
2013
Abstract Aim of this paper is the response evaluation of fractional visco-elastic Euler–Bernoulli beam under quasi-static and dynamic loads. Starting from the local fractional visco-elastic relationship between axial stress and axial strain, it is shown that bending moment, curvature, shear, and the gradient of curvature involve fractional operators. Solution of particular example problems are studied in detail providing a correct position of mechanical boundary conditions. Moreover, it is shown that, for homogeneous beam both correspondence principles also hold in the case of Euler–Bernoulli beam with fractional constitutive law. Virtual work principle is also derived and applied to some c…
Occupational emerging risks affecting international virtual project Team Results
2017
The expansion of internet access, high-speed connection services, collaborative work platforms and tools, allowed employees to interact virtually offering companies the possibility to develop projects around the world, reducing operational costs and gain competitive advantage. Realizing the advantages and disadvantages of developing a project team in an international virtual work environment, requires adopting specific strategies to construct an effective team and ensure the project success. One of the most important disadvantages that we identified is that the new work environment brings new risks for both team members and managers. So, it becomes mandatory to identify and analyze the occu…
A link between the residual-based gradient plasticity theory and the analogous theories based on the virtual work principle
2009
A link is shown to exist between the so-called residual-based strain gradient plasticity theory and the analogous theories based on the (extended) virtual work principle (VWP). To this aim, the former theory is reformulated and cast in a residual-free form, whereby the insulation condition and the (nonlocal) Clausius–Duhem inequality, on which the theory is grounded, are substituted with equivalent residual-free ingredients, namely the energy balance condition and the residual-free form of the Clausius–Duhem inequality. The equivalence of the residual-free formulation to the original one is shown, also in their ability to cope with energetic size effects and interfacial energy ones. It emer…
Thermodynamics-based gradient plasticity theories with an application to interface models
2008
AbstractIn the framework of small deformations, the so-called residual-based gradient plasticity theory is reconsidered and improved. Using the notion of moving geometrically necessary dislocations (GNDs), suitable micromechanics interpretations are heuristically given for the higher order boundary conditions and the long distance particle interactions. Also, a comparison is made between this theory and the analogous virtual work principle (VWP)-based one, whereby their respective conceptual and methodological features are pointed out. The conditions under which the two theories lead to a same constitutive model are investigated, showing that, correspondingly, a certain indeterminacy exhibi…