1,721,109 research outputs found
Symbolic Manipulation in Buckling and Postbuckling Analysus
No full textA perturbation procedure for the buckling and postbuckling analysis of elastic structures is shown to be well suited to be implemented as an automatic symbolic manipulation procedure. The postbuckling analysis of a circular arch is considered as an example, and the asymptotic description of the bifurcated equilibrium path is given. The main purposes of the automatic procedure are to generate the representation of the Fréchet operator for the strain field and to perform integration by parts. This allows the manipulation of correct expressions of the basic relationships, as the strain-displacement one, without introducing any simplifying assumption or restriction. The perturbation equations are automatically generated and a solution procedure leads to parametric expressions for the coefficients of the asymptotic expansion of the bifurcated path. The symbolic manipulation system used is REDUCE
Non-Standard Models for Thin-Walled Beams with a View to Applications
No full textA direct theory of a one-dimensional structured continuum is introduced in order to study the postbuckling behavior of thin-walled beams. A simply supported beam bent by end couples is analyzed showing that in the case of nonsymmetric cross sections lateral buckling gives rise to imperfection sensitivity. Tlien an axially loaded beam is studied taking also into account the interaction between torsional and exural buckling. The results obtained prove that in this case imperfection sensitivity though slighter than in the previous case arises also for symmetric cross sections
Analisi in piu’ parametri perturbativi per murature a struttura regolare: identificazione 3D con modelli 2D di piastra
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On the derivation of the elastic properties of lattice nanostructure: The case of graphene sheets
No full textSeveral nanomechanics approaches based on common two or three-body potentials are compared. Numerical simulations and analytical approaches are used to investigate the not negligible differences among the prediction of the in-plane elastic constants of graphene sheets in the literature, exploring separately the role of the bonding potentials and that of the structural descriptions (beams and trusses) of the original Molecular Mechanics (MM) model. The energetic differences between structural models and MM models will be highlighted through exact discrete homogenization procedure. By the way, some theoretical expression of graphene elastic constants available in the literature are recovered and supported by numerical experimentation. The results provide also an assessment of the accuracy of the selected potentials with repost to both ab-initio reference solutions and the experimental measurements available. Some suggestions towards a reparametrization of the modified Morse potential are consequently formulated
Continuum modelling of a beam-like latticed truss: identification of the constitutive functions for the contact and inertial actions
No full textThe derivation of a continuum model apt to give a compendious description of the mechanical behaviour of a latticed structure is envisaged here as a procedure leading to the identification (of the constitutive parameters) of a "coarse" model starting from a prescribed "finer" one. The fine model considered describes a planar modular beam whose module is made up of a pair of rigid diaphragms connected by straight elastic bars; diaphragms and bars have both mass. The coarse model is a one-dimensional continuum endowed with Euclidean structure. An interesting result is that the value of the density of the inertial actions at a point depends not only on the value of the acceleration at that same point - as is usually taken for granted in conventional continuum models - but also of its first and second derivatives with respect to the material coordinate
A 1D higher gradient model derived from Koiter's shell theory
No full textA thin rectangular plate is modelled as an (initially flat) shell. Following Koiter, the two fundamental forms of the deformed middle surface are then used to define the strain measures of the body. On the middle surface of the plate two local coordinates are introduced: we will call them longitudinal and transversal, respectively. It is assumed that the components of the displacement field which characterize the middle surface kinematics can be expressed as a product of two functions: one defined along the longitudinal coordinate and one defined along the transversal coordinate. Given an explicit expression of the latter functions, the 2D plate fields are reduced to 1D ones. The functions of the transversal coordinate are chosen so that the stretch along it together with the membrane shear vanish. It is worth noting that the linearization of these constraints leads to the well-known Vlasov’s assumptions. It is shown that by modelling each side of a thin walled beam as a 1D continuum, the entire assembly can be reduced to a 1D model as well. This procedure gives rise to an hyperelastic 1D beam model in which at least the warping effect is taken into account. The main features of the model are shown by means of some simple applications
Coupled instabilities in a two-bar frame: a qualitative approach
No full textA direct one-dimensional beam model is kinematical ly described by the axis displacement, the rotation of the cross-sections and an average measure of their warping. The mechanical power is introduced as a linear functional of the kinematic descriptors
and their first derivatives: the mechanical actions natural ly result as duals of the former ones. By means of the balance between external and internal power, the local balance equations for the mechanical actions are obtained. Inner constraints of shear indeformability and of a linear relationship between twist and warping are assumed, and non-linear hyperelastic constitutive relations are formulated. Thus, field equations in terms of displacements are obtained, and the various possibilities of buckling in a two-bar frame are examined. The critical value of the load multiplier is found for both the in-plane (single) and the out-of-plane (coupled) bifurcations
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