Periodic beam-like structures homogenization by transfer matrix eigen-analysis: A direct approach

Penta, Francesco; Monaco, Michela; Pucillo, Giovanni Pio; Gesualdo, Antonio

doi:10.1016/j.mechrescom.2017.08.007

Cited by 26 publications

(14 citation statements)

References 44 publications

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“…In [16], it is shown that this method is equivalent to modelling the discrete girder by a Timoshenko beam whose stiffness has to be evaluated by a suitable homogenization procedure (i.e. [17][18][19][20]). However, it gives unsatisfactory results when the cell size is not small compared with the girder length or non-negligible transversal shear forces and bending moments are induced in the chords [21,22].…”

Section: Introductionmentioning

confidence: 99%

Self-moments stiffening effect and buckling strength of periodic Vierendeel beams

Penta

2020

Acta Mech

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This paper deals with the buckling phenomenon of periodic Vierendeel beams. Closed-form solutions for critical loads and deformed shapes are presented. They are built by exploiting several auxiliary solutions obtained for the discrete periodic girder and for a geometrically nonlinear micro-polar equivalent model. In particular, the girder when subjected to sinusoidal self-equilibrated systems of inner bending moments (self-moments) is analysed. The corresponding results are used for solving the large-deflection equilibrium problem of the continuous equivalent model by means of the eigenfunction expansion technique. Girder buckling conditions are then defined in terms of kinematics of the micro-polar model: more precisely, they are attained when special distributions of self-moments, able to bend the continuous system without violating compatibility of shear strains, act in the girder. It is shown that these systems, neglected in the theories presented so far, have a significant stiffening effect on the buckling girder behaviour. Moreover, they are governed by the continuity equation for micro-rotations that is solved in closed form by the Galerkin method, with the micro-polar model eigenfunctions as basis functions. The accuracy of the proposed solutions is verified by comparing them with those achieved by a series of finite element girder models.

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Section: Introductionmentioning

confidence: 99%

Self-moments stiffening effect and buckling strength of periodic Vierendeel beams

Penta

2020

Acta Mech

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“…To this end, a sandwich panel may be modeled as an equivalent single-layer (ESL) beam or plate based on the first-order shear deformation theory (FSDT) [15]. In this study, the focus is on web-core (I-core) sandwich panels for which different ESL-FSDT models based on classical [16,17], couple-stress [18][19][20][21] and micropolar [22] continuum theories have been developed. Recently, analytical solutions founded on discrete classical models have also been formulated for web-core plates [23][24][25].…”

Section: Introductionmentioning

confidence: 99%

Two-scale constitutive modeling of a lattice core sandwich beam

Karttunen

Reddy

Romanoff

2019

Composites Part B: Engineering

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Constitutive equations are derived for a 1-D micropolar Timoshenko beam made of a web-core lattice material. First, a web-core unit cell is modeled by discrete classical constituents, i.e., the Euler-Bernoulli beam finite elements (FE). A discrete-to-continuum transformation is applied to the microscale unit cell and its strain energy density is expressed in terms of the macroscale 1-D beam kinematics. Then the constitutive equations for the micropolar web-core beam are derived assuming strain energy equivalence between the microscale unit cell and the macroscale beam. A micropolar beam FE model for static and dynamic problems is developed using a general solution of the beam equilibrium equations. A localization method for the calculation of periodic classical beam responses from micropolar results is given. The 1-D beam model is used in linear bending and vibration problems of 2-D web-core sandwich panels that have flexible joints. Localized 1-D results are shown to be in good agreement with experimental and 2-D FE beam frame results.

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“…After his study the behaviour of tall, slender structures subjected to ground motion was exstensively analyzed with that model [2,3]. The motion of rigid bodies under base excitation includes in fact the behaviour of piece of equipments, hospital devices, statues, storage tanks, or even that of tall buildings [4,5]. Only in the following decades the model has been used to represent the behaviour of particular rigid bodies, i.e.…”

Section: Introductionmentioning

confidence: 99%

Seismic Protection of Statues. A Case Study

Guadagnuolo¹,

Aurilio²,

Iannuzzo³

et al. 2019

Proceedings of the 7th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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The analysis of rocking behaviour is a key aspect of safety assessment the maintenance of artifacts, like statues vases, since the rocking itself can be the cause of damage at the base of the object, due to impact with the support. By seismic excitation, a freestanding object may in fact enter a rocking state which would cause overturning, so that often the sliding is desirable, given the possibility of evaluating relative displacements to avoid collisions. In the majority of cases, museum exhibitions are not equipped with isolation devices for every single contained object. This paper presents the theoretical numerical bases of a simple low cost isolation system to protect small art objects. Smaller artifacts are in fact the more prone to overturning since the rocking response is highly influenced by the size of the object. The insertion of a further rigid body between the moving base the statue can reduce the effect of base motion due to earthquakes. The case study is a real marble statue by Donatello, placed in the Museo dell'Opera del Duomo in Florence.

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Periodic beam-like structures homogenization by transfer matrix eigen-analysis: A direct approach

Cited by 26 publications

References 44 publications

Self-moments stiffening effect and buckling strength of periodic Vierendeel beams

Self-moments stiffening effect and buckling strength of periodic Vierendeel beams

Two-scale constitutive modeling of a lattice core sandwich beam

Seismic Protection of Statues. A Case Study

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