Mechanics Colloquim
PROGRAM
PROGRAM ZA NOVEMBAR 2009.
Pozivamo Vas da učestvujete u radu sednica Odeljenja i to:
SREDA, 11. novembar 2009. u 18
sati:
E.E. Gdoutos,
Office of Theoretical and Applied Mechanics of the Academy of Athens
School of Engineering, Democritus University of Thrace, GR-671 00
Xanthi, Greece
E-mail: egdoutos@civil.duth.gr
FAILURE MECHANISMS OF COMPOSITE SANDWICH STRUCTURES
Sandwich panels consist typically of two thin face sheets (or
facings, or skins) and a lightweight thicker core. They display
various failure modes under general bending, shear and in-plane
loading. The failure modes can be predicted by conducting a thorough
stress analysis and applying appropriate failure criteria in the
critical regions of the beams. The analysis is difficult because of
the nonlinear and inelastic behavior of the constituent materials and
the complex interactions of failure modes.
A thorough investigation of the failure mechanisms of composite
sandwich beams under four- and three-point bending and cantilever
beams was undertaken. The beams were made of unidirectional
carbon/epoxy (AS4/3501-6) facings and a PVC closed-cell foam
(Divinycell) core. Two types of core material H100 and H250 with
densities 100 and 250 kg/m3, respectively, were used. The thickness
of the facings and core were 1 mm and 25.4 mm, respectively.
Sandwich beams were loaded under bending moment and shear and failure
modes were observed and compared with analytical predictions. The
failure modes investigated are face sheet compressive failure, core
failure, facing wrinkling and indentation failure. The various modes
have been studied separately and both initiation and ultimate failure
have been determined. Initiation of a particular failure mode and
triggering and interaction with other failure modes was also
investigated. A detailed stress and failure analysis was performed
taking into account that a biaxial state of stress is developed in
both the core and the facings. The stress state was combined with the
Tsai-Wu failure criterion for both the core and the facings. A
failure map for the entire specimen was constructed. Failure in the
core occurs in the form of crack initiation. The crack initiation was
predicted and compared with experimental observations
The initiation of the various failure modes depends on the material
properties of the constituents (facings, adhesive, core), geometric
dimensions and type of loading. The appropriate failure criteria
should account for the complete state of stress at a point, including
two- and three-dimensional effects. Failure modes were discussed
according to the type of loading applied. In sandwich columns under
compression, or beams in pure bending, compressive failure of the
skins takes place if the core is sufficiently stiff in the
through-the-thickness direction. Otherwise, facing wrinkling takes
place, which can be predicted by Heath˙˙s formula. In the case of
beams subjected to bending and shear the type of failure initiation
depends on the relative magnitude of the shear component. When the
shear component is low (long beams), facing wrinkling occurs first
while the core is still in the linear elastic range. The critical
stress at wrinkling can be predicted satisfactorily by an expression
by Hoff and Mautner and depends only on the facing and core moduli.
When the shear component is relatively high (e.g., short beams), core
shear failure takes place first and is followed by compression facing
wrinkling. Wrinkling failure follows but at a lower than predicted
critical stress. The predictive expression must be adjusted to
account for the reduced core moduli.
SREDA, 18. novembar 2009. u 18 sati:
akademik Vladan D. Djordjevic, Masinski fakultet Beograd
LUDVIG PRANTL I TEORIJA GRANICNOG SLOJA ˙˙ POVODOM 105 GODINA OD
NASTANKA TEORIJE - 2. DEO
U nastavku prethodno odrzanog saopstenja bice govora o metodama
resavanja jednacina teorije granicnog sloja koje je izveo L. Prandtl
i o doprinosima nasih autora ovim metodama. Takodje, bice pokazano
kako je ova teorija dovela do razvoja jedne nove matematicke metode
˙˙ metode singularnih poremecaja. Primena ove metode u okviru teorije
granicnog sloja omogucila je izracunavanje aproksimacija viseg reda,
dok je u okviru teorije talasnih kretanja tecnosti i hidrodinamicke
teorije stabilnosti njenom primenom stvorena mogucnost izvodjenja
mnogih tipova tzv. evolucionih jednacina.
SREDA, 25. novembar 2009. u 18 sati:
Srdjan Jovic, Faculty of Technical Sciences, Kosovska Mitrovica
38 220 Kosovska Mitrovica, Ul. Kralja Petra I br. 149/12, Serbia
VIBROIMPACT SYSTEM DYNAMICS: HEAVY MATERIAL PARTICLE OSCILLATIONS
ALONG ROUGH CIRCLE WITH TWO SIDE MOVING IMPACT LIMITERS
Paper present analytical results and some visualizations of the nonlinear dynamics of vibro-impact system with one degree of freedom and two side moving impact limits. Mechanical energy of a heavy material particle oscillations along a rough circle in vertical plane, with Coulomb˙˙s type friction and with two side moving impact limits of the angle elongation is object/subject of the analytical research. The corresponding ordinary nonlinear differential equations of dynamic equilibrium states are derived accompanying with corresponding initial conditions and corresponding conditions of the ideally elastic or no elastic impact conditions, as well as conditions of the alternation of the friction force of the Coulomb˙˙s type for the case large initial conditions. First integrals of the governing nonlinear differential equations of the material particle motion in considered case, earlier published, with corresponding integral constants are used for analytical and graphical analysis of the kinetic, potential and total mechanical energies of the corresponding vibroimpact system, as well as power of the friction force works in characteristic interval of the motions between impacts and of the alternations of the friction force direction. Also, bifurcations of the possible different solutions of the material particle nonlinear dynamics along rough circle with two side limit impacts ate considered. Also, a theorem of the total mechanical energy of the considered vibroimpact system with friction is formulates. Analytical expressions of the phase trajectory branch in the intervals between two impacts, as well as between impacts and positions of the alternations of friction force directions are presented. By use analytical expressions of the phase trajectory by use MathCad a visualization of the vibroimpact oscillations was presented. Conditions for corresponding numbers of impacts and positions of the alternations of the friction force directions, before oscillations with out impacts are analyzed, as well as conditions up to heavy material particle rest state on the rough line with friction of Coulomb˙˙s type are pointed out. In the considered cases we conclude that phase trajectories present line of the kinetic energy dependence of the generalized coordinate.
PETAK, 27. novembar 2009. u 14 sati:
(ZAJEDNICKI SASTANAK OBA ODELJENJA)
SARADNJA MATEMATICARA I MEHANICARA PREKO ODELJENJA MI
SANU
Sadrzaj: U Matematickom institutu SANU se sa visedecenijskom
tradicijom odrzavaju redovni sastanci tematskih
seminara kao i dva opsta seminara: Odeljenja za
matematiku i Odeljenja za mehaniku. Na
sastancima se saopstavaju naucni rezultati, ali i
diskutuje o vaznim pitanjima iz zivota i rada
istrazivaca.
Ovaj, zajednicki, sastanak Odeljenja posvecujemo dosadasnjoj saradnji
kao i mogucnostima dalje saradnje matematicara i mehanicara.
Povod je izbor upravnika oba Odeljenja u redovne clanove SANU.
Sednice se održavaju u zgradi SANU, Knez Mihailova 35, u sali 2 na prvom
spratu.