INSEGNAMENTO DEL CORSO DI DOTTORATO DI RICERCA IN INGEGNERIA CIVILE ED ARCHITETTURA:
DYNAMIC MODELS FOR STRUCTURES UNDER IMPULSIVE LOADING
DOCENTE:
DURATA DEL CORSO:
CREDITI:
Lingua:
Flavio Stochino
10 ore
2
Inglese
ABSTRACT:
The effects of impulsive loading on structures can be very dangerous: damages and failures are expected with serious threats
to structural safety and human life. Materials stresses and strains are often pushed to the limit and the modelling of these
phenomena can be very complex. This short course presents a synthesis of simplified models in order to highlight the main
characteristics of this problem and of its solutions.
Starting from the scratches, the course will analyse the steps necessary to build a reliable non-linear dynamic model considering
the possible collapse scenarios with particular attention to the flexural failure.
The numerical methods necessary to solve the problem equations will be presented with a detailed analysis of the algorithms
and of their implementation.
A comparison between simplified models and advanced ones will be provided in order to highlight advantages and
disadvantages of several approaches.
562
F. Stochino / Engineering Failure Analysis 66 (2016) 544–565
Table 11
CONTENTS:
P (t)
Fitting performance for low-load maximum deflection results, considering different parameters as independentEvariables x and y. For each case the fitting performance
indicator, presented in Section 3.3, and the number of the polynomial coefficients are reported.
- Modelling of impulsive loading (0.5 h)
R-square
AR-square
RMSE m
Coefficients
x–y
Fit type
SSE m
- Constitutive behaviour of materials under static andSlend.–P.load
dynamic loadpoly(0.5 h) 0.58467087
0.796950663
0.794757906
0.017767865
21
Slend.–P.load
poly
0.591579941
0.794551224
0.793003171
0.017843657
15
Concrete
M (t) 0.017889756
Slend.–P.load
poly
0.59624080
0.792932562
0.791932236E
10
Slend.–P.load
poly
0.601406477
0.791138583
0.790579233
0.017947828
6
Steel
Slend.–P.load
poly
0.75360261
0.738282651
0.738002739
0.020074761
3
u
(t)
Slend.–Span
poly
1.249337712
0.566119663
0.561434130
0.02597284
21
E
- Single Degree of freedom model (3 h)
Slend.–Span
poly
1.255508783
0.563976523
0.560691093
0.025994832
15
KE(t)
Slend.–Span
poly
1.264076134
0.561001182
0.558880415
0.026048348
10
Modal method
Slend.–Span
poly
1.265849822
0.560385201
0.559207872
0.026038678
6
1.327557523
0.53895484
0.538461744
0.026644395
3
Slend.–Span
poly
Equivalent SDOF method
P.load–R.ratio
poly
2.128770294
0.260703041
0.259912349
0.033739885
3
C.stren.–P.load
poly
2.351506343
0.183349423
0.182476000
0.035461106
3
- Lumped-mass multi-degree of freedom (1 h)
Modal Analysis
Elasto-plastic Analysis
- Structures with distributed mass and load (3 h)
Euler-Bernoulli Beam Theory
Timoshenko Beam Theory
- Numerical methods (2 h)
Finite Elements
Finite Differences
2
55
44
33
22
11
55
44
33
22
11
11
11
Fig. 18. Low load, max. deflection, peak load - slenderness 5th polyn. fitting.
DATES AND LOCATION:
March, 16 – h: 9:00-11:00 –
March, 17 – h: 9:00-11:00 –
March, 20 – h: 9:00-11:00 –
March, 27 – h: 9:00-11:00 –
March, 28 – h: 9:00-11:00 –
The case of low-load has been analysed considering as dependent variable the maximum displacement and the maximum velocity. If we consider the former case a synthesis of the analysis is shown in Table 11: the lowest SSE is obtained by a 5th degree
polynomial function of slenderness and peak load (see Fig. 18). This function also presents the best AR-square index. These results
underline the importance of peak load and slenderness in the estimation of beam response under blast load.
Table 12 presents a synthesis of the fitting performance in case of low load, considering velocity as a dependent variable. Also
in this situation the lowest SSE is obtained by a 5th degree polynomial function of slenderness and peak load (see Fig. 19). The
same function obtains the best AR-square index. From these results, it is clear that the most important parameters for fitting maximum velocity/low load results are peak load and slenderness. Other variables obtained dramatically worse results. Actually, a
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Table 12
Fitting performance for low-load maximum velocity results, considering different parameters as independent variables x, and y. For each case the fitting performance
indicator, presented in Section 3.3, and the number of the polynomial coefficients are reported.
x–y
Fit type
SSE m2/s2
R-square
AR-square
RMSE m/s
Coefficients
Slend.–P.load
Slend.–P.load
Slend.–P.load
Slend.–P.load
Slend.–P.load
Slend.–Span
Slend.–Span
Slend.–Span
Slend.–Span
R.ratio–Slend.
Slend.–Span
poly55
poly44
poly33
poly22
poly11
poly55
poly44
poly33
poly22
poly11
poly
74.15608153
74.91211988
75.21087461
75.41919317
132.1395093
1026.960884
1031.492396
1038.129148
1038.440420
1054.338630
1073.179019
0.951244314
0.950747238
0.950550815
0.950413851
0.913121725
0.324800050
0.321820699
0.317457208
0.317252555
0.306799897
0.294412834
0.950717795
0.95037612
0.95031193
0.950281055
0.913028807
0.317508474
0.316710629
0.314159900
0.315424094
0.306058507
0.293658195
0.200102675
0.200795136
0.200924961
0.200987377
0.265824828
0.744657315
0.745092446
0.746481871
0.745793567
0.750877786
0.757556944
21
15
10
6
3
21
15
10
6
3
3
Flavio Stochino:
Flavio Stochino is a Post Doc researcher at University of Cagliari. His research deals with computational mechanics and
extreme loads (blast, impact, fire etc.) on structures and construction materials.
After his PhD, obtained in 2013 at University of Cagliari (Italy), he has worked as Post Doc Researcher at University of Sassari
(Italy). Then he has improved his computational mechanics skills at Technical University of Dresden (Germany) under the
Dresden Junior Fellow program.
He has produced several papers for international journals and he has participated and presented academic papers in several
international conferences
Selected Publications:
Stochino F. “Flexural models of reinforced concrete beams under blast load” Ph.D. Thesis in Structural Engineering,
Supervisor: Prof. S.Tattoni, University of Cagliari, (2013).
Francesconi L., Pani L., Stochino F. ”Punching shear strength of reinforced recycled concrete slabs”, Construction and
Building Materials, 127, 248-263. (2016).
Cazzani A., Cattani M., Mauro R., Stochino F ”A simplified model for railway catenary wire dynamics ”, European Journal of
Environmental and Civil Engineering, (2016), in press doi: 10.1080/19648189.2016.1245631
Cazzani A., Rizzi N.L, Stochino F, Turco E. ”Modal analysis of laminates by a mixed assumed-strain finite element model”,
Mathematics and Mechanics of Solids, (2016), in press doi: 10.1177/1081286516666405.
Stochino F. “RC beams under blast load: reliability and sensitivity analysis”, Engineering Failure Analysis, (2016) 66, 544-565.
Cazzani A., Stochino F., Turco E. “An analytical assessment of finite element and isogeometric analyses of the whole spectrum
of Timoshenko beams ”, Zeitschrift für Angewandte Mathematik und Mechanik - ZAMM, 96, 1220–1244, (2016).
Cazzani A., Stochino F., Turco E. “On the whole spectrum of Timoshenko beams. Part II: further applications”, Zeitschrift
für Angewandte Mathematik und Physik - ZAMP, 67, article n. 25 (2016).
Cazzani A., Stochino F., Turco E. “On the whole spectrum of Timoshenko beams. part I: a theoretical revisitation”, Zeitschrift
für Angewandte Mathematik und Physik - ZAMP, 67, article n. 24 (2016).
Cazzani A., Wagner N., Ruge P., Stochino F. ”Continuous transition between mass and travelling oscillator using mixed
variables”, International Journal of Non-Linear Mechanics, 80, 82-95 (2016).
Buffa F, Causin A, Cazzani A., Poppi S., Sanna G., Solci M., Stochino F, Turco E. ”The Sardinia Radio Telescope: a
comparison between close range photogrammetry and FE models”, Mathematics and Mechanics of Solids, (2015), in press
doi: 10.1177/1081286515616227.
Stochino F, Cazzani A., Poppi S., Turco E. ”Sardinia Radio Telescope finite element model updating by means of
photogrammetric measurements”, Mathematics and Mechanics of Solids, (2015) , in press doi: 10.1177/1081286515616046
Cazzani A., Malagù M., Stochino F., Turco E. “Constitutive models for strongly curved beams in the frame of isogeometric
analysis”, Mathematics and Mechanics of Solids, 21, 182-209, (2016.
Stochino F., Carta G. “SDOF models for reinforced concrete beams under impulsive loads accounting for strain rate effects.”
Nuclear Engineering and Design, 276, 74-86, (2014).
Tattoni S., Stochino F. “Collapse of prestressed reinforced concrete jetties: durability and faults analysis”. Case Studies in
Engineering Failure Analysis, 1, 131-138, (2013).
Carta G., Stochino F. “Theoretical models to predict the flexural failure of reinforced concrete beams under blast loads”
Engineering Structures, 49, 306–315, (2013).
Acito M. Stochino F. Tattoni S “Structural response and reliability analysis of RC beam subjected to explosive loading”.
Applied Mechanics and Materials 82 (2011), 434-439.