Prof. Roman Bogacz, Ph.D., Dr. Habil., Eng.

Department of Intelligent Technologies (ZTI)
Division of Control and System Dynamics (PSiDU)
retiree
telephone: (+48) 22 826 12 81 ext.: 313
room: 434
e-mail: rbogacz
personal site: http://bluebox.ippt.pan.pl/~rbogacz/

Doctoral thesis
1970Współdziałanie ruchomego układu nieliniowego oscylatorów z falami bieżącymi w sprężystych ośrodkach ciągłych 
supervisor -- Prof. Sylwester Kaliski, Ph.D., Dr. Habil., Eng., IPPT PAN
177 
Habilitation thesis
1978O stateczności wzajemnego oddziaływania układów ciągłych i dyskretnych w ruchu względnym 
Professor
1990Title of professor
Supervision of doctoral theses
1.2015-11-18Konop Jacek  
(PW)
Dynamika układu pojazd szynowy - tor 
2.2001Ryczek Bogusław  Drgania samowzbudne układów dyskretnych wzbudzane tarciem suchym; teoria i weryfikacja doświadczalna 
3.1993Brzozowski Marek  Analiza numeryczna deformacji niesprężystych w zagadnieniu kontaktu tocznego 
4.1992Imiełowski Szymon  Stateczność układów dyskretno-ciągłych poddanych obciążeniom niekonserwatywnym 
5.1991Niespodziana Aleksandra  Wpływ lokalnej utraty sztywności na stateczność układów dyssypatywnych poddanych obciążeniom cyrkulacyjnym 
6.1991Sikora Janusz  Drgania w strefie kontaktu ciał z tarciem suchym w ujęciu dyskretnym 
7.1989Nowakowski Sławomir  Stateczność pewnych układów ciągłych w ruchu względnym 
8.1987Krzyżyński Tomasz  Zagadnienia stateczności układów hybrydowych z falą bieżącą 

Recent publications
1.Chudzikiewicz A., Bogacz R., Kostrzewski M., Konowrocki R., Condition monitoring of railway track systems by using acceleration signals on wheelset axle-boxes, Transport, ISSN: 1648-4142, DOI: 10.3846/16484142.2017.1342101, Vol.-, No.-, pp.1-12, 2017
Abstract:

The aim of this paper is to demonstrate the possibilities of estimating the track condition using axle-boxes and car-bodies motions described by acceleration signals. In the paper, the results presented indicate the condition of tracks obtained from the preliminary investigation on the test track. Furthermore, the results from the supervised runs (on Polish Railway Lines) of electric multiple unit (EMU-ED74) with the prototype of track quality monitoring system installed on-board are described. As track quality indicator (TQI) algorithm, used in the mentioned prototype, a modified Karhunen–Loève transformation is used in preliminary preparing acceleration signals. The transformation is used to extract the principal dynamics from measurement data. Obtained results are compared to other methods of evaluating the geometrical track quality, namely methods which apply the Jsynth Synthetic Coefficient and Five Parameters of Defectiveness W5. The results from the investigation showed that track condition estimation is possible with acceptable accuracy for in-service use and for defining cost-effective maintenance strategies.

Keywords:

railway track monitoring, wheel–rail interaction, track quality indicator, acceleration signals, experimental investigation, track degradation.

Affiliations:
Chudzikiewicz A.-other affiliation
Bogacz R.-IPPT PAN
Kostrzewski M.-other affiliation
Konowrocki R.-IPPT PAN
2.Bogacz R., Frischmuth K., On dynamic effects of wheel–rail interaction in the case of Polygonalisation, MECHANICAL SYSTEMS AND SIGNAL PROCESSING, ISSN: 0888-3270, DOI: 10.1016/j.ymssp.2016.03.001, Vol.79, pp.166-173, 2016
Abstract:

Following earlier work of the authors [1], we study here the influence of surface imperfections of a certain type on the vertical loading, in particular in the form of fluctuations in the progressive speed of a moving force. The problem is partly associated with another line of work, where we analyzed configurations of regions in the parameter space with qualitatively different solutions for supported beams under moving loads [2]. In this paper, we study the rolling motion of a polygonalised railway wheel on the rail. For uniform guiding motion, the trajectory of the contact point and vertical accelerations are evaluated first in the rigid case, then in the case of elastic and visco-elastic contact. It will be pointed out that a wavy form of the wheel changes considerably the longitudinal velocity of contact points, even for constant speed of the wheel center which can be are as on for instability.

Keywords:

Railway mechanics, Contact problem, Wave generation

Affiliations:
Bogacz R.-other affiliation
Frischmuth K.-University of Rostock (DE)
3.Bogacz R., Kurnik W., On some rotor-dynamical phenomena of high-speed trains, ARCHIVE OF APPLIED MECHANICS, ISSN: 0939-1533, DOI: 10.1007/s00419-014-0966-3, Vol.85, No.9, pp.1343-1352, 2015
Abstract:

The paper is devoted to radial and out-of-plane vibration of railway wheels and to wheelset stability as key elements affecting high-speed vehicle dynamics, noise emission, and safety. In the present study, railway wheel tire is treated as a curved beam with various beam models, and the wheel plates are modeled as Winkler’s elastic foundation. New results are presented concerning the influence of the residual stresses on the corrugation and poligonalization of wheels as well as wave propagation in the wheel tire

Keywords:

Elastic wheel, Wheel–rail interaction, Traveling waves, Wheel poligonalization, Corrugation

Affiliations:
Bogacz R.-other affiliation
Kurnik W.-Warsaw University of Technology (PL)
4.Bogacz R., Czyczuła W., Konowrocki R., Effect of periodicity of railway track and wheel–rail interaction on wheelset–track dynamics, ARCHIVE OF APPLIED MECHANICS, ISSN: 0939-1533, DOI: 10.1007/s00419-014-0981-4, Vol.85, pp.1321-1330, 2015
Abstract:

The paper deals with the investigation of some phenomena which are essential for dynamic interaction of a wheelset or bogie with the railways track. The track is modeled as discrete–continuous system composed of rails, fastening systems and sleepers interacting with ballast by means of viscous–elastic elements. Transient and stationary problems are investigated. The stationary periodic problems are connected with wave propagation in stopping bound, passing bound and mistuning. In this paper, a review of selected problems and exemplary results of simulation and experimental investigations is given supplemented by a few results of analysis and simulation.

Keywords:

Moving load, Resonance, Periodicity, Passing band, Mistuning

Affiliations:
Bogacz R.-other affiliation
Czyczuła W.-Cracow University of Technology (PL)
Konowrocki R.-IPPT PAN
5.Bogacz R., Czyczuła W., Konowrocki R., Influence of Sleepers Shape and Configuration on Track-Train Dynamics, SHOCK AND VIBRATION, ISSN: 1070-9622, DOI: 10.1155/2014/393867, Vol.2014, pp.393867-1-7, 2014
Abstract:

The paper is devoted to the study of dynamical behaviour of railway tracks as continuous systems (rails) supported by periodically spaced sleepers and subjected to moving concentrated loads. Several cases of dynamical problems, where elastically supported beams are excited by a moving concentrated force, are considered. In particular, the study is focused on interactions with structure periodic in the space. Results on one-dimensional structures are extended to the case of a two-dimensional system. The problems of stopping bands, passing bands, and mistuning are also mentioned.

Keywords:

railway track, moving load, dubble sleepers, vibration

Affiliations:
Bogacz R.-other affiliation
Czyczuła W.-Cracow University of Technology (PL)
Konowrocki R.-IPPT PAN
6.Bogacz R., Konowrocki R., On new effects of wheel-rail interaction, ARCHIVE OF APPLIED MECHANICS, ISSN: 0939-1533, Vol.82, pp.1313-1323, 2012
Abstract:

The paper is devoted to the experimental, theoretical analysis and computer simulation of influence of elastic properties of contact stiffness and wheel-plate stiffness on the forces of vehicle-track interaction. Three types of wheels are considered with different contact stiffness and wheel-plate design. Exemplary simulation of freight car interaction with track which posses one corrugated rail for each type of wheel is presented.

Keywords:

Contact stiffness, Rail corrugation, Elastic wheel, Wheel-rail interaction, Simulation

Affiliations:
Bogacz R.-other affiliation
Konowrocki R.-IPPT PAN
7.Bogacz R., Czyczuła W., Pawlak-Burakowska A., Wpływ tłumienia na stateczność strumienia oscylatorów oddziałującego z belką. Stateczność przepływu cieczy, Symulacja w Badaniach i Rozwoju, ISSN: 2081-6154, Vol.3, No.2, pp.71-77, 2012
Abstract:

W niniejszej pracy rozważana jest stateczność ruchu układu złożonego ze strumienia gęsto rozłożonej masy (oscylatorów) oddziałującego sprężyście lub lepko-sprężyście z belką na podłożu Winkera (np. modelującej rurę). Układ taki może być uproszczonym modelem układu pociąg - tor lub modelem rurociągu, przez który przepływa ciecz (dla uproszczenia nieściśliwa).

Keywords:

stateczność przepływu, ruch względny, tłumienie

Affiliations:
Bogacz R.-other affiliation
Czyczuła W.-Cracow University of Technology (PL)
Pawlak-Burakowska A.-other affiliation
8.Konowrocki R., Bogacz R., Numerical analysis of vibration in a brake system for high speed train, VIBRATIONS IN PHYSICAL SYSTEMS, ISSN: 0860-6897, Vol.25, pp.235-240, 2012
Abstract:

The paper is devoted to a computer simulation of brake pad/brake disc dynamic interaction. The main purpose of the studies is a numerical analysis of friction pair dynamics, aiming at describe generation of vibration related to the process of transition phenomena associated with braking. To investigation will be used environment of Automatic Dynamic Analysis of Mechanical Systems. In the analysis is used two-dimensional friction model. The results show the slip-stick and creep phenomenon

Keywords:

vibrations excited by friction, self-excited of vibrations, slip-stick, creepage

Affiliations:
Konowrocki R.-IPPT PAN
Bogacz R.-other affiliation
9.Bogacz R., Frischmuth K., On some corrugation related dynamical problems of wheel/rail interaction, ARCHIVES OF TRANSPORT, ISSN: 0866-9546, Vol.XXII, No.1, pp.27-41, 2010
Abstract:

We simulate the motion of a corrugated disk over a corrugated track under unilateral elastic contact forces. In particular, the trajectory of the geometrical contact point and the magnitude of normal forces are studied. Effects like generation of waves and cumulation of plastic deformation are considered.

Keywords:

railway mechanics, contact geometry, friction, bouncing, wave generation, plastic deformation

Affiliations:
Bogacz R.-IPPT PAN
Frischmuth K.-University of Rostock (DE)
10.Imiełowski Sz., Bogacz R., Stability constraints in optimization of cracked columns subjected to compressive follower load, ENGINEERING TRANSACTIONS (ROZPRAWY INŻYNIERSKIE), ISSN: 0867-888X, Vol.55, No.4, pp.281-292, 2007
Abstract:

Maximization of the critical force of cracked columns, subjected to generalized follower force is discussed in the paper. The crack is assumed to be formed according to the opening and sliding modes and is modeled by a localized loss of stiffness. Influence of the crack stiffness and its localization on the value of the critical force is analyzed. The optimization process is based on the multimodal approach. The localization of crack with the critical force of the system equal to 137.17 EJ/L2 is found

Keywords:

STABILITY CONSTRAINTS, OPTIMIZATION OF CRACKED COLUMNS, FOLLOWER LOAD, localization of crack

Affiliations:
Imiełowski Sz.-IPPT PAN
Bogacz R.-IPPT PAN
11.Bogacz R., Professor Karl Popp and his contribution to Polish - German co-operation in applied mechanics, Machine Dynamics Research, ISSN: 2080-9948, Vol.30, No.1, pp.21-31, 2006
Abstract:

The paper is devoted to an outstanding scientific activity of Professor Karl Popp in applied mechanics and his contribution to Polish-German cooperation. His international collaboration was very impressive. Cooperation with Polish scientists covers over twenty years of his scientific activity. We can mention here by name Polish scientists which cooperate with Professor Popp in the various framework, i.e. beginning with A.v. Humboldt fellows: J. Socha and T. Krzyżyński DAAD fellows: S. Nowakowski, J. Danielski and W. Kurnik, visiting professors: J. Kisilowski and R. Bogacz and a few DFG fellows. The scientific interests of Professor Karl Popp were very extensive and include engineering application of friction, computational methods in engineering (particularly discrete and continuum mechanics), machine dynamics - vibration of machinery, stability, fluid structure interaction, simulation of transportation systems, biomechanics and others. Selected problems were chosen as session topics of German-Polish Workshops on Dynamical Problems of Mechanical Systems and EUROMECH Colloquium 409.

Keywords:

Professor Karl Popp, applied mechanics, cooperation in applied mechanics, Karl Popp - scientific activity

Affiliations:
Bogacz R.-IPPT PAN
12.Bogacz R., Meinke P., On evaluation of wheel sets and railway track quality, ZESZYTY NAUKOWE INSTYTUTU POJAZDÓW / POLITECHNIKA WARSZAWSKA, ISSN: 1642-347X, Vol.1, pp.15-20, 2006
Abstract:

The cost of maintenance and the safety of railway operation depend (among other things) on the quality of the wheel sets interaction with the rails. There is the necessity to monitor the rolling behaviour of regular vehicles. Of most importance is the time behaviour of the travelling contact forces between the wheel sets and the trucks. The rolling wheel set obtains a very different position relative to the track, which creates restraints in the wheel set and the track panel structure, and which will discharge continuously by friction induced vibration. Those vibrations cause corrugation, ballast deterioration, wear, squealing noise and other environmental impacts.

Keywords:

wheel sets, railway track, monitoring, motion, rolling performance, system dynamics

Affiliations:
Bogacz R.-IPPT PAN
Meinke P.-other affiliation
13.Bajer C.I., Bogacz R., Propagation of perturbances generated in classic track, and track with Y-type sleepers, ARCHIVE OF APPLIED MECHANICS, ISSN: 0939-1533, DOI: 10.1007/s00419-005-0403-8, Vol.74, pp.754-761, 2005
Abstract:

Railway track with classic and Y-shaped sleepers or slab track is composed of two rails that are assumed to be infinitely long and joined with sleepers by viscoelastic pads. Numerous assumptions are used in railway-track modelling, leading to different simplifications. The two-dimensional periodic model of track consists of two parallel infinite Timoshenko beams (rails) coupled with equally spaced sleepers on a viscoelastic foundation.

Nowadays the interest of engineers is focused on slab track and track with Y-shaped sleepers. The fundamental qualitative difference between the track with classic and Y-shaped sleepers is related to local longitudinal symmetric or antisymmetric features of the railway track. The sleeper spacing influences the periodicity of the foundation elasticity coefficient, mass density (rotational inertia) and the effective shear rigidity. Track with classic concrete sleepers is affected much more by rotational inertia and shear deflections than track with Y-shaped sleepers. The increase of the elastic-wave velocity in track with Y-shaped sleepers and more uniform load distribution will be proved by analysis and simulation.

The analytical and numerical analyses allows us to evaluate the track properties in a range of moderate and high train speeds. However, the correct approach is not simple, since the structure of the track interacts with the wheels, wheelsets and vehicles, which constitute complex inertial loads. We note that the growth of amplitude in selected velocity ranges depends strongly on the track type.

Keywords:

Track dynamics, Vibrations, Moving load, Y-type track

Affiliations:
Bajer C.I.-IPPT PAN
Bogacz R.-IPPT PAN
14.Bogacz R., Frischmuth K., Mechanical problems with moving load, Scientific papers of Techn. Univ. Radom TRANSPORT, Vol.3, No.23, pp.35-42, 2005
Abstract:

We study periodic structures composed of beams, columns and plates subjected to moving constant or harmonic loads. Such structures occur in civil engineering, e.g. classical tracks or maglev guideways, highways or tarmacs of airports. We discuss the influence of speed and frequencies as well as parameters describing the construction itself.

Keywords:

periodic structures, moving constant loads, moving harmonic loads

Affiliations:
Bogacz R.-IPPT PAN
Frischmuth K.-University of Rostock (DE)
15.Bogacz R., Ryczek B., O badaniach teoretyczno-doświadczalnych dotyczących drgań samowzbudnych typu przyleganie-poslizg, Prace IPPT - IFTR Reports, ISSN: 2299-3657, No.8, pp.1-22, 1996
16.Niespodziana A., Bogacz R., O wpływie stopnia niekonserwatywności obciążenia na charakter utraty stateczności kolumny dyskretno ciągłej, Prace IPPT - IFTR Reports, ISSN: 2299-3657, No.36, pp.1-20, 1990
17.Bogacz R., Imiełowski Sz., Stateczność kolumn ze zlokalizowaną nieciągłością przemieszczeń obciążonych siłą cyrkulacyjną, Prace IPPT - IFTR Reports, ISSN: 2299-3657, No.6, pp.1-16, 1988
18.Bogacz R., Irretier H., Szolc T., Transient Vibration Analysis of a continuous Model of a Turbogenerator Rotor Shaft System Using Torsional Elastic Waves, Prace IPPT - IFTR Reports, ISSN: 2299-3657, No.53, pp.1-33, 1988
19.Bogacz R., Niespodziana A., O stateczności ciągłych kolumn Beck`a ze zlokalizowaną utratą sztywności, Prace IPPT - IFTR Reports, ISSN: 2299-3657, No.27, pp.1-23, 1987
20.Bogacz R., Irretier H., Sikora J., O pewnych rozwiązaniach ruchomego układu o dwóch stopniach swobody z tarciem suchym, Prace IPPT - IFTR Reports, ISSN: 2299-3657, No.39, pp.1-27, 1987
21.Bogacz R., Janiszewski R., Zagadnienie analizy i syntezy kolumn obciążonych siłami śledzącymi ze względu na stateczność, Prace IPPT - IFTR Reports, ISSN: 2299-3657, No.6, pp.1-92, 1986
22.Bogacz R., Krzyżyński T., O belce Bernoulli`ego-Eulera spoczywającej na lepkosprężystym podłożu poddanej działaniu ruchomego oscylacyjnego obciążenia, Prace IPPT - IFTR Reports, ISSN: 2299-3657, No.38, pp.1-40, 1986
23.Bogacz R., Niespodziana A., O obszarach niestateczności pewnych modeli kolumn obciążonych silą śledzącą, Prace IPPT - IFTR Reports, ISSN: 2299-3657, No.36, pp.1-16, 1984
24.Bogacz R., O stateczności wzajemnego oddziaływania układów ciągłych i dyskretnych w ruchu względnym (Praca habilitacyjna), Prace IPPT - IFTR Reports, ISSN: 2299-3657, No.61, pp.1-75, 1977
25.Bogacz R., Podolak K., Analiza tłumiącego działania ośrodka sprężysto - plastycznego, Prace IPPT - IFTR Reports, ISSN: 2299-3657, No.1, pp.1-16, 1972
26.Bogacz R., O stateczności pewnego tłumionego układu z falą bieżącą, Prace IPPT - IFTR Reports, ISSN: 2299-3657, No.54, pp.1-17, 1972

List of chapters in recent monographs
1.
336
Konowrocki R., Bogacz R., Kukulski J., Walczak S., Selected Dynamical Problems in Mechanical Systems, rozdział: Experimental and Numerical Investigation of Oscillations in a Brake System, Oficyna Wydawnicza Politechniki Warszawskiej, pp.75-84, 2014
2.
236
Konowrocki R., Bogacz R., Bajer C.I., Symulacja w Badaniach i Rozwoju, rozdział: Badanie oddziaływania koła z drogą z uwzględnieniem poślizgów bocznych, PTSK, PW, IPPT, Warszawa, pp.124-131, 2006
3.
169
Bogacz R., Dżuła S., Materiały IX Warsztatów Polskiego Towarzystwa Symulacji Komputerowej "Symulacja w badaniach i rozwoju", rozdział: Dynamical problem of an unbalanced railway wheel in rolling motion, PTSK, Bobrowski L., Tylikowski A. (Eds.), pp.77-84, 2005
4.
170
Bogacz R., Chudzikiewicz A., Frischmuth K., Materiały IX Warsztatów Polskiego Towarzystwa Symulacji Komputerowej "Symulacja w badaniach i rozwoju", rozdział: Friction, wear and heat, PTSK, Bobrowski L., Tylikowski A. (Eds.), pp.67-76, 2005

Conference papers
1.Konowrocki R., Bajer C.I., Bogacz R., Badania eksperymentalne współpracy koła z drogą z uwzględnieniem poślizgów bocznych, XIV Warsztaty Polskiego Towarzystwa Symulacji Komputerowej, 2007-09-26/09-29, Zakopane (PL), Vol.14, pp.158-171, 2008
Abstract:

Praca opisuje zagadnienia dynamicznego oddziaływania podziemnego pojazdu szynowego na tor. Oddziaływanie to wywołuje drgania, które za pośrednictwem konstrukcji toru, tunelu oraz gruntu propagowane są na pobliskie konstrukcję i budynki. Ze względu na zagęszczenie ruchu ulicznego podziemna komunikacja jest obecnie jedyną alternatywą płynnego przemieszczania się osób w wielkich aglomeracjach miejskich. Sprzyja to rozwojowi i modernizacji podziemnej kolei miejskiej, w której jako jednym z celów stawianych projektantom jest minimalizacja powstania drgań propagujących się na otaczające środowisko W nauce również można zaobserwować wzrost zainteresowania zjawiskami powstawania i propagacji drgań w gruncie, wywołanych przejazdem pojazdów kolei podziemnej. Głównym pytaniem nurtującym badaczy jest kwestia kontroli układu pojazd/tor i zmniejszenie powstających szkodliwych wibracji i hałasu. Ze względu na wielorakie rozwiązana konstrukcyjne pojazdów i torowisk kolei podziemnej trudno jest zaproponować jednoznaczne rozwiązanie.

Keywords:

metro, oddziaływania podziemnego pojazdu szynowego, wibroizolacja, grunt

Affiliations:
Konowrocki R.-IPPT PAN
Bajer C.I.-IPPT PAN
Bogacz R.-IPPT PAN
2.Bogacz R., Frischmuth K., Models of surface pattern development in rolling contact, TRANSCOMP, X Miedzynarodowa Konferencja Komputerowe Systemy Wspomagania Nauki, Przemysłu i Transportu, 2006-12-04/12-07, Zakopane (PL), Vol.I, pp.59-64, 2006
Abstract:

We study the rolling motion of a railway wheel on corrugated track. For uniform guiding motion, the trajectory of the contact point, vertical accelerations are evaluated first in the rigid case, then in the case of elastic and visco-elastic contact. Resulting energy dissipation due to friction and percussive effects are calculated and resulting progress of pattern formation is simulated.

Keywords:

rolling contact, surface pattern, railway wheel, corrugated track

Affiliations:
Bogacz R.-IPPT PAN
Frischmuth K.-University of Rostock (DE)
3.Bogacz R., Selected problems of dynamics of continuous systems subjected to traveling and oscillating loads, TRANSCOMP, X Miedzynarodowa Konferencja Komputerowe Systemy Wspomagania Nauki, Przemysłu i Transportu, 2006-12-04/12-07, Zakopane (PL), Vol.I, pp.65-72, 2006
Abstract:

We studied several cases of dynamical problems, where the motion is driven by a concentrated force or distributed load applied at a moving position. The velocity of motion is assumed as constant. In particular, we studied interactions with periodic structure of the medium. Earlier results on one-dimensional structuresare extended to the case of an array of plates

Keywords:

dynamic, continuous systems, traveling load, oscillating loads

Affiliations:
Bogacz R.-IPPT PAN
4.Szolc T., Bogacz R., Analysis of the airport runway n excited by motion of heavy aircrafts, XXII Symposium Vibration in Physical Systems, 2006-04-19/04-22, Poznań-Będlewo (PL), pp.343-348, 2006
Abstract:

In the presented paper by means of the continuous model a dynamic interaction between the airport runway and the aircraft landing-gear is considered in order to investigate the controlled cracking process of the initially notched runway plates. For this purpose normal stresses induced by the static and dynamic loads in the runway plate notched areas are going to be determined by means of the continuous mechanical model and analytical mathematical solution of the problem.

Keywords:

dynamic load, analytical mathematical solution, airport runway

Affiliations:
Szolc T.-IPPT PAN
Bogacz R.-IPPT PAN
5.Bogacz R., Imiełowski Sz., Frischmuth K., On stability and optimization of cracked columns subjected to compressive circulatory load, XXII Symposium Vibration in Physical Systems, 2006-04-19/04-22, Poznań-Będlewo (PL), pp.83-88, 2006
Abstract:

Maximization of the critical force of cracked columns, subjected to generalized follower force is discussed in the paper. The crack is assumed to be formed according to the opening and sliding modes and is modeled by a localized loss of stiffness. Influence of the crack stiffness and its localization on the value of the critical force is analyzed. The optimization process is based on the multimodal approach.

Keywords:

localization of crackoptimization of cracked columns, stability constraints, follower load,

Affiliations:
Bogacz R.-IPPT PAN
Imiełowski Sz.-IPPT PAN
Frischmuth K.-University of Rostock (DE)