Application of non-classical operational calculus to indicate hazards in numerical solutions of engineering problems

Mieloszyk, Eligiusz; Wyroślak, Mariusz

doi:10.2478/sgem-2019-0047

Abstract

The article addresses the application of non-classical operational calculus to approximative solutions of engineering problems. The engineering-sound examples show that a continuous–discrete problem transformation from differential unequivocal problem to a differential wildcard problem, triggering a change in solution quality. A number of approximative methods are capable to alter both quantitative and qualitative solution effects.

References

M. Abramski, E. Mieloszyk, A. Milewska, Analysis of compressive forces in cylindrical pillars and their coatings using laboratory tests and metric spaces, (2018) (in preparation).
Search in Google Scholar Back to article
M. J. Afshari, M. Gholhaki, Shear degradation of steel plate shear walls with optional located opening, Arch. Civ. Mech. Eng., 18 (2018) 1547–1561.
Search in Google Scholar Back to article
API6S3, Tank inspection, repair, alternation and reconstruction, American Petroleum Institute, Washington, USA, 2005.
Search in Google Scholar Back to article
T. Dahlberg, B. Aakesson, S. Westberg, Modelling the dynamic interaction between train and track, Railway Gazette International, 149 (1994).
Search in Google Scholar Back to article
G. Diana, F. Cheli, S. Bruni, and A. Collina, Interaction between railroad superstructure and railway vehicles, Vehicle System Dynamics, 23 (1994).
Search in Google Scholar Back to article
I. Herle, Constitutive Modelling of Granular Materials, Chapter: Numerical predictions and reality, Springer, (2003) 333–351.
Search in Google Scholar Back to article
G. Li, Stress analysis of stepped shell wall and bottom plate of large cylindrical storage, Mechanics and Practise, 1(4) (1979).
Search in Google Scholar Back to article
E. Mieloszyk, Application of non-classical operational calculus to solving some boundary value problem, Integral Transforms and Special Functions, 9 (4) (2000) 287–292.
Search in Google Scholar Back to article
E. Mieloszyk, Non-classical operational calculus in application to generalized dynamical systems, Polish Academy of Science, Scientific Publishers, (2008).
Search in Google Scholar Back to article
E. Mieloszyk, S. Grulkowski, Generalized Taylor formula and shell structures for the analysis of the interaction between geosynthetics and engineering structures of transportation lines, CRC Press Taylor & Francis Group, (2017) 561–564.
Search in Google Scholar Back to article
E. Mieloszyk, W. Koc, General dynamic method for determination transition curve equations, Rail International, 22 (10) (1991) 32–40.
Search in Google Scholar Back to article
A. Milewska, A solution of non-linear differential problem with application to selected geotechnical problems, Archives of Civil Engineering, LVIII (2) (2011) 187–197.
Search in Google Scholar Back to article
M. Moravčik, Experimental investigation of the vehicle-rail interaction, TESE Proceedings, 1 (1994) 73–78.
Search in Google Scholar Back to article
E. Selig, J. Waters, Track Geotechnology and Substructure Management, University of Massachusetts (1994).
Search in Google Scholar Back to article
S. K. Shukla, S. Chandra, A study on a new mechanical model for foundations and its elastic settlement response, International Journal for Numerical Methods in Geomechanics, 20 (1996) 594–604.
Search in Google Scholar Back to article
S. Timoshenko, S. Woinowsky-Krieger, Theory of plates and shells, McGraw-Hill, Incorporated (1959).
Search in Google Scholar Back to article
T. Wu, More accurate method devised for tank-bottom annular plate design, Oil Gas Journal, 94 (21) (1996).
Search in Google Scholar Back to article
T. Y. Wu, G. R. Liu, Comparison of design method for a tank-bottom annular plate and concrete ringwall, International Journal of Pressure Vessels and Piping, 77 (2000) 511–517.
Search in Google Scholar Back to article

Application of non-classical operational calculus to indicate hazards in numerical solutions of engineering problems

Abstract

Paradigm

My account