ADVANCES IN THE MECHANICS OF INHOMOGENEOUS MEDIA

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2 ADVANCES IN THE MECHANICS OF INHOMOGENEOUS MEDIA EDITED BY: CZESŁAW WOŹNIAK MIECZYSŁAW KUCZMA ROMUALD ŚWITKA KRZYSZTOF WILMAŃSKI ZIELONA GÓRA 2010

3 EDITORIAL BOARD Krzysztof Urbanowski (chairman), Marian Adamski, Rafał Ciesielski, Michał Drab, Andrzej Maciejewski, Maria Fic, Beata Gabryś, Bohdan Halczak, Janusz Matkowski, Anna Walicka, Zdzisław Wołk, Ryszard Błażyński (secretary) TYPESETTING Tomasz Socha ISBN Copyright by University of Zielona Góra Zielona Góra, Poland, 2010 All rights reserved. No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Printed by the University of Zielona Góra Press ul. Podgórna 50, Zielona Góra, Poland

4 INDEX OF AUTHORS: Volodymyr BOYCHUK Bohdan BOZHENKO Krzysztof DEMS Mykola HACHKEVYCH Oleksandr HACHKEVYCH Jarosław JĘDRYSIAK Zygmunt KASPERSKI Anna KOSIŃSKA Sławomir KOSIŃSKI Tomasz KRYKOWSKI Mieczysław KUCZMA Krzysztof KULA Daniel LEWANDOWSKI Bohdan MICHALAK Wiesław NAGÓRKO Elżbieta RADASZEWSKA Alina RADZIKOWSKA Jowita RYCHLEWSKA Rainer SCHLEBUSCH Urszula SIEDLECKA Gwidon SZEFER Romuald ŚWITKA Barbara TOMCZYK Krystyna URBAŃSKA Barbara WIECZOREK Ewaryst WIERZBICKI Krzysztof WILMAŃSKI Artur WIROWSKI Jacek WIŚNIEWSKI Czesław WOŹNIAK Bernd W. ZASTRAU Grażyna ZIĘTEK Adam ZYBURA

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6 CONTENTS PREFACE... 9 PART 1. 1 CHAPTER 1. CHAPTER 2. CHAPTER 3. CHAPTER 4. CHAPTER 5. MATHEMATICAL METHODS AND MODELLING ON THE TOLERANCE MODELLING OF PDEs WITH NON-UNIFORMLY OSCILLATING COEFFICIENTS (Jowita RYCHLEWSKA, Czesław WOŹNIAK) AN INTEGRATED MODEL OF A FIBROUS COMPOSITE MATERIAL (Romuald ŚWITKA) TOLERANCE MODELLING OF QUASI-LINEAR HEAT CONDUCTION IN FUNCTIONALLY GRADED LAMINATES (Urszula SIEDLECKA, Ewaryst WIERZBICKI, Czesław WOŹNIAK) MODELLING AND OPTIMIZATION OF THERMAL PROPERTIES OF FIBER REINFORCED COMPOSITE MATERIAL SUBJECTED TO THERMAL LOAD (Krzysztof DEMS, Elżbieta RADASZEWSKA) SOME PROBLEMS ON THE MODELLING OF HEAT CONDUCTION FOR TRANSVERSALLY GRADED LAMINATES (TGL) (Jarosław JĘDRYSIAK, Alina RADZIKOWSKA)... 67

7 CHAPTER 6. CHAPTER 7. CHAPTER 8. PART 2. CHAPTER 9. CHAPTER 10. CHAPTER 11. CHAPTER 12. COMBINED MODELLING OF PERIODICALLY STIFFENED CYLINDRICAL SHELLS (Barbara TOMCZYK) ON THE MODELLING OF STABILITY OF COMPOSITE THIN PLATES WITH CERTAIN LONGITUDINALLY GRADED MATERIALS (Bohdan MICHALAK) THE TOLERANCE MODELING OF DYNAMIC BEHAVIOUR OF LONGITUDINARY GRADED ANNULAR PLATES (Artur WIROWSKI) COUPLED FIELDS DIFFUSION AND HEAT CONDUCTION IN NONLINEAR THERMOPOROELASTIC MEDIA (Krzysztof WILMAŃSKI) FUNDAMENTAL SOLUTION FOR THE QUASI- STATIC PROBLEM OF ELASTIC THERMODIFFUSION IN THE MICROPOLAR SOLID (Barbara WIECZOREK) FEM MODELLING OF CONCRETE COVER DEGRADATION CAUSED BY REBARS CORROSION IN REINFORCED CONCRETE (Tomasz KRYKOWSKI, Adam ZYBURA) LOVE WAVES IN DEFORMED FOAM RUBBER (Anna KOSIŃSKA, Sławomir KOSIŃSKI)

8 CHAPTER 13. PART 3. CHAPTER 14. CHAPTER 15. CHAPTER 16. CHAPTER 17. CHAPTER 18. METHOD OF OPTIMIZATION OF HEATING TREATMENT OF GLASS-MADE PIECEWISE- HOMOGENEOUS SHELLS OF REVOLUTION WITH ALLOWANCE FOR THE TEMPERATURE SENSITIVITY OF ALLOWABLE STRESSES (Bohdan BOZHENKO, Volodymyr BOYCHUK, Oleksandr HACHKEVYCH, Mykola HACHKEVYCH, Zygmunt KASPERSKI) THEORY OF MATERIALS AND STRUCTURES FOUNDATIONS OF MECHANICS OF CARBON NANOTUBES (Gwidon SZEFER) OPTIMAL FIBERS ARRANGEMENT IN COMPOSITE MATERIALS (Krzysztof DEMS, Jacek WIŚNIEWSKI) ON THE MODELLING OF DYNAMICS AND STABILITY PROBLEMS FOR THIN FUNCTIONALLY GRADED PLATES (Jarosław JĘDRYSIAK) VIBRATIONS AND WAVES IN A PERIODICALLY RIBBED ELASTIC PLATE (Wiesław NAGÓRKO) THE IDENTIFICATION OF THE PARAMETERS OF MAGNETORHEOLOGICAL COMPOSITE MODEL (Daniel LEWANDOWSKI, Grażyna ZIĘTEK)

9 CHAPTER 19. CHAPTER 20. ON DELAMINATION PROBLEM IN FIBER REINFORCED SHELLES (Krzysztof KULA, Rainer SCHLEBUSCH, Mieczysław KUCZMA, Bernd W. ZASTRAU) MODERN TESTING OF MECHANICAL PROPERTIES OF BRICK MASONRY (Krystyna URBAŃSKA, Mieczysław KUCZMA) REFERENCES INDEX