Advanced Structured Materials

Volume 110

Series Editors

Andreas Öchsner, Faculty of Mechanical Engineering, Esslingen University ofApplied Sciences, Esslingen, GermanyLucas F. M. da Silva, Department of Mechanical Engineering, Faculty ofEngineering, University of Porto, Porto, PortugalHolm Altenbach, Faculty of Mechanical Engineering,Otto-von-Guericke-Universität Magdeburg, Magdeburg, Sachsen-Anhalt, Germany

Common engineering materials reach in many applications their limits and newdevelopments are required to fulfil increasing demands on engineering materials.The performance of materials can be increased by combining different materials toachieve better properties than a single constituent or by shaping the material orconstituents in a specific structure. The interaction between material and structuremay arise on different length scales, such as micro-, meso- or macroscale, and offerspossible applications in quite diverse fields.

This book series addresses the fundamental relationship between materials and theirstructure on the overall properties (e.g. mechanical, thermal, chemical or magneticetc) and applications.

The topics of Advanced Structured Materials include but are not limited to

• classical fibre-reinforced composites (e.g. glass, carbon or Aramid reinforcedplastics)

• metal matrix composites (MMCs)• micro porous composites• micro channel materials• multilayered materials• cellular materials (e.g., metallic or polymer foams, sponges, hollow sphere

structures)• porous materials• truss structures• nanocomposite materials• biomaterials• nanoporous metals• concrete• coated materials• smart materials

Advanced Structured Materials is indexed in Google Scholar and Scopus.

More information about this series at http://www.springer.com/series/8611

Holm Altenbach • Jacek Chróścielewski •

Victor A. Eremeyev • Krzysztof WiśniewskiEditors

Recent Developmentsin the Theory of Shells

123

EditorsHolm AltenbachFaculty of Mechanical EngineeringOtto-von-Guericke-Universität MagdeburgMagdeburg, Germany

Jacek ChróścielewskiFaculty of Civil and EnvironmentalEngineeringGdańsk University of TechnologyGdańsk, Poland

Victor A. EremeyevFaculty of Civil and EnvironmentalEngineeringGdańsk University of TechnologyGdańsk, Poland

Krzysztof WiśniewskiInstitute of Fundamental TechnologicalResearchPolish Academy of SciencesWarsaw, Poland

ISSN 1869-8433 ISSN 1869-8441 (electronic)Advanced Structured MaterialsISBN 978-3-030-17746-1 ISBN 978-3-030-17747-8 (eBook)https://doi.org/10.1007/978-3-030-17747-8

© Springer Nature Switzerland AG 2019This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or partof the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations,recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmissionor information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilarmethodology now known or hereafter developed.The use of general descriptive names, registered names, trademarks, service marks, etc. in thispublication does not imply, even in the absence of a specific statement, that such names are exempt fromthe relevant protective laws and regulations and therefore free for general use.The publisher, the authors and the editors are safe to assume that the advice and information in thisbook are believed to be true and accurate at the date of publication. Neither the publisher nor theauthors or the editors give a warranty, expressed or implied, with respect to the material containedherein or for any errors or omissions that may have been made. The publisher remains neutral with regardto jurisdictional claims in published maps and institutional affiliations.

This Springer imprint is published by the registered company Springer Nature Switzerland AGThe registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

This book is dedicated to a truly outstandingscientist and person, our dear friend andteacher Prof. Wojciech Pietraszkiewiczon the occasion of his 80th birthday.

Preface

Professor Wojciech Pietraszkiewicz is one of the leading Polish scientists in thetheory of shells (thin-walled structures) and in continuum mechanics. His scientificcontribution covers several areas, such as:

• Statics and dynamics of classical and non-classical theory of shells, includingsix-parameter theory of shells;

• Mechanics of classical and Cosserat continua;• Finite rotations in mechanics of solids and structures;• Non-linear mechanics and FE analysis of multi-fold shell structures;• Intrinsic non-linear theory of thin shells;• Non-linear phase transitions in shells;• Refined thermomechanics of shells;• Differential geometry of surface in 3D space.

This volume of the Advanced Structured Materials Series is dedicated to Prof.W. Pietraszkiewicz on the occasion of his 80th birthday, and it contains papers onbeams, plates and shells prepared by his friends and colleagues from Austria,Belarus, France, Germany, India, Italy, Mexico, Poland, Russia, Slovenia, UK,Ukraine and USA.

Prof. W. Pietraszkiewicz was born on January 23rd 1939 in Wilno (then inPoland; currently Vilnius, the capital of Lithuania). He received a MSc degree in1961 and a PhD degree in 1966 from the Department of Civil Engineering of theGdańsk University of Technology. The same department honored him with a DScdegree (habilitation) in 1977. He became the Extraordinary Professor in 1983 andreceived the title of Full Professor from the President of Poland in 1990.

In the period 1961–1966 he worked in the Gdańsk University of Technology.Next he moved to the Institute of Fluid-Flow Machinery of the Polish Academy ofSciences in Gdańsk, where in the years 1966–2009 he held the positions of a Headof Division, a Deputy Director, a Director, and a Head of the Department ofMechanics of Structures and Materials. He retired in 2010, and, since 2016, he is aFull Professor at the Gdańsk University of Technology.

vii

From the beginning of his scientific carrier Prof. W. Pietraszkiewicz wasinternationally active. He was a visiting professor in 1971–1972 at the University ofIllinois Urbana-Champaign (USA) on the Fulbright Scholarship. In the years 1976–

Wojciech Pietraszkiewicz

viii Preface

1997, he had several appointments as a visiting professor at the Ruhr-UniversitätBochum (Germany), where he spent in total over 5 years. In 2001 he was a visitingprofessor at RWTH Aachen (Germany). In 2000–2007, he visited several times theUniversité de Poitiers (France). During his carrier, he lectured in over 30 scientificinstitutions in Germany, USA, Netherlands, Switzerland, Italy, Belgium, France,UK, Hungary, Czech Republic, Brazil, China, Russia and Ukraine.

Prof. W. Pietraszkiewicz organized several international conferences: ShellStructures: Theory and Applications (SSTA) (many times since 1986), EuromechColloquium 197 Finite Rotations in Structural Mechanics (Jabłonna, 1985), and3rd Meeting Scientific Foundations of Mechanics of Materials, Machinery,Structures and Technological Processes (Gdańsk, 1984). Especially famous is thelarge international SSTA conference; Prof. Pietraszkiewicz chaired the International

Wojciech Pietraszkiewicz with Leonid Zubov and Victor Berdichevski, during IUTAM symposium, Tbilisi, (1978)

Preface ix

Advisory Board of its seven editions: Szklarska Porȩba (1986), Jurata (1998, 2002,2005, 2009) and Gdańsk (2013, 2017). Four volumes of post-conference paperswere published by Balkema as a follow-up of the last four editions of the SSTAconference. In the years 2006–2016, he co-chaired the session on shells and plateswithin the Solid Mechanics (SOLMECH) conference, which is organized bienniallyby the Institute of Fundamental Technological Research of the Polish Academy ofSciences (IPPT PAN).

With Philippe Ciarlet (on the left) and Satya Atluri (on the right), ICCES’11, Nanjing (2011)

Ireneusz Kreja, Jacek Chróścielewski, J.N. Reddy, Wojciech Pietraszkiewicz, and Victor Eremeyev, at the SSTA conference, Jurata, (2009)

x Preface

He co-edited special issues of several international journals, such as: Archives ofCivil Engineering (1999, 2003), Journal of Theoretical and Applied Mechanics(2003), ZAMM (2014) and Mathematics and Mechanics of Solids (2015).

Prof. Pietraszkiewicz received several awards for outstanding researchachievements from the Polish Academy of Sciences (1975, 1979, 1982) and anaward of the Polish Ministry of National Education (2002). Since 2005 he is theHonorary Member of the Polish Society of Theoretical and Applied Mechanics. In2011 he obtained The Wei-Zhang Chien Award at the ICCES’11 in Nanjing, China,for his “fundamental contributions in the intrinsic theory of shells”.

Prof. W. Pietraszkiewicz published 5 monographs, 4 textbooks and lecture notes,178 original refereed papers in journals and books, presented 174 lectures at sci-entific meetings (most published in Proceedings), edited 17 volumes of collectedpapers, and supervised 11 PhD dissertations. It is also worth to mention, that heserved as a section editor and wrote several entries for the section Shells inEncyclopedia of Continuum Mechanics (Springer, Berlin, Heidelberg, 2019).

The 80th birthday of Prof. W. Pietraszkiewicz is a good occasion to thank Himnot only for his excellent and well known papers on shells but also for his friendlyand supportive attitude, which helped many of us to stay in science and work onshells. On behalf of ourselves and all the contributors to this volume,

Best wishes Prof. Pietraszkiewicz on the occasion of your 80th birthday !

Selected publications of Prof. Wojciech Pietraszkiewicz

(A list of publications with full texts are available at http://www.imp.gda.pl/en/wpietraszkiewicz/.)

Books

1. Pietraszkiewicz, W.: Elastic Materials (in Polish). Bulletin No. 652, Institute ofFluid-Flow Machinery of PASci., Gdańsk (1969)

2. Pietraszkiewicz, W.: Introduction to the Non-Linear Theory of Shells. Mitt. Inst.f. Mech., Nr. 10 Ruhr-Universität Bochum, Bochum (1977)

3. Pietraszkiewicz, W.: Finite Rotations and Lagrangean Description in theNon-linear Theory of Shells. Polish Scientific Publishers, Warszawa—Poznań(1979)

4. Pietraszkiewicz, W.: Finite rotations in the non-linear theory of thin shells. In:Olszak, W. (ed.) Thin Shell Theory, New Trends and Applications, CISMCourses and Lectures, vol 240, Springer, Wien, pp 153–208 (1980)

Preface xi

5. Pietraszkiewicz, W.: Geometrically non-linear theories of thin elastic shells(published also in Mitt. Inst. f. Mech. Nr 55, Ruhr-Universität Bochum,Bochum, 1988). Adv. Mech. 12(1):51–130 (1989)

6. Pietraszkiewicz, W.: Non-linear theories of shells (in Polish). In: Woźniak, Cz.(ed.) Mechanics of Elastic Plates and Shells, pp. 424–497. Polish ScientificPublishers, Warszawa (2001)

7. Makowski, J., Pietraszkiewicz, W.: Thermomechanics of Shells with SingularCurves. Zeszyty Naukowe, vol 528/1487. IMP PAN, Gdańsk (2002)

8. Chróścielewski, J., Makowski, J., Pietraszkiewicz, W.: Statics and Dynamics ofMultyfolded Shells. Nonlinear Theory and Finite Elelement Method (in Polish).Wydawnictwo IPPT PAN, Warszawa (2004)

Edited Books

1. Pietraszkiewicz, W. (ed.): Finite Rotations in Structural Mechanics, Proc.Euromech Colloquium 197, Jabłonna (Poland), 1985, Lecture Notes inEngineering, vol 19. Springer, Berlin (1986)

2. Pietraszkiewicz, W., Szymczak, C. (eds.): Shell Structures: Theory andApplications — Proceedings of the 8th SSTA Conference. CRC Press, BocaRaton (2005)

3. Pietraszkiewicz, W., Kreja, I. (eds.): Shell Structures: Theory and Applications— Proceedings of the 9th SSTA Conference, vol 2. CRC Press, Boca Raton(2010)

4. Pietraszkiewicz, W., Górski, J.: (eds) Shell Structures: Theory and Applications—Proceedings of the 10th SSTA 2013 Conference, vol 3. CRC Press, BocaRaton (2014)

5. Pietraszkiewicz, W., Witkowski, W. (eds.): Shell Structures: Theory andApplications — Proceedings of the 11th SSTA 2017 Conference, vol 4. CRCPress, Boca Raton (2018)

Selected Papers

1. Bielewicz, Eu., Pietraszkiewicz, W.: Design of cylindrical shell roofs.Confrontation of folded plate methods and Schorer’s approximation (in Polish).Arch. Inż. Ląd. 9(1):89–105

2. Bouby, C., Fortuné, D., Pietraszkiewicz, W., Vallée, C.: Direct determinationof the rotation in the polar decomposition of the deformation gradient bymaximizing a Rayleigh quotient. ZAMM 85(3):155–162 (2005)

xii Preface

3. Chróścielewski, J., Makowski, J., Pietraszkiewicz, W.: Non-linear dynamics offlexible shell structures. Comput. Assist. Mech. Eng. Sci. 9(3):341–357 (2002)

4. Chróścielewski, J., Pietraszkiewicz, W., Witkowski, W.: On shear correctionfactors in the non-linear theory of elastic shells. Int. J. Solids Struct. 47(25–26):3537–3545 (2010)

5. Chróścielewski, J., Konopinska, V., Pietraszkiewicz, W.: On modelling andnon-linear elasto-plastic analysis of thin shells with deformable junctions.ZAMM 91(6):477–484 (2011)

6. Eremeyev, V.A., Pietraszkiewicz, W.: The nonlinear theory of elastic shellswith phase transitions. J. Elast. 74(1):67–86 (2004)

7. Eremeyev, V.A., Pietraszkiewicz, W.: Local symmetry group in the generaltheory of elastic shells. J. Elast. 85(2):125–152 (2006)

8. Eremeyev, V.A., Pietraszkiewicz, W.: Phase transitions in thermoelastic andthermoviscoelastic shells. Arch. Mech. 61(1):41–67 (2009)

9. Eremeyev, V.A., Pietraszkiewicz, W.: Thermomechanics of shells undergoingphase transition. J. Mech. Phys. Solids 59(7):1395–1412 (2011)

10. Eremeyev, V.A., Pietraszkiewicz, W.: Material symmetry group of thenon-linear polarelastic continuum. Int. J. Solids Struct. 49(14):1993–2005(2012)

11. Eremeyev, V.A., Pietraszkiewicz, W.: Editorial: Refined theories of plates andshells. ZAMM 94(1–2):5–6 (2014)

12. Eremeyev, V.A., Pietraszkiewicz, W.: (2016) Material symmetry group andconstitutive equations of micropolar anisotropic elastic solids. Math. Mech.Solids 21(2):210–221

13. Górski, J., Pietraszkiewicz, W.: The 10th jubillee conference “Shell Structures:Theory and Applications”, SSTA2013, Oct. 16-18, 2013, Gdansk (Poland).Arch. Civ. Eng. 59(4):579–581 (2013)

14. Konopinska, V., Pietraszkiewicz, W.: Exact resultant equilibrium conditions inthe nonlinear theory of branching and self-intersecting shells. Int. J. SolidsStruct. 44(1):352–369 (2007)

15. Makowski, J., Pietraszkiewicz, W.: Incremental formulation of the non-lineartheory of thin shells in the total Lagrangian description. ZAMM 64(4):T65–T67 (1984)

16. Makowski, J., Pietraszkiewicz, W.: Work-conjugate boundary conditions in thenonlinear theory of thin shells. J. Appl. Mech. Trans. ASME 56(2):395–402(1989)

17. Makowski, J., Pietraszkiewicz, W., Stumpf, H.: On the general form of jumpconditions for thin irregular shells. Arch. Mech. 50(3):483–495 (1998)

18. Makowski, J., Pietraszkiewicz, W., Stumpf, H.: Jump conditions in thenon-linear theory of thin irregular shells. J. Elast. 54(1):1–26 (1999)

19. Opoka, S., Pietraszkiewicz, W.: Intrinsic equations for non-linear deformationand stability of thin elastic shells. Int. J. Solids Struct. 41(11–12):3275–3292(2004)

20. Opoka, S., Pietraszkiewicz, W.: On modified displacement version of thenon-linear theory of thin shells. Int. J. Solids Struct. 46(17):3103–3110 (2009)

Preface xiii

21. Opoka, S., Pietraszkiewicz, W.: On refined analysis of bifurcation buckling forthe axially compressed circular cylinder. Int. J. Solids Struct. 46(17):3111–3123 (2009)

22. Pietraszkiewicz, W.: The case of axial symmetry of shallow shells (in Polish).Rozpr. Inż. 14(2):241–262 (1966)

23. Pietraszkiewicz, W.: On a solving equation for shallow shells. Bull. Acad.Polon. Sci., Serie. sci. techn. 15(5):265–270 (1967)

24. Pietraszkiewicz, W.: On the linear theory of shallow shells (in Polish). Rozpr.Inż. 15(2):349–358 (1967)

25. Pietraszkiewicz, W.: On the multivaluedness of solutions of shallow shells.Bull. Acad. Polon. Sci., Serie. sci. techn. 15(10):877–881 (1967)

26. Pietraszkiewicz, W.: On the multivaluedness of stress functions in the lineartheory of shells. Bull. Acad. Polon. Sci., Serie. sci. techn. 15(10):871–876(1967)

27. Pietraszkiewicz, W.: Multivalued stress functions in the linear theory of shells.Arch. Mech. Stos. 20(1):37–45 (1968)

28. Pietraszkiewicz, W.: Multivalued solutions for shallow shells. Arch. Mech.Stos. 20(1):3–10 (1968)

29. Pietraszkiewicz, W.: Stresses in an isotropic elastic solid after successivesuperposition of two small deformations (in Polish). Trans. Inst. Fluid-FlowMach. 52:129–141 (1971)

30. Pietraszkiewicz, W.: Material equations of motion for nonlinear theory ofshells. Bull. Acad. Polon. Sci., Serie. sci. techn. 19(6):261–266 (1971)

31. Pietraszkiewicz, W.: On the elasticity tensors of deformed isotropic solids. Bull.Acad. Polon. Sci., Serie. sci. techn. 19(9):641–646 (1971)

32. Pietraszkiewicz, W.: On the Lagrangean non-linear theory of moving shells.Trans. Ins. Fluid-Flow Mach. 64:91–103 (1974)

33. Pietraszkiewicz, W.: Lagrangian non-linear theory of shells. Arch. Mech.—Arch. Mech. Stos. 26(2):221–228 (1974)

34. Pietraszkiewicz, W.: Stress in isotropic elastic solid under superposed defor-mations. Arch. Mech.—Arch. Mech. Stos. 26(5):871–884 (1974)

35. Pietraszkiewicz, W.: Some exact reduction of the non-linear shell compatibilityconditions. ZAMM 57(5):T133–T134 (1977)

36. Pietraszkiewicz, W.: Simplified equations for the geometrically non-linear thinelastic shells. Pol. Akad. Nauk. Pr. Inst. Masz. Przeplyw. 75:165–173 (1978)

37. Pietraszkiewicz, W.: Some relations of the non-linear theory of Reissner typeshells (in Russian), Vestnik Leningradskogo Un-ta, Seriia Mat., Mech. Astr.1:115–124 (1979)

38. Pietraszkiewicz, W.: Consistent second approximation to the elastic strainenergy of a shell. ZAMM 59(5):T206–T208 (1979)

39. Pietraszkiewicz, W.: Finite rotations in shells. In: Koiter, W.T., Mikhailov, G.K. (eds.) Theory of Shells, pp. 445–471. North-Holland P.Co., Amsterdam(1980)

40. Pietraszkiewicz, W.: Certain problems of nonlinear shell theory (in Polish).Mech. Theoret. Stos. 18(2):169–192 (1980)

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41. Pietraszkiewicz, W.: Three forms of geometrically non-linear bending shellequations. Works Inst. Fluid-Flow Mach. 81:79–92 (1981)

42. Pietraszkiewicz, W.: On consistent approximations in the geometricallynon-linear theory of shells. Ruhr-Universität Bochum., Mitt. Inst. f. Mech. Nr.26:1–43 (1981)

43. Pietraszkiewicz, W.: Determination of displacements from given strains in thenon-linear continuum mechanics. ZAMM 62(3–4):T154–T156 (1982)

44. Pietraszkiewicz, W.: A simplest consistent version of the geometricallynon-linear theory of shells undergoing large/small rotations. ZAMM 63(5):T200–T202 (1983)

45. Pietraszkiewicz, W.: Lagrangian description and incremental formulation in thenonlinear theory of thin shells. Int. J. Nonlin. Mech. 19(2):115–140 (1984)

46. Pietraszkiewicz, W.: Addendum to: Bibliography of monographs and surveyson shells. Appl. Mech. Rev. 45(6):249–250 (1992)

47. Pietraszkiewicz, W.: Unified Lagrangian displacement formulation of thenon-linear theory of thin shells. R. BCM—J. Braz. Soc. Mech. Sci. 14(4): 327–345 (1992)

48. Pietraszkiewicz, W.: Explicit Lagrangian incremental and buckling equationsfor the non-linear theory of thin shells. Int. J. Nonlin. Mech. 28(2):209–220(1993)

49. Pietraszkiewicz, W.: Work-conjugate boundary conditions associated with thetotal rotation angle of the shell boundary. J. Appl. Mech., Transact. ASME 60(3):785–786 (1993)

50. Pietraszkiewicz, W.: On the vector of change of boundary curvature in thenon-linear T-R type theory of shells. Trans. St-Petersburg Acad. Sci. StrengthProb. 1:140–148 (1997)

51. Pietraszkiewicz, W.: On deformational boundary quantities in the nonlineartheory of shear-deformable shells. ZAMM 77(S1):S265–S266 (1997)

52. Pietraszkiewicz, W.: Deformational boundary quantities in the nonlinear theoryof shells with transverse shears. International J. Solids Struct. 35(7–8):687–699(1998)

53. Pietraszkiewicz, W.: Bernoulli numbers and rotational kinematics. J. Appl.Mech., Transact. ASME 66(2):576 (1999)

54. Pietraszkiewicz, W.: On the Alumäe type non-linear theory of thin irregularshells. Izvestiya VUZov, Severo-Kavkazskii Region, Yestestvennye Nauki,Spetzvypusk, 127–136 (2000)

55. Pietraszkiewicz, W.: Development of intrinsic formulation of W.-Z. Chienof the geometrically nonlinear theory of thin elastic shells. CMES—Comput.Model. Eng. Sci. 70(2):153–190 (2010)

56. Pietraszkiewicz, W.: On constitutive restrictions in the resultant thermome-chanics of shells with interstitial working. Advanced Structured Materials15:251–260 (2011)

57. Pietraszkiewicz, W.: Refined resultant thermomechanics of shells. Int. J. Eng.Sci. 49(10):1112–1124 (2011)

Preface xv

58. Pietraszkiewicz, W.: On exact expressions of the bending tensor in the non-linear theory of thin shells. Appl. Math. Model. 36(4):1821–1824 (2012)

59. Pietraszkiewicz, W.: On a description of deformable junction in the resultantnonlinear shell theory. Advanced Structured Materials 60:457–468 (2016)

60. Pietraszkiewicz, W.: The resultant linear six-field theory of elastic shells: Whatit brings to the classical linear shell models? ZAMM 96(8):899–915 (2016)

61. Pietraszkiewicz, W., Badur, J.: Finite rotations in the description of continuumdeformation. Int. J. Eng. Sci. 21(9):1097–1115 (1983)

62. Pietraszkiewicz, W., Eremeyev, V.: On natural strain measures of the non-linearmicropolar continuum. Int. J. Solids Struct. 46(3–4):774–787 (2009)

63. Pietraszkiewicz, W., Eremeyev, V.: On vectorially parameterized natural strainmeasures of the non-linear Cosserat continuum. Int. J. Solids Struct. 46(11–12):2477–2480 (2009)

64. Pietraszkiewicz, W., Górski, J.: Foreword. Math. Mech. Solids 20(7):789(2015)

65. Pietraszkiewicz, W., Konopinska, V.: On unique kinematics for the branchingshells. Int. J. Solids Struct. 48(14–15):2238–2244 (2011)

66. Pietraszkiewicz, W., Konopinska, V.: Drilling couples and refined constitutiveequations in the resultant geometrically non-linear theory of elastic shells. Int.J. Solids Struct. 51(11–12):2133–2143 (2014)

67. Pietraszkiewicz, W., Konopinska, V.: Singular curves in the resultant ther-momechanics of shells. Int. J. Eng. Sci. 80:21–31 (2014)

68. Pietraszkiewicz, W., Konopinska, V.: Junctions in shell structures: A review.Thin-Wall. Struct. 95:310–334 (2015)

69. Pietraszkiewicz, W., Kreja, I.: The 9th Conference ”Shell Structures: Theoryand Applications”, SSTA2009, Oct. 14–16, 2009, Jurata (Poland). Arch. Civ.Eng. 55(4):449–451 (2009)

70. Pietraszkiewicz, W., Szwabowicz, M.: Determination of the midsurface of adeformed shell from prescribed fields of surface strains and bendings. Int.J. Solids Struct. 44(18–19):6163–6172 (2007)

71. Pietraszkiewicz, W., Vallée, C.: A method of shell theory in determinationof the surface from components of its two fundamental forms. ZAMM 87(8–9):603–615 (2007)

72. Pietraszkiewicz, W., Eremeyev, V., Konopinska, V.: Extended non-linearrelations of elastic shells undergoing phase transitions. ZAMM 87(2):150–159(2007)

73. Pietraszkiewicz, W., Szwabowicz, M.: Entirely Lagrangian non-linear theory ofthin shells. Arch. Mech. 33(2):273–288 (1981)

74. Pietraszkiewicz, W., Szwabowicz, M.: Hu-Washizu variational functional forthe Lagrangian geometrically non-linear theory of thin elastic shells. ZAMM62(4):T156–T158 (1982)

75. Pietraszkiewicz, W., Szwabowicz, M., Vallée, C.: Determination of the mid-surface of a deformed shell from prescribed surface strains and bendings via thepolar decomposition. Int. J. Nonlin Mech. 43(7):579–587 (2008)

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76. Schieck, B., Pietraszkiewicz, W., Stumpf, H.: Theory and numerical analysis ofshells undergoing large elastic strains. Int. J. Solids Struct. 29(6):689–709(1992)

77. Schmidt, R., Pietraszkiewicz, W.: Variational principles in the geometricallynon-linear theory of shells undergoing moderate rotations. Ing.-Arch. 50(3):187–201 (1981)

78. Szwabowicz, M.L., Pietraszkiewicz, W.: Determination of the deformedposition of a thin shell from surface strains and height function. Int. J. Nonlin.Mech. 39(8):1251–1263 (2004)

79. Szwabowicz, M.L., Pietraszkiewicz, W.: Erratum: Determination of thedeformed position of a thin shell from surface strains and height function(international journal of non-linear mechanics (2004) 39(1251–1263). Int.J. Nonlin. Mech. 39(10):1737 (2004)

80. Visarius, H., Nolte, L.P., Pietraszkiewicz, W.: Closed-form force-elongationrelations for the uniaxial viscoelastic behavior of biological soft tissues. Mech.Res. Commun. 24(5):575–581 (1997)

Magdeburg, Germany/ Lublin, Poland Holm AltenbachGdańsk, Poland Jacek ChróścielewskiGdańsk, Poland/ Rostov on Don, Russia Victor A. EremeyevWarsaw, Poland Krzysztof WiśniewskiSeptember, 2019

Preface xvii

Contents

Tribute to Professor Wojciech Pietraszkiewicz . . . . . . . . . . . . . . . . . . . . 1Igor V. Andrianov

Computer Modeling of Nonlinear Deformation and Loss of Stabilityof Composite Shell Structures Under a Combined Effectof Quasi-static and Pulsed Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5N. A. Abrosimov, L. A. Igumnov, S. M. Aizikovich and A. V. Elesin

Analytical Buckling Analysis of Cylindrical Shells with Elliptic CrossSection Subjected to External Pressure . . . . . . . . . . . . . . . . . . . . . . . . . 33Igor I. Andrianov and Alexander A. Diskovsky

Subclasses of Mechanical Problems Arising from the Direct Approachfor Homogeneous Plates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43Marcus Aßmus, Konstantin Naumenko and Holm Altenbach

Large Oscillations Around Curled Equilibrium Configurationsof Uniformly Loaded Euler–Bernoulli Beams: Numericaland Experimental Evidences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65D. Baroudi, I. Giorgio and E. Turco

Unsymmetrical Wrinkling of Nonuniform Annular Platesand Spherical Caps Under Internal Pressure . . . . . . . . . . . . . . . . . . . . . 79Svetlana M. Bauer and Eva B. Voronkova

Two-Dimensional Model of a Plate, Made of Material with the GeneralAnisotropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91A. K. Belyaev, N. F. Morozov, P. E. Tovstik, T. P. Tovstikand A. V. Zelinskaya

An Alternative Approach to the Buckling Resistance Assessmentof Steel, Pressurised Spherical Shells . . . . . . . . . . . . . . . . . . . . . . . . . . . 109Paweł Błażejewski and Jakub Marcinowski

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Asymptotically-Accurate Nonlinear Hyperelastic Shell ConstitutiveModel Using Variational Asymptotic Method . . . . . . . . . . . . . . . . . . . . . 135Ramesh Gupta Burela and Dineshkumar Harursampath

Three-Dimensional Finite Element Modelling of Free Vibrationsof Functionally Graded Sandwich Panels . . . . . . . . . . . . . . . . . . . . . . . . 157Vyacheslav N. Burlayenko, Tomasz Sadowski, Holm Altenbachand Svetlana Dimitrova

Recent Achievements in Constitutive Equations of Laminatesand Functionally Graded Structures Formulated in the ResultantNonlinear Shell Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179Stanisław Burzyński, Jacek Chróścielewski, Karol Daszkiewicz,Agnieszka Sabik, Bartosz Sobczyk and Wojciech Witkowski

On Optimal Archgrids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203R. Czubacki and T. Lewiński

Cylindrical Shell Model of Helical Type Wire Structures Accountingfor Layers’ Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227Alexander N. Danilin and Sergey I. Zhavoronok

Buckling of Cylindrical Shell Stiffened by Annular Plate UnderExternal Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251S. B. Filippov and V. S. Sabaneev

2D Theory of Shell-like Tensegrity Structures . . . . . . . . . . . . . . . . . . . . 271Wojciech Gilewski, Paulina Obara and Anna Al Sabouni-Zawadzka

On Some Recent Discrete-Continuum Approaches to the Solutionof Shell Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285Ya. M. Grigorenko, A. Ya. Grigorenko and E. Bespalova

A Composite Wave Model for a Cylindrical Shell . . . . . . . . . . . . . . . . . 315J. Kaplunov, B. Erbaş and M. Palsü

A Beam—Just a Beam in Linear Plane Bending . . . . . . . . . . . . . . . . . . 329Reinhold Kienzler and Patrick Schneider

Inflation of a Cylindrical Membrane Partially Stretchedover a Rigid Cylinder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351A. M. Kolesnikov

Singular Surface Curves in the Resultant Thermodynamicsof Shells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367Violetta Konopińska-Zmysłowska and Victor A. Eremeyev

Hybrid-Mixed Shell Finite Elements and Implicit Dynamic Schemesfor Shell Post-buckling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383Marko Lavrenčič and Boštjan Brank

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Development of Invariant-Based Triangular Element for NonlinearThermoelastic Analysis of Laminated Shells . . . . . . . . . . . . . . . . . . . . . . 413Stanislav V. Levyakov

Interaction of a Spherical Wave with a Rectangular Platein a Ground . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 443Natalya A. Lokteva and Dmitrii V. Tarlakovskii

Localized Parametric Vibrations of Laminated Cylindrical ShellUnder Non-uniform Axial Load Periodically Varying with Time . . . . . . 459Gennadi Mikhasev and Rovshen Atayev

Numerical Analysis of Free Vibration of Laminated Thin-WalledClosed-Section Shell Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 479Bartosz Miller, Barbara Markiewicz and Leonard Ziemiański

Abnormal Buckling of Thin-Walled Bodies with Shape MemoryEffects Under Thermally Induced Phase Transitions . . . . . . . . . . . . . . . 493Dmitry V. Nushtaev and Sergey I. Zhavoronok

On the Homogenization of Nonlinear Shell . . . . . . . . . . . . . . . . . . . . . . 525Erick Pruchnicki

A Non-linear Theory of Thin-Walled Rods of Open Profile Deducedwith Incremental Shell Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 541Jakob Scheidl and Yury Vetyukov

Buckling of Elastic Circular Plate with Surface Stresses . . . . . . . . . . . . 577Denis N. Sheydakov

Asymptotic Derivation of Nonlinear Plate Modelsfrom Three-Dimensional Elasticity Theory . . . . . . . . . . . . . . . . . . . . . . . 591Milad Shirani and David J. Steigmann

Selected Stability Problems of Thin-Walled Columns and Beams . . . . . 615Czesław Szymczak and Marcin Kujawa

Higher-Order Weak Formulation for Arbitrarily ShapedDoubly-Curved Shells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 627Francesco Tornabene and Michele Bacciocchi

Strong Formulation: A Powerful Way for Solving Doubly CurvedShell Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 659Francesco Tornabene and Nicholas Fantuzzi

On a Simple Shell Model for Thin Structures with FunctionallyGraded Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 687Werner Wagner and Friedrich Gruttmann

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On Performance of Nine-Node Quadrilateral Shell Elements 9-EAS11and MITC9i . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 711K. Wiśniewski and E. Turska

Higher Order Theory of Electro-Magneto-Elastic Plates and Shells . . . . 727V. V. Zozulya

Exact Solutions of Nonlinear Micropolar Elastic Theoryfor Compressible Solids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 771L. M. Zubov, A. M. Kolesnikov and O. V. Rudenko

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