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Shell Structures: Theory and Applications

Volume 3

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## Book Description

Shells are basic structural elements of modern technology and everyday life. Examples are automobile bodies, water and oil tanks, pipelines, aircraft fuselages, nanotubes, graphene sheets or beer cans. Also nature is full of living shells such as leaves of trees, blooming flowers, seashells, cell membranes, the double helix of DNA or wings of insects. In the human body arteries, the shell of the eye, the diaphragm, the skin or the pericardium are all shells as well.

*Shell Structures: Theory and Applications, Volume 3 *contains 137 contributions presented at the 10th Conference “Shell Structures: Theory and Applications” held October 16-18, 2013 in Gdansk, Poland. The papers cover a wide spectrum of scientific and engineering problems which are divided into seven broad groups: general lectures, theoretical modelling, stability, dynamics, bioshells, numerical analyses, and engineering design. The volume will be of interest to researchers and designers dealing with modelling and analyses of shell structures and thin-walled structural elements.

## Table of Contents

*General lectures*

Actual developments in the nonlinear shell theory – state of the art and new applications of the six-parameter shell theory

H. Altenbach & V.A. Eremeyev

Nonlinear vibrations of shells: Experiments, simulations and applications

M. Amabili & F. Alijani

3D-shell mathematical models and finite elements: From mathematical and physical insight to application examples

D. Chapelle

Mechanics design and analyses of stretchable electronics

Y. Zhang, K.C. Hwang & Y. Huang

On geometrically non-linear FEA of laminated FRP composite panels

I. Kreja

*Theoretical modelling*

An analytical solution to the problem of interaction of a circular plate with an inhomogeneous soft layer

S.M. Aizikovich, A.S. Vasiliev, S.S. Volkov, B.I. Mitrin & E.V. Sadyrin

Laminated smart shell structures; theory and analysis

T.M.B. Albarody & H.H. Al-Kayiem

On the surface vis impressa caused by a fluid-solid contact

J. Badur, P. Ziółkowski, W. Zakrzewski, D. Sławinski, M. Banaszkiewicz, O. Karczmarczyk, S. Kornet & P.J. Ziółkowski

Nonclassical theories for bending analysis of orthotropic circular plate

S. Bauer & E. Voronkova

On the characterization of drilling rotation in the 6-parameter resultant shell theory

M. Bîrsan & P. Neff

Existence of solutions of dynamic contact problems for elastic von Kármán-Donnell shells

I. Bock & J. Jarušek

On the effectiveness of higher-order terms in layer-wise shell models

E. Carrera, A. Lamberti & M. Petrolo

The free material design of thin elastic shells

S. Czarnecki, R. Czubacki, G. Dzierzanowski & T. Lewinski

Moderately large deflections of thin densely ribbed plates

Ł. Domagalski & M. Gajdzicki

Theory of shells as a product of analytical technologies in elastic body mechanics

V. Eliseev & Y. Vetyukov

On effective stiffness of a three-layered plate with a core filled with a capillary fluid

V.A. Eremeyev, E.A. Ivanova, H. Altenbach & N.F. Morozov

General dynamic theory of micropolar elastic orthotropic multilayered thin shells

A.J. Farmanyan & S.H. Sargsyan

Stationary deformation of compound shell structures under arbitrary loadings

Y.M. Grigorenko, E.I. Bespalova & G.P. Urusova

TUBA finite elements: Application to the solution of a nonlinear Kirchhoff-Love shell theory

V. Ivannikov, C. Tiago & P.M. Pimenta

On the tolerance modeling of thin microstructured plates

J. Jedrysiak

Some problems of modelling stability of thin functionally graded plates

M. Ka´zmierczak-Sobinska & J. Jedrysiak

Comparison of various linear plate theories in the light of a consistent second-order approximation

R. Kienzler & P. Schneider

Pure bending of a pressurized curved tube

A.M. Kolesnikov & A.V. Popov

On jump conditions at non-material singular curves in the resultant shell thermomechanics

V. Konopinska & W. Pietraszkiewicz

The GRADELA plates and shells

K.A. Lazopoulos, K.A. Alnefaie, N.H. Abu-Hamdeh & E.C. Aifantis

Equations of motion for growing shells

S. Lychev &T. Lycheva

A plane stress elastic-plastic analysis of sheet metal cup deep drawing processes

Z. Nowak, M. Nowak & R.B. Pecherski

Thermoelasticity in a two-phase hollow cylinder with longitudinally graded material properties

P. Ostrowski

On refined constitutive equations in the six-field theory of elastic shells

W. Pietraszkiewicz &V. Konopinska

Fractional thermoelasticity of thin shells

Y. Povstenko

Two-dimensional model of fifth order in thickness for homogeneous plates

E. Pruchnicki

Continuum shell models for closed cage carbon nanoparticles

M. Todt, F.G. Rammerstorfer & M.A. Hartmann

Two-dimensional linear model of anisotropic shells

P.E. Tovstik & T.P. Tovstik

Improving an inverse technique for characterisation of laminated plates

M.Wesolowski & E. Barkanov

Analytical aspects of the 3D-based hierarchical shell and transition models for adaptive FEM

G. Zboinski

Nonlinear deformations of elastic shells with distributed dislocations

L.M. Zubov

*Stability*

Unsymmetric equilibrium states of inhomogeneous circular plates under normal pressure

S. Bauer, E. Voronkova & K. Ignateva

Non-linear stability analysis of a porous-cellular cylindrical panels

T. Belica & E. Magnucka-Blandzi

A new approach to the buckling resistance assessment of pressurized spherical shells

P. Bła˙zejewski & J. Marcinowski

Externally pressurized toricones – buckling tests

J. Błachut

Effect of surface imperfections on axial load carrying capacity of a thin cylinder

G.S. Brar, M.P. Singh & J. Kapoor

The suggestion of analysis methods to estimate minimum strength for elastic buckling of shell structures

M. Ishinabe & K. Hayashi

Stabilisation of post-critical behaviour of sandwich cylindrical shells

P. Jasion

Non-linear patterns of bends and solitons on surfaces of loaded shells

V.V. Kiselev & D.V. Dolgikh

Artificial damping method for local instability problems in shells

T. Kobayashi, Y. Mihara & F. Fujii

Buckling simulation of single layer graphene sheets by the molecular mechanics method

S.N. Korobeynikov, V.V. Alyokhin, B.D. Annin & A.V. Babichev

“Static resonance” in cylindrical shells with periodical initial imperfections under external pressure

V.L. Krasovsky, M.V. Kolesnikov & R. Schmidt

Thin-walled composite channel-section beams subjected to pure bending

T. Kubiak & Z. Kolakowski

Deformation and buckling of axially compressed elastic cylindrical shells with transversal cut in experiments and numerical simulations

O.V. Lykhachova & R. Schmidt

Linear buckling analysis as a measure of the buckling resistance of shells

J. Marcinowski

Buckling of composite multilayered shells – an experimental analysis

A. Muc, A. Bondyra & P. Romanowicz

Stability of an inhomogeneous rectangular plate of micropolar material

D.N. Sheydakov

Comparative buckling analysis of cylindrical steel silos with flat or corrugated sheets

M. Sondej, M. Wójcik, P. Iwicki & J. Tejchman

Experimental and numerical analysis of the post-buckling behaviour of integrally sub-stiffened rectangular plates subjected to shear

Ł. Swiech

Cylindrical shells under axial compression and simultaneous internal pressure: Buckling mechanics and EN-conforming design proposal

M.B. Tekleab & W. Guggenberger

Modelling of thin film buckling in compound specimens under uniaxial stretching

F. Toth, F.G. Rammerstorfer, M.J. Cordill & F.D. Fischer

Influence of geometric imperfections on the local stability of thin-walled elements

R.Walentynski, M. Cybulska & R. Cybulski

Buckling mode switching in self-similar nanotubes

Y.C.Wang & C.Y.Wu

Buckling of encased liner under external pressure and the effects of voids in backfilling grout

J.H.Wang, M. Nakano, Z.H. Shi & A. Koizumi

Improved knockdown factors for cylindrical shells using worst multi-perturbation load approach

B.Wang, P. Hao, G. Li, K. Tian, X.J.Wang, X. Zhang & X.H. Tang

Computations of critical load value of composite shell with random geometric imperfections

K.Winkelmann & A. Sabik

Plastic buckling of orthotropic sandwich cylindrical shells

J. Zielnica

*Dynamics*

Natural frequencies and modal shapes of composite cylindrical panels with local damages

M. Barski & P. Romanowicz

The problem of flutter of a non-symmetric non-homogeneous over thickness rectangular plate

M.V. Belubekyan &A.M. Grishko

Rayleigh variational principle and vibrations of prestressed shells

V.A. Eremeyev & H. Altenbach

Vibrations and buckling of cylindrical shell made of a general anisotropic elastic material

S. Filippov & N. Naumova

Free vibrations of continuously inhomogeneous cylindrical bodies

A.Y. Grigorenko & T.L. Efimova

Dynamic response of FGM thin-walled plate structure subjected to a thermal pulse loading

J. Jankowski & K. Kowal-Michalska

Static and dynamic analysis of shear deformable composite shells of revolution by semi-analytical approach

A. Kayran

Nonlinear vibrations of laminated shells with layers of variable thickness

L.V. Kurpa & T.V. Shmatko

Parametric vibrations and dynamic instability of thin laminated plates with complex form

L.V. Kurpa, O.S. Mazur & V.V. Tkachenko

Homotopy perturbation solution for strong geometrical nonlinear vibration of flat prestressed orthotropic membrane structure

C.J. Liu, X.Y. Yang, H. Zhao & Z.L. Zheng

Dynamic response of FGM thin plate subjected to combined loads

R.J. Mania

Numerical analyses of explosive shape influence on steel I-beam behaviour subjected to pressure wave

L. Mazurkiewicz, D. Kolodziejczyk, J. Malachowski, M. Klasztorny, K. Damaziak & P. Baranowski

Preliminary assessment of correlation between vibrations and buckling load of stainless steel cylinders

E. Skukis, K. Kalnins & A. Chate

Eigenvalue analysis of graphene plates embedded into the elastic Pasternak foundation

M. Taczała & R. Buczkowski

Dynamic modelling of thin micro-periodic cylindrical shells

B. Tomczyk

Application of a three-field dual-mixed variational principle to modeling cylindrical shell problems in elastodynamics

B. Tóth

Variational Formulations of Vekua-type shell theories and some of their applications

S.I. Zhavoronok

*Bioshells*

Static and dynamic modelling blow-out type trauma of orbital wall

P. Kłosowski, A. Skorek & M. Zmuda Trzebiatowski

Mechanical compatibility of implants used in hernia repair with abdominal wall

I. Lubowiecka, K. Szepietowska, A. Tomaszewska & C. Szymczak

Cough influence on fascia-mesh system built for a hernia repair – an experimental research

A. Tomaszewska, I. Lubowiecka & C. Szymczak

Chosen aspects of skeletal system modeling: Numerical solid and shell models of femur part

W.Wojnicz, H. Olszewski & E.Wittbrodt

*Numerical analysis*

Geometrically nonlinear analysis of shells – Benchmark problems for Autocad Robot Structural Analysis Professional

A. Ambroziak & P. Kłosowski

Locking effects in the finite element method

A. Ambroziak

Numerical modeling of delamination growth in composite plates

P. Bajurko, J.Wilk, D. Szelag & P. Czarnocki

Elastoplastic material law in 6-parameter nonlinear shell theory

S. Burzynski, J. Chróscielewski & W.Witkowski

A direct approach to shakedown analysis on a piping nozzle structure under superposed thermal mechanical loadings

G. Chen, J.-W. Simon & D.Weichert

Equivalent 4-node Enhanced Assumed Strain and hybrid stress shell elements in 6-parameter theory

J. Chró´scielewski, K. Daszkiewicz & W.Witkowski

Failure analysis of footbridge made of composite materials

J. Chró´scielewski, I. Kreja, A. Sabik, B. Sobczyk & W.Witkowski

Numerical modeling of plate damage caused by a low energy impact

P. Dobrza´nski, Z. Lorenc & P. Czarnocki

Coupling of shell and beam computational models in failure analysis of steel frames

J. Dujc, B. Brank & A. Ibrahimbegovic

High-precision rectangular finite element for FGM plates

W. Gilewski & J. Pełczynski

Physical super-geometric FE formulation for moderately thick plates

W. Gilewski & J. Pełczynski

Modelling and numerical study of blind rivet nut/bolt joints of composite shell segments

M. Klasztorny & D. Nycz

On consistent estimations of drilling rotations in shell elements

S. Kugler, P.A. Fotiu & J. Murin

Method of imperfections modeling in plane state of stress structures using FEM

M. Mackiewicz, T. Chyzy & S. Matulewicz

Modeling of construction response in terms of large displacements and rotations using the standard plane finite elements

S. Matulewicz, T. Chyzy & M. Mackiewicz

On dynamic FE analysis of viscoplastic thin-walled structures with anisotropic gradient damage

A.D. Nguyen, M. Stoffel & D.Weichert

Nonlinear transient finite element analysis of layered composite plates and shells based on finite rotation theory

M.N. Rao & R. Schmidt

Strength of dented thin cylindrical shells under external pressure

N. Rathinam & B. Prabu

Enhanced displacement mode finite elements for explicit transient analysis focussing on efficiency

C. Schmied, K. Schweizerhof & S. Mattern

A numerical investigation into the plastic buckling of circular cylinders

R. Shamass, G. Alfano & F. Guarracino

A parametric study on flange vertical buckling of hybrid steel girders

T. Ueda, Y. Matoge, S. Shimizu, G. Fujita & N. Tanaka

Cylindrical shell finite element based on the proper generalized decomposition

P. Vidal, L. Gallimard & O. Polit

A consistently linearized multi-scale model for shell structures

W.Wagner & F. Gruttmann

Quasi-conforming elements based on Reissner-Mindlin plate theory

C.S.Wang & P. Hu

Curved shell finite elements for interlaminar stress analysis

R.G.Winkler

On some problems of choice of the shape function in the tolerance averaging technique in modeling free vibrations of the composite plate resting on elastic foundation

A.Wirowski

On mixed/enhanced Hu-Washizu shell elements with drilling rotation

K.Wisniewski & E. Turska

A higher order shell element for wave propagation in isotropic shell structures

A. Z˙ak & M. Krawczuk

Large rotation static and dynamic FE analysis for piezoelectric integrated smart structures

S.Q. Zhang & R. Schmidt

*Engineering design*

The improved measurements and stress analysis of cylinder/pipe with out-of-roundness

A.V. Bogdan, I.V. Orynyak & I.V. Lokhman

Response of a steel tank during earthquakes and mining tremors – experimental investigation

D. Burkacki & R. Jankowski

Shell Structures by three masters: Torroja, Sánchez R. and Candela

P. Cassinello

Assessment of existing natural draught cooling towers

T. Chmielewski, M. Simon & P. Osterrieder

Assessment of tensile forces in Sopot Forest Opera membrane by in situ measurements and iterative numerical strategy for inverse problem

J. Chróscielewski, M. Miskiewicz, Ł. Pyrzowski & K.Wilde

Numerical study on seismic response of a base-isolated building modelled with shell elements

T. Falborski & R. Jankowski

Safety of erection and repair of steel tanks with geometric imperfections using heavylift jack-up system

J. Górski, T. Mikulski & P. Sorn

Analysis of EN 1993-1-6 guidelines about determining amplitudes of equivalent imperfections of steel cylindrical shells subjected to uniform external pressure

T. Heizig

Stress state in axially compressed steel cylindrical shells supported discretely

E. Hotała & Ł. Skotny

Damage to a shell of a cooling tower caused by defective repairs

M. Kami´nski & M. Maszczak

Ultrasound testing of carbon composite shells by Phased Array technique

T. Katz & D. Szelag

Influence of geometrical imperfections on stresses in cylindrical shells

D. Kowalski

Numerical and experimental tests of the side lock of railway wagon loading platform for intermodal transport

W. Kraso´n, T. Niezgoda & M. Stankiewicz

Field test and three-dimensional numerical analysis of soil-steel arch with ribs

B. Kunecki & L. Korusiewicz

Stiffness analysis of sandwich panels with corrugated plywood and GFRP core

E. Labans, K. Kalnins & K. Zudrags

Numerical analysis of a temporary steel grandstand

N. Lasowicz & R. Jankowski

Analysis of interaction of reinforced concrete and prestressed concrete cylindrical silo structures with soil

P.M. Lewinski

Strength of pressure vessel head provided with a connector pipe

J. Lewinski & K. Magnucki

Calculation of an ultimate load value of a silo with geometric imperfections in the shape of eigenforms

M. Oziebło, K.Winkelmann & J. Górski

Numerically based assessment of suction bucket foundation shells

P. Schaumann & M. Gottschalk

The influence of selected imperfections on stability of turbofan engine casing

E. Szymczyk, J. Jachimowicz, T. Niezgoda & K. Puchała

Modular “ribbon” shell – a case study

R. Tarczewski

The use of Response Surface Methodology for reliability estimation of aluminum silo subjected to wind load

K.Winkelmann

Evaluation of safety of RC cooling tower with imperfections

R. Wróblewski & M. Kaminski

Application of the Bodner-Partom constitutive equations for modelling the technical fabric Valmex used for the hanging roof of the Forest Opera in Sopot

K. Zerdzicki, P. Kłosowski & K.Woznica

Author index