CI MN E BARCELONA

The finite element method in the 1990's

A BOOK DEDICA'ED '0 o.c. ZIENKIEWICZ EDI'ED BY E. OMA'E, J.PERIAUX, A.SAMUELSSON

CI M NE BARCELONA

Springer-Verlag Berlin Heidelberg GmbH

First edition, October 1991

© Centro Internacional de Metodos Numericos en lngenieria, Barcelona

© Springer-Verlag Berlin Heidelberg 1991 Originally published by Springer-Verlag Berlin, Hidelberg, New York,

London, Paris, Tokyo, Hong Kong, Barcelona, Budapest in 1991.

Softcover reprint of the hardcover 1 st edition 1991

Cover designed by Jordi Pallo.

Printed by Artes Gnificas Torres S.A., Morales 17, 08029 Barcelona Deposito legal: B-35590-91

ISBN 978-3-662-10328-9 ISBN 978-3-662-10326-5 (eBook) DOI 10.1007/978-3-662-10326-5

Cover: Unstructured mesh of triangular finite elements for analysis 01' hypersonic air flow past a double ellipse. From O. C. Zienkiewicz, K. Morgan, J. Peraire. 1. Peiro and L. Formaggia. «Finite elements in fluid mechanics. Compressible flow, shallol\' water equations and transport», in ASME Conjel'f!nce on Recent Development in Fluid Dynamies, AMD 95. American Society of Mechanical Engineers, December 1988.

O. C. Zienkiewicz. at dass.

THIS BOOK IS DEDICATED TO

OLGJERD C. ZIENKIEWICZ

WITH OCCASION OF HIS

70TH BIRTHDAY

PREFACE

This book is dedicated to Olgierd C. Zienkiewicz with occasion of his 70th birthday.

Olgierd C. Zienkiewicz , (Olek for his many friends) was born on May 18, 1921 in England of a British mother and Polish father.

Already 1922 the family moved to Poland where they settled after a few years in Katowice. Here and in Poznan Olek got his school education. When this finished in 1939, he went to Warsaw for entrance examination to the Polytechnic.

Just one of these days the Germans invaded Poland and Olek got involved in the defense of Warsaw. After a few days, howewer, he joined his family and together they moved to France. There, in Angiers, they stayed for ab out a year until the Germans also invaded France and the Zienkiewicz family had to move again now to England. In the autumn Olek started the course in Civil engineering at Imperial College. He graduated in 1943 with first class honours. Two years later he got his PhD on adam analysis project under supervision of Prof. Richard Southwell, famous for the method of relaxation based on finite differences.

Now Olek started professional work. For four years he lOok part in surveying, design and construction of dam projects in ScotIand. In 1949 he accepted an offer to become a lecturer in Civil Engineering at Edinburgh. Here he stayed for seven years during which time he started research in hydraulics resuIting in series of papers.

In Edinburgh he met a Canadian chemist named Helen who in 1952 became his wife. While in Edinburgh they got two sons, Andrewand David. In 1956 Olek was offered a position as Associate Professor at Northwestern University. He accepted it and settled in Evanston with his family that soon was enlarged with a daugter, Krystina. After a year he was promoted to full professor. However he did not stay long here. In 1961 he applied for and gOI the chair of Professor of Civil Engineering in Swansea.

In Swansea Olek has with great skilI, energy and enthusiasm created an international cent re for Computational Mechanics a combination of engineering, mechanics, numerical analysis and computer science. The centre has had and still has a tremendous importance for the development of this new science. Under Olek's supervision a great number of research students from all over the world have got their education there and senior researchers from all countries have spent long or short periods at the centre.

Olek has given important contribution lo almost all disciplines within

Computational Mechanics. His special interest is the development of The

Finite Element Method to a universal tool for solution of all problems that can be modelIed with panial differential equations. He has published more than 400 papers of wh ich a large number has opened new avenues for research in structural and solid mechanics, in compressible and incompressible flow, in geomechanics, biomechanics, electromagnetics and so on.

Olek has spread his ideas not only by publishing papers but also by giving lectures for engineers and scientists all around the world, by organizing conferences - often several every year - and by writing books. His famous book The Finite Element Method, first edition published in 1967, has probably meant more than anything else to make the method and the new science known at industries and at universities.

In 1969 Olek staned the International Journal of Numerical Methods in Engineering which still is the leading journal in its field, now on its 31st volume. Olek has also been very active in bringing the computational mechanics society together by initiating IACM, the International Asociation for Computational Mechanics of which he was the first president. Olek's great accomplishments have been recognized in many ways. He has received honorary degrees and fellowships from a large number of universities and has been rewarded with many medals. He is a fellow of the Royal Sociefy and Commander of the British Empire.

Today, Olek has left management of the department in Swansea is as active as ever. He shares his time between Swansea, Barcelona, Austin and Göteborg. His presence at international conferences is strongly apreciated. His lectures and comments 10 contributions from others are always the highlights. This book contains papers written by some of Olek's numerous friends. Most of them were his students at one time.To all of them the editors want to expess their gratitude for their contribution in this volume, which undoubtly will be a point of reference for the development of the finite element method in the next decade.

Finally, the editors want to thank the valuable help of Merce Alberich, Edith Wolf and Adriana Hanganu in the edition of this book.

E.ONATE J.PERIAUX A. SAMUELSSON

Barcelona, Paris, Göteborg

October 1991

SECTION 1 PERSONAL ADDRESSES

SECTION 2 STRUCTURAL AND SOLID MECHANICS

E. Stein and K. Peters

A New Boundary-Type finite element for 2D- and 3D-Elastic Solids .................................. 35

J. Jirousek

New Trends in Hybrid-Treffz p-Element approach 49

S. Glaser and B. Kröplin

Thermo Mechanical coupling in Elasto-Plastic analysis 59

G. Fonder and C. Massonnet

A variational formulation of Shallow Shells1 68

W. P. De Wilde

Stiffness identification of structural components by mixed experimental and numerical techniques ..... 80

Q. LingXi and Z. Xiong

Rigid finite element method in structural analysis 89

P. Ballesteros and P. R. Reyes

Seismic finite element analysis of "masonry buildings reinforced with ferrocement ..................... 99

I. M. Smith

Are there any new elements? . . . . . . . . . . . . . . . . . . .. 109

M. Pastor

Generalized plasticity modelling of saturated sand Behaviour under Earthquake Loading ............ 119

E. Oiiate and J. Castro

Adaptive mesh refinement techniques for structural problems ...................................... 133

T. H. H. Pi an

Remarks on selection of stresses to suppress zero energy deformation modes in hybrid element formulations 146

A. Samuelsson and N. E. Wiberg

Finite element adaptivity in dynamics and elastoplasticity ................................. 152

J. Donea and J. P. Halleux

On the use of finite elements in fast transient dynamics ..................................... 163

T. Shiomi

Industrial use of liquefaction analysis in 1980s 172

T. Kawai

Discrete limit analysis of reinforced concrete structures using rigid Bodies-spring models ................. 182

K. Wisniewski, E. Turska, L. Simoni and B. A. Schrefler

Error analysis of staggered predictor-corrector scheme for consolidation of porous media ............... 192

c. V. Ramakrishnan, A. C. Paul and D. K. Sehgal

Optimal shape design under transient dynamic loading 202

R. L. Taylor and P. Papadopoulos

A finite element method for dynamic contact problems 212

I. Cormeau

The Taylor impact test problem revisiting the standard 2-Node rod finite element ....................... 225

A. Selrnan and E. Hinton

One dimensional Transient dynamic analysis with adaptive mesh refinement ....................... 234

M. Kleiber, T. D. Hien and E. Postek

Incremental finite element analysis of nonlinear structural design sensitivity problems ............. 241

C. H. Liu, G. HofsteUer and H. A. Mang

A Comparison of Two variational formulations for Rubber-Like materials .......................... 248

C. Corni, A. Corigliano and G. Maier

Convergence of the Newton-Raphson method in Elastic-Plastic-Softening structural dynamics ............. 258

M. A. Crisfield, X. Peng and J. Shi

So me recent research on the Non-Linear analysis of Shells ........................................ 266

z. Mroz and S. Jerniolo

Constitutive modelling of geomaterials with account for deformational anisotropy ....................... 274

M. Geradin and A. Cardona

The Co-Rotational approach to substructuring for flexible multibody analysis ...................... 285

A. K. Noor and J. M. Peters

Reduced basis technique for calculating sensitivity derivatives of the nonlinear structural response 296

Z. Waszczyszyn, M. Janus and J. Pieczara

A numerical approach to the exact finite element linear Buckling analysis of structures ................... 313

J. Yu, D. Peric and D. R. J. Owen

An assessment of the cosserat continuum through the finite element simulation of astrain localisation problem ...................................... 321

F. DiMasi, P. Tong, J. H. Marcus, H. C. Gabler III and R. H. Eppinger

Simulated head impacts with upper interior structures using rigid and anatomie brain models ........... 333

N. Bicanic and J. Maca

Mass Lumping by spectral Matching ............. 346

R.Ohayon

Vibrations of Fluid-Structure coupled systems ..... 357

P. M. Calderale and C. Bignardi

Biomechanics needs fern ........................ 367

SECTION 3 FLUID MECHANICS

I. Harari and T. J. R. Hughes

Numerical methods for the Helmholtz equation with Non-Reflecting Boundary conditions in exterior domains ...................................... 379

R. E. Newton

Finite element study of shock induced cavitation ... 389

N. P. Weatherill

Generalised mesh and adaptivity techniques for computational fluid dynamies ................... 398

R. Glowinski and T. W. Pan and J. Periaux and M. Ravachol

A fietitious domain method for the ineompressible Navier-Stokes equations ........................ 410

R. Löhner

Simple elements and linelets for ineompressible flows ......................................... 419

K. Kashiyama and M. Kawahara

Finite element analysis of Tsunami Wave propagation using optimal Mesh ............................ 431

R. W. Lewis, A. S. Usmani and J. T. Cross

Finite element modelling of mould filling ......... 441

J. Peraire, J. Peiro, K. Morgan and O. Hassan

The computation of aerodynamic flows using unstructured meshes ............................ 452

J. C. Heinrich and B. R. Dyne

On the penalty method for incompressible fluids ... 465

SECTION 4 GENERAL APPLICATIONS OF TUE FINITE

ELEMENT METUOD

S. N. Atluri

The finite element method in the 1990's: A personal perspective .................................... 479

E. R. de arantes e Oliveira

Concerning the future of dvil engineering. . . . . . . .. 487

R. H. Gallagher

Reflections on technical journal editing ........... 494

L. Bottura

The quench propagation in superconducting magnets. A finite element solution ....................... 499

J. Simkin and C. W. Trowbridge

Finite elements and magnetic scalar potentials ..... 509

c. S. Desai

Unity and Hierarchy in modelling. Olek Zienkiewicz's contributions and impact ....................... 518

T. L. Geers

A fully consistent formulation of early-time approximations for acoustic media 521

M. A. Bossak

Application of a polydescriptive approach: bond graphs and finite elements to design analysis ............. 529

W. Wunderlich and H. eramer

A unified approach to the dynamic analysis of soils as multiphase media .............................. 537

SECTION 5 MATHEMATICAL ASPECTS OF THE FINITE

ELEMEND METHOD

E. M. Salonen

A note on the derivation of weak forms .......... 549

C. Militello and C. A. Felippa

The individual element test revisited .............. 554

B. Tabarrok and L. Tong

Dualities in minimum surfaces ................... 565

K. K. Gupta

Multidisciplinary finite element modeling and simulation of Aerospace vehicles ........................... 574

T. Belytschko and Y. Y. Lu

A new approach to stability analysis of partitioned systems ....................................... 585

J. Z. Zhu

Further tests on the derivative recovery technique and aposteriori error estimator ..... . . . . . . . . . . . . . . . .. 595

I. Babuska

Olek and a mathematician ...................... 605

J. L. Lions

Remarks on approximate controllability for parabolic systems 0....................................... 612

J. Orkisz and M. Pazdanowski

On a new feasible directions solution approach in constrained optimization 621

A. Craig

Hierarchical or domain decomposition preconditioning for the P-Version finite element method ........... 633