Direct Methods: Methodological Progress and Engineering Applications PDF
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Lecture Notes in Applied and Computational Mechanics 95 Aurora Angela Pisano Konstantinos Vassilios Spiliopoulos Dieter Weichert Editors Direct Methods Methodological Progress and Engineering Applications Lecture Notes in Applied and Computational Mechanics Volume 95 Series Editors Peter Wriggers, Institut für Kontinuumsmechanik, Leibniz Universität Hannover, Hannover, Niedersachsen, Germany Peter Eberhard, InstituteofEngineering andComputational Mechanics, University of Stuttgart, Stuttgart, Germany This series aims to report new developments in applied and computational mechanics-quickly,informallyandatahighlevel.Thisincludesthefieldsoffluid, solid and structural mechanics, dynamics and control, and related disciplines. The applied methods can be of analytical, numerical and computational nature. The series scope includes monographs, professional books, selected contributions from specialized conferences or workshops, edited volumes, as well as outstanding advanced textbooks. Indexed by EI-Compendex, SCOPUS, Zentralblatt Math, Ulrich’s, Current Mathematical Publications, Mathematical Reviews and MetaPress. More information about this series at http://www.springer.com/series/4623 Aurora Angela Pisano (cid:129) Konstantinos Vassilios Spiliopoulos (cid:129) Dieter Weichert Editors Direct Methods Methodological Progress and Engineering Applications 123 Editors Aurora AngelaPisano Konstantinos Vassilios Spiliopoulos PAU Institute of Structural Analysis & University Mediterranea of ReggioCalabria Antiseismic Research,National Technical ReggioCalabria, Italy University of Athens Athens, Greece DieterWeichert IAM RWTH Aachen University Aachen, Germany ISSN 1613-7736 ISSN 1860-0816 (electronic) Lecture Notesin AppliedandComputational Mechanics ISBN978-3-030-48833-8 ISBN978-3-030-48834-5 (eBook) https://doi.org/10.1007/978-3-030-48834-5 ©TheEditor(s)(ifapplicable)andTheAuthor(s),underexclusivelicensetoSpringerNature SwitzerlandAG2021 Thisworkissubjecttocopyright.AllrightsaresolelyandexclusivelylicensedbythePublisher,whether thewholeorpartofthematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseof illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmissionorinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilar ordissimilarmethodologynowknownorhereafterdeveloped. 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ThisSpringerimprintispublishedbytheregisteredcompanySpringerNatureSwitzerlandAG Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland Foreword WhenMaximilianTytusHuberpublishedin1904hisworkentitled“Specificwork of strain as a measure of material effort” (in Polish), he probably did not realize what effect this article would have on the development of the theory of plasticity. His pioneering work opened the prospect of an extraordinary development of this fieldofknowledge,bothinthecontextofconstitutivemodelingofmaterials,andin the context of direct methods in mechanics. The same approach, based on the concept of shear energy as the driving force of inelastic deformation, has been independentlyappliedbyvonMises(1913)andHencky(1924).Forthisreason,the most popular yield function ever is called Huber-von Mises-Hencky (HMH). This showsthatgreatdiscoverieshaveoftenamultinationaldimension,andwhenallthe components are there, the breakthrough is shared by many enlightened minds, working independently of each other. The HMH yield function was at the origin of expansion of the constitutive models,startingfromthesimplestone—theperfectrigid-plasticmodel.Evenifthe model was preceded by the Nadai (1923), as well as the Hencky (1924) and Ilyushin(1943)deformationtheory,therealbreakthroughcamewiththevonMises (1913) flow theory (inspired by the work of Levy, 1870), that involved the HMH yield function, and—finally—gave birth to the Prandtl (1924) and Reuss (1930) theoryofplasticflowfortheelastic-perfectlyplasticcontinuum.Fromthismoment on, a bifurcation has been observed, with the constitutive models of materials (including highly dissipative phenomena) developing in one way, and the direct methodsinmechanicsfollowingtheirownway,involvingtheclassicaltheoremsof limit loads and the problems of adaptation (shakedown) to cyclic loads. In partic- ular,moreandmoreadvancedconstitutivemodelsinvolvesuchphenomenalikethe evolution of microstructure, the phase transformations, the evolution of micro-damage or non-standard modes of inelastic behavior, whereas the direct methods address the variables and the limits set to determine the structural safety. Thus, modern, physically based, multiscale constitutive models of materials are usually built by using local approach, and are defined at the level of a point, whereas, the direct methods apply to the structure as a whole. v vi Foreword Thefirstideasrelatedtotheso-calledloadcarryingcapacitymaybetracedback to the eighteenth century, however—historically—the first limit carrying capacity (LCC)ofstructureswascalculated byKazinczy(1914),Kist(1917),andIngerslev (1923). A major contribution was brought by Hill (1951, 1952), Prager (1951, 1952), and Drucker (1954). The limit load was defined for a structure made of rigid-plastic hardening material as the yield stress load. It is accompanied by an infinitesimal deformation of the structure. Prager (1952, 1955) used another defi- nition,basedontheelastic-perfectlyplasticmaterial.Thelimitloadwasinterpreted assuchaloadthatresultsinunconstrainedplasticflow.Basedontheseapproaches, the so-called extremum theorems of limit analysis were established for the struc- turesmadeofrigid-plasticmaterialandsubjectedtoquasistaticloads.Thetheorems refer to the statically admissible stress fields or the kinematically admissible dis- placementfields,accompanyingthemechanismofplasticcollapseofarigid-plastic body, and constituting the lower and the upper bounds of the limit load. The extremum theorems corresponding to the HMH yield surface were proved by Hill (1956,1957),andextendedtolargestrainsin1958.Anotherwayofestablishingthe limit loads based on the rigid-perfectly plastic model was the so-called method of characteristics, formulated by Hencky (1923) and Prandtl (1923), and followed by Geiringer (1930), Geiringer and Prager (1933), Sokolovsky (1950, 1958), Shield (1953), Mróz (1967), Kachanov (1969), Dietrich (1970), Szczepiński (1974), Martin (1975), and many others. Going even further, a more advanced concept ofthedecohesive carrying capacity (DCC) was introduced byŻyczkowski (1973), based on the assumption of unbounded dissipation energy. The limit analysis was extended to variable loads, in particular to cyclic loads, that constitute an important part of the technical reality of structures. In the light of the early achievements in limit analysis, Melan (1930) formulated a theorem, also called the static shakedown theorem, that constitutes a natural generalization of the lower bound theorem for quasistatic loads. A proof of the theorem for three-dimensional continuum was provided by Melan (1938), and later on by Symonds (1951) and Koiter (1955). Extrapolation of the Melan theorem to the structures made of strain hardening material is due to Neal (1950), as well as SymondsandPrager(1950).TheMelantheoremhasbeenwidelyrecognizedasthe mostcommonandefficienttoolfortheshakedownanalysis.Lateron,Koiter(1956, 1960) formulated a theorem, often called the kinematic inadaptation theorem, that forms a direct extrapolation of the upper bound theorem for quasistatic loads. The theorem has been generalized to thermal cycles and non-associated flow rules by Maier (1969), as well as to dynamic loads by Corradi and Maier (1973). The theoremshavebeenexpressedintermsofthegeneralizedstressesbyKönig(1966, 1974). Both theorems have become a turning point in the development of direct methods in mechanics. In particular, the shakedown theorem provides a limit againstexcessivedeformation,andthisapproachismassivelyusedinthedesignof structures,forinstancenuclearpowerplants.Thermalloadswereincluded intothe shakedown analysis already by Prager (1956) and by Rozenblyum (1957, 1958, 1965), as well as by Gokhfeld (1961, 1965, 1970). Shakedown of rigid hardening Foreword vii structures was addressed by Prager (1974). As both theorems were derived under the assumption of geometrically linear theory, an extension to geometrical non- linearities was inevitable and is due to Weichert (1986). More recently, an exten- sion of limit and shakedown analysis to general class of yield conditions was proposed by Ponter (2000). With the development of constitutive models, there were many attempts to extrapolatethetheoremstomorecomplexmathematicaldescriptions.Fastprogress of numerical methods, in parallel with much faster processing of data, made it possible to compute the nonlinear behavior of structures in more time-effective way. The finite element method can accommodate mathematically complicated constitutive models in order to solve any sophisticated problem of inelastic behavior of the complex structures. However, the direct methods retain their original, extremely important feature of solving this part of the problem, that is necessary to assess the limit state. They take advantage of the modern computa- tional methods in order to employ the variables required in the design context, to findtheboundsforenergydissipation,andtosettheappropriatesafetyfactors.This is of primary importance for safe design of structures and efficient communication with the engineers and industry. Inthepresentvolume,novelandimportantachievementsinthedomainofdirect methods, presented at the 4. Polish Congress of Mechanics and 23. International Conference on Computer Methods in Mechanics (PCM-CMM-2019) in Cracow/Poland, during the session on “Direct Methods: Methodological Progress and Engineering Applications”, are contained. The topics stretch from the limit analysis and shakedown problems of different types of structures (including bone-structures)tothelimitanalysis-basedoptimizationandadvanced engineering applications. This book is the best proof that the direct methods in a modern form are actively developing for the benefit of science, technology, and industrial applications. Cracow, Poland Błażej Skoczeń Preface “Direct Methods”, embracing Limit- and Shakedown Analysis, allow to answer without cumbersome step-by-step computation one of the oldest and most impor- tant questions of design engineering, which is to determine the load carrying capacity of structures and structural elements. This book is the peer-reviewed collection of papers presented at the Workshop on Direct Methods, held September 10–11, 2019 in Cracow, Poland, giving an insightintothelatestdevelopmentsofthisfastprogressingfieldofresearch.Itisin line with similar books on the same subject which have been published as docu- mentation of the previous workshops, held regularly since 2008 at Aachen, Lille, Athens, Reggio Calabria, and Oxford. Most of the contributions are related to new numerical developments rendering the methods attractive for industrial design in a large panel of engineering appli- cations. Extensions of the general methodology to new horizons of application are presented as well as specific technological problems. It might be worth noting that the success of the workshops and the growing interest in Direct Methods in the scientific community were motivations to create theassociationIADiMe(http://www.iadime.unirc.it/)asaplatformforexchangeof ideas, advocating scientific achievements and not least, promotion of young sci- entists working in this field. It is open for all interested researchers and engineers. The editors warmly thank all the scientists who have contributed by their out- standing papers to the quality of this edition. Special thanks go to the organizers of the 4th Polish Congress of Mechanics & 23rd International Conference on Computer Methods in Mechanics, PCM-CMM-2019,September8–12,2019,Cracow,whohostedourmeetinginthe most comfortable and generous manner. Reggio Calabria, Italy Aurora Angela Pisano Athens, Greece Konstantinos Vassilios Spiliopoulos Aachen, Germany Dieter Weichert ix Contents Evaluation of Human Bones Load Bearing Capacity with the Limit Analysis Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Aurora Angela Pisano and Paolo Fuschi TheLinearMatchingMethodandItsSoftwareToolforCreepFatigue Damage Assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 Manu Puliyaneth, Graeme Jackson, Haofeng Chen, and Yinghua Liu Limit Analysis of Complex 3D Steel Structures Using Second-Order Cone Programming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 Chadi El Boustani, Jeremy Bleyer, and Karam Sab Limit Fire Analysis of 3D Framed Structures Based on Time-Dependent Yield Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 Domenico Magisano, Francesco Liguori, Leonardo Leonetti, and Giovanni Garcea LimitAnalysisofDryMasonryBlockStructureswithNon-associative Coulomb Friction: A Novel Computational Approach . . . . . . . . . . . . . . 83 Nicola A. Nodargi, Claudio Intrigila, and Paolo Bisegna Homogenization of Ductile Porous Materials by Limit and Shakedown Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 Zhang Jin, Abdelbacet Oueslati, Wanqing Shen, and Géry de Saxcé Recent Updates of the Residual Stress Decomposition Method for Shakedown Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 Ioannis A. Kapogiannis and Konstantinos V. Spiliopoulos Stress Compensation Method for Shakedown Analysis and Its Engineering Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 Heng Peng, Yinghua Liu, and Haofeng Chen xi
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