Belytschko T. - Introduction (779635), страница 2
Текст из файла (страница 2)
Forexample, in the selection of an element, the analyst must be aware of stability andlocking characteristics of various elements. A judicious selection of an elementfor a problem involves factors such as the stability of the element for the problemat hand, the expected smoothness of the solution and the magnitude ofdeformations expected. In addition, the analyst must be aware of the complexityof nonlinear solutions: the appearance of bifurcation points and limit points, thestability and instability of equilibrium branches.
The possibility of both physicaland numerical instabilities must be kept in mind and checked in a solution.Thus the informed use of nonlinear software in both industry and researchrequires considerable understanding of nonlinear finite element methods. It is theobjective of this book to provide this understanding and to make the reader awareof the many interesting challenges and opportunities in nonlinear finite elementanalysis.1.2. RELATED BOOKSFINITE ELEMENTSANDHISTORYOFNONLINEARSeveral excellent texts and monographs devoted either entirely or partiallyto nonlinear finite element analysis have already been published. Books dealingonly with nonlinear finite element analysis include Oden(1972), Crisfield(1991),Kleiber(1989), and Zhong(1993).
Oden’s work is particularly noteworthy since itpioneered the field of nonlinear finite element analysis of solids and structures.Some of the books which are partially devoted to nonlinear analysis areBelytschko and Hughes(1983), Zienkiewicz and Taylor(1991), Bathe(1995) andCook, Plesha and Malkus(1989). These books provide useful introductions tononlinear finite element analysis. As a companion book, a treatment of linearfinite element analysis is also useful. The most comprehensive are Hughes (1987)and Zienkiewicz and Taylor(1991).Nonlinear finite element methods have many roots. Not long after thelinear finite element method appeared through the work of the Boeing group andthe famous paper of Cough, Topp, and Martin (??), engineers in several venuesbegan extensions of the method to nonlinear, small displacement static problems,Incidentally, it is hard to convey the excitement of the finite element communityand the disdain of classical researchers for the method.
For example, for manyyears the Journal of Applied Mechanics banned papers, either tacitly, because itwas considered of no scientific substance [sentence does not finish]. Theexcitement in the method was fueled by Ed Wilson's liberal distribution of his firstprograms. In many laboratories throughout the world, engineers developed newapplications by modifying and extending these early codes.1-4T. Belytschko, Introduction, December 16, 1998This account form those in many other books in that the focus is not on thepublished works, buut on the software. In nonlinear finite element analysis, as inmany endeavors in this information-computer age, te software represents a moremeaningful indication of the state-of-the-art than the literature since it representswhat can be applied in practice.Among the first papers on nonlinear finite element methods were Marcaland King (??) and Gallagher (??).
Pedro Marcal taught at Brown in those earlyyears of nonlinear FEM, but he soon set up a firm to market the first nonlinearfinite element program in 196?; the program was called MARC and is still amajor player in the commercial software scene.At about the same time, John Swanson (??) was developing a nonlinearfinite element program at Westinghouse for nuclear applications. He leftWestinghouse in 19?? to market the program ANSYS, which for the period 198090 dominated the commercial nonlinear finite element scene.Two other major players in the early commercial nonlinear finite elementscene were David Hibbitt and Klaus-Jürgen Bathe.
David worked with PedroMarcal until 1972, and then co-founded HKS, which markets ABAQUS. Jürgenlaunched his program, ADINA, shortly after obtaining his Ph.D. at Berkeleyunder the tutelage of Ed Wilson while teaching at MIT.All of these programs through the early 1990's focused on static solutionsand dynamic solutions by implicit methods. There were terrific advances in thesemethods in the 1970's, generated mainly by the Berkeley researchers and thosewith Berkeley roots: Thomas J.R. Hughes, Michael Ortiz, Juan Simo, and RobertTaylor (in order of age), were the most fertile contributors, but there are manyother who are referenced throughout this book.Explicit finite element methods probably have many different origins,depending on your viewpoint.
Most of us were strongly influenced by the work inthe DOE laboratories, such as the work of Wilkins (??) at Lawrence Livermoreand Harlow (??) at Los Alamos.In ???, Costantino (??) developed what was probably the first explicitfinite element program. It was limit to linear materials and small deformations,and computed the internal nodal forces by multiplying a banded form of K by thenodal displacements. It was used primarily on IBM 7040 series computers, whichcost millions of dollars and had a speed of far less than 1 megaflop and 32,000words of RAM. The stiffness matrix was stored on a tape and the progress of acalculation could be gauged by watching the tape drive; after every step, the tapedrive would reverse to permit a read of the stiffness matrix.In 1969, in order to sell a proposal to the Air Force, we conceived whathas come to be known as the element-by-element technique: the computation ofthe nodal forces without use of a stiffness matrix.
The resulting program,SAMSON, was a two-dimensional finite element program which was used for adecade by weapons laboratories in the U.S. In 1972, the program was extended tofully nonlinear three-dimensional transient analysis of structures and was calledWRECKER. This funding program was provided by the U.S. Department ofTransportation by a visionary program manager, Lee Ovenshire, who dreamt inthe early 1970's that crash testing of automobiles could be replaced by simulation.However, it was not to be, for at that time a simulation of a 300-element nodal1-5T.
Belytschko, Introduction, December 16, 1998over ?? msec of simulation time took 30 hours of computer time, which cost theequivalent of three years of salary of an Assistant Professor ($35,000). Theprogram funded several other pioneering efforts, Hughes' work on contact-impact(??) and Ted Shugar and Carly Ward's work on the modeling of the head at PortHueneme. But the DOT decided around 1975 that simulation was too expensive(such is the vision of some bureaucrats) and shifted all funds to testing, bringingthis far flung research effort to a screeching halt. WRECKER remained barelyalive for the next decade at Ford.Parallel work proceeded at the DOE national laboratories.
In 1975, SamKey completed PRONTO, which also featured the element-by-element explicitmethod. However, his program suffered from the restrictive disseminationpolicies of Sandia.The key work in the promulgation of explicit finite element codes wasJohn Hallquist's work at Lawrence Livermore Laboratories. John drew on thework which preceded his with discernment, he interacted closely with manyBerkeley researchers such as Bob Taylor, Tom Hughes, and Juan Simo. Some ofthe key elements of his success were the development of contact-impact interfaceswith Dave Benson, his awesome programming productivity and the widedissemination of the resulting codes, DYNA-2D and DYNA-3D. In contrast toSandia, LLN seemed to place no impediments on the distribution of the programand it was soon to be found in many government and academic laboratories and inindustry throughout the world.Key factors in the success of the DYNA codes was the use of one-pointquadrature elements and the degree of vectorization which was achieved by johnHallquist.
The latter issue has become somewhat irrelevant with the newgeneration of computers, but this combination enabled the simulation with modelsof suffiecient sizeto make full-scale simulation of problems such as car crashmeaningful. The one-point quadrature elements with consistent hourglass controldiscussed in Chapter 8 increased the speed of three-dimensional analysis byalmost an order of magnitude over fully integrated three-dimensional elements.1.3 NOTATIONNonlinear finite element analysis represents a nexus of three fields: (1)linear finite element methods, which evolved out of matrix methods of structuralanalysis; (2) nonlinear continuum mechanics; and (3) mathematics, includingnumerical analysis, linear algebra and functional analysis, Hughes(1996).
![](https://s.studizba.com/z.php?f=/templates/si/i/noavatar.png&w=100&h=100&t=1"){kind=avatar}
