SMS swMATH ID: 1085 Software Authors: Korelc, Jože Description: Automatic generation of finite-element code by simultaneous optimization of expressions. The paper presents a MATHEMATICA package SMS (Symbolic Mechanics System) for the automatic derivation of formulas needed in nonlinear finite element analysis. Symbolic generation of the characteristic arrays of nonlinear finite elements (e.g. nodal force vectors, stiffness matrices, sensitivity vectors) leads to exponential behavior, both in time and space. A new approach, implemented in SMS, avoids this problem by combining several techniques: symbolic capabilities of Mathematica, automatic differentiation technique, simultaneous optimization of expressions and a stochastic evaluation of the formulas instead of a conventional pattern matching technique. SMS translates the derived symbolic formulas into an efficient compiled language (FORTRAN or C). The generated code is then incorporated into an existing finite element analysis environment. SMS was already used to developed several new, geometrically and materially nonlinear finite elements with up to 72 degrees of freedom. The design and implementation of SMS are presented. Efficiency of the new approach is compared with the efficiency of the manually written code on an example. Homepage: http://www.sciencedirect.com/science/article/pii/S0304397597000674 Dependencies: Mathematica Keywords: SMS; a program package for simulation and gaming of stochastic market processes and learning behavior Related Software: Mathematica; AceGen; AceFEM; FINGER; Matlab; ABAQUS; HYPLAS; ADIC; FEAP; Triangle; ODESSA; PyChecker; FFC; UFC; UFL; Analysa; Boost; Feel++; SyFi; FEniCS Cited in: 33 Publications Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year Automatic generation of finite-element code by simultaneous optimization of expressions. Zbl 0893.68084Korelc, Jože 1997 all top 5 Cited by 49 Authors 8 Wriggers, Peter 6 Korelc, Jože 4 Rodič, Tomaž 4 Schröder, Jörg 3 Neto, Alfredo Gay 3 Pimenta, Paulo M. 3 Saje, Miran 3 Schwarz, Alexander 2 Averweg, Solveigh 2 Brank, Boštjan 2 Gams, Matjaz 2 Holzapfel, Gerhard Alfred 2 Krstulović-Opara, Lovre 2 Nisters, Carina 2 Planinc, Igor 2 Stupkiewicz, Stanisław 2 Viebahn, Nils 1 Alnæs, Martin Sandve 1 Balzani, Daniel 1 Birk, Carolin 1 Bohinc, Uroš 1 César de Sá, José M. A. 1 de Mattos Pimenta, Paulo 1 Doltsinis, Ioannis St. 1 Dutko, Martin 1 Gilbert, Rose Rogin 1 Grešovnik, Igor 1 Hartmann, Stefan 1 Ibrahimbegović, Adnan 1 Khandelwal, Kapil 1 Kiousis, D. E. 1 Kiran, Bangalore Ravi 1 Kunc, Robert 1 Lengiewicz, Jakub 1 Logg, Anders 1 Ølgaard, Kristian B. 1 Prebil, Ivan 1 Reichel, Maximilian 1 Rognes, Marie E. 1 Schwarz, Carina 1 Seabra, Mariana R. R. 1 Šolinc, Urša 1 Šuštarič, Primož 1 Weißenfels, Christian 1 Wells, Garth N. 1 Žerovnik, Andrej 1 Zupan, Dejan 1 Zupan, Eva 1 Zupan, Nina all top 5 Cited in 10 Serials 12 Computer Methods in Applied Mechanics and Engineering 10 Computational Mechanics 3 International Journal for Numerical Methods in Engineering 1 ACM Transactions on Mathematical Software 1 Theoretical Computer Science 1 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 1 Engineering Computations 1 CMES. Computer Modeling in Engineering & Sciences 1 International Journal of Fatigue 1 International Journal of Computational Methods all top 5 Cited in 9 Fields 26 Mechanics of deformable solids (74-XX) 7 Numerical analysis (65-XX) 5 Computer science (68-XX) 3 Fluid mechanics (76-XX) 1 Number theory (11-XX) 1 Partial differential equations (35-XX) 1 Mechanics of particles and systems (70-XX) 1 Optics, electromagnetic theory (78-XX) 1 Biology and other natural sciences (92-XX) Citations by Year