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- W2484080485 abstract "Publisher Summary This chapter discusses the fundamental mathematical problems in the theory of nonlinear elasticity. It is high time to resolve the open problems of nonlinear continuum physics, either by subsuming them under the various nonlinear operator theories or by attacking them with effective numerical procedures. Unfortunately, such a program does not yet seem viable because there are serious gaps in the existing knowledge of the physical problem and of mathematical methods. The chapter explores the delicate interrelationship between mathematics and physics that is the source of these difficulties. It also reviews the governing equations and explores their mathematical structure. The chapter discusses a number of important specific problems. The difficulties presented by the three-dimensional theory of nonlinear elasticity have resulted in the development of innumerable, scarcely distinguishable, theories of rods and shells, each endowed by its creator with special virtues that are not recognized by other such creators. Rod theories and shell theories characterize the behavior of bodies by a finite number of equations in just one and two independent spatial variables, respectively." @default.
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- W2484080485 date "1976-01-01" @default.
- W2484080485 modified "2023-09-27" @default.
- W2484080485 title "FUNDAMENTAL MATHEMATICAL PROBLEMS IN THE THEORY OF NONLINEAR ELASTICITY**This work was partially supported by N.S.F. Grant MPS 73-08587 A2." @default.
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- W2484080485 doi "https://doi.org/10.1016/b978-0-12-358503-5.50007-5" @default.
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