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Mathematical Aspects of the Theory of Viscoelasticity

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Trends in Applications of Mathematics to Mechanics

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Abstract

It is very common to speak about applications of mathematics, We have the ISIMM symposia “Trends in Applications of Mathematics to Mechanics”. We often forget about an influence and applications of other sciences to mathematics. Polish mathematician MAURIN /1/ writes: Analysis arised for “requirements” of mechanics and geometry. Many ideas of mathematical analysis originated from mechanics. Here it is necessary to mention variational principles-theorems and methods. The powerful Galerkin method is in fact the application of the principle of virtual work. Also modern numerical methods such as the finite element method and the boundary element method have been proposed by engineers. The basic idea of such a theoretical part of analysis, as the theory of distribution is has its origin in mechanics. In fact, in solutions of the influence of concentrated forces in mechanics using Fourier transform or an expansion into Fourier series there is an idea of application of functionals to such a “function”. NADAI /2/ published in 1922 his solution of a circular plate supported at the boundary by concentrated forces expressed in the form of an expansion into Fourier series, what was incorrect from the point of view of mathematics of that time.

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References

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Author information

Authors and Affiliations

  1. Institute of Applied Mathematics and Computing Technique, Comenius University, CZ-84215, Bratislava, Czechoslovakia

    J. Brilla

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  1. J. Brilla
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Editor information

Editors and Affiliations

  1. Technological University, Mekelweg 2, NL-2628 CD, Delft, The Netherlands

    Johannes F. Besseling

  2. Mathematisch Instituut, Rijksuniversiteit Utrecht, Budapestlaan 6, NL-3584 CD, Utrecht, The Netherlands

    Wiktor Eckhaus

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© 1988 Springer-Verlag Berlin Heidelberg

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Brilla, J. (1988). Mathematical Aspects of the Theory of Viscoelasticity. In: Besseling, J.F., Eckhaus, W. (eds) Trends in Applications of Mathematics to Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-73933-0_23

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  • DOI: https://doi.org/10.1007/978-3-642-73933-0_23

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-73935-4

  • Online ISBN: 978-3-642-73933-0

  • eBook Packages: Springer Book Archive

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