Abstract
In this chapter we shall select topics from finite deformation continuum mechanics and minimum surface type problems in differential geometry, and use them to illustrate a general duality theory for n-dimensional nonconvex finite deformation systems in which the geometrical mapping Λ is a nonlinear partial differential operator. The methods and ideas can certainly be generalized to many other problems.
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“I am the Alpha and the Omega”, says the Sovereign God, who is and who was and who is to come, the Almighty.
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The general laws of nature are to be expressed in equations which are valid for all coordinate systems
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Elasticity led to a vast range of mathematical problems involving linear algebra, differential geometry, ordinary and partial differential equations (mostly nonlinear), elliptic functions and the calculus of variations.
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© 2000 Springer Science+Business Media Dordrecht
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Gao, D.Y. (2000). Duality in Finite Deformation Systems. In: Duality Principles in Nonconvex Systems. Nonconvex Optimization and Its Applications, vol 39. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3176-7_6
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DOI: https://doi.org/10.1007/978-1-4757-3176-7_6
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4419-4825-0
Online ISBN: 978-1-4757-3176-7
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