Tensor calculus of locally Cartesian coordinates on a curved surface (Q1081375)
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scientific article; zbMATH DE number 3970218
| Language | Label | Description | Also known as |
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| English | Tensor calculus of locally Cartesian coordinates on a curved surface |
scientific article; zbMATH DE number 3970218 |
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Tensor calculus of locally Cartesian coordinates on a curved surface (English)
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1987
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A tensor calculus is developed for locally Cartesian coordinates on a curved surface which is regarded as elementarily flat. In this tensor calculus the sequence of repeated differentiation of tensors is immaterial for all shapes of surface - unlike the situation for covariant differentiation. The paper concludes with a few notes pertaining to the application of locally Cartesian coordinates in classical shell theory, vis-à-vis finite element analysis which uses flat elements.
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Mainardi-Codazzi equation
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coordinate transformation in terms of Taylor series expansion
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Riemann-Christoffel curvature tensor
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tensor calculus
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locally Cartesian coordinates
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curved surface
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elementarily flat
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repeated differentiation
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