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Title

Derivation of nonlinear geometrical relations of the theory of shells with MathTensor
Authors

Ryszard A. Walentynski
Organization: Silesia University of Technology, Poland
Department: Department of Building Structuresí Theory, Faculty of Civil Engineering
Gautam Dasgupta
Organization: Columbia University
Department: Department of Civil Engineering and Engineering Mechanics
Conference

2004 International Mathematica Symposium
Conference location

Banff, Canada
Description

Necessary differential equations to study deformation of shells in Lagrangian (material) coordinates are derived using MathTensor. To account for the shell curvatures the ordinary derivatives (OD) are symbolically replaced by covariant derivatives (CD). CD's embedded operations, which include curvature tensors, yield the final nonlinear kinematic relations.
Subjects

*Mathematica Technology > Application Packages > Applications from Independent Developers > MathTensor
*Mathematics > Calculus and Analysis > Differential Equations
*Mathematics > Geometry > n-Dimensional Geometry
Keywords

differential equations, deformation of shells, Lagrangian coordinates, MathTensor, ordinary derivatives, covariant derivatives, curvature tensors, nonlinear kinematic relations
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*New Ideas in Symbolic Computation: Proceedings of the 6th International Mathematica Symposium   [in Books]