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

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

2004 International Mathematica Symposium
Conference location

Banff, Canada

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.

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

differential equations, deformation of shells, Lagrangian coordinates, MathTensor, ordinary derivatives, covariant derivatives, curvature tensors, nonlinear kinematic relations
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