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Derivation of nonlinear geometrical relations of the theory of shells with MathTensor
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| Organization: | Silesia University of Technology, Poland |
| Department: | Department of Building Structures’ Theory, Faculty of Civil Engineering |
| Organization: | Columbia University |
| Department: | Department of Civil Engineering and Engineering Mechanics |
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2004 International Mathematica Symposium
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Banff, Canada
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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.
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differential equations, deformation of shells, Lagrangian coordinates, MathTensor, ordinary derivatives, covariant derivatives, curvature tensors, nonlinear kinematic relations
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