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quadratic forms

[FEM] How we are using shell geometry properties in time of calculation?

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I'm interested in methods and approaches for FEM, that are used for taking into account the shell geometry properties (curvatures, quadratic forms) in time of calculation. I'm not telling about NURBS, the shells are defyned by analytical expressions: sphere, Monge surfaces, Joachimstahl surface. In Zienkewich book they are use the flat elements, but in time of calculation they don't use the shell geometry, only for mesh generation. Maybe someone somehow have used in shape functions the coefficients of quadratic forms...

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