Considering large-strain elastic or elastoplastic deformations of shells the stresses may exhibit a complicated and a priori unknown behavior across the thickness which makes it difficult to establish a mathematical model which is both efficient and satisfying. We try to resolve the problem by introducing a class of shell theories based on a unified variational principle which allows to distinguish between "equilibrium stresses" and "constitutive stresses". While it is sufficient to define stress resultants based on polynomials (of low degree) to approximate the "equilibrium stresses" on has to use expansions with respect to general biorthogonal function systems for the "constitutive stresses". Examples are biorthogonal splines or, even more effective, biorthogonal wavelets with compact support. The shell models derived are able to accommodate the flow theory of large strain elastoplasticity including the effects due to unloading while maintaining the features of a fully two-dimensional resultant-based theory.
|Effective start/end date||1/01/93 → 31/01/15|
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