Mathematically justified refined theories for thin structures

Abstract eng:
The uniform approximation approach is a dimension reduction procedure. It can be applied to derive analytical theories for thin structures from the settled theory of three-dimensional linear elasticity without the use of a-priori assumptions. In the talk, we show how the approach can be extended by arguments from duality theory, in order to proof its approximation property, which provides the mathematical justification for the approach. We treat the specific example of an isotropic, linear elastic beam with constant rectangular cross-section. The first-order approximation coincides with the Euler-Bernoulli beam theory, whereas the second-order approximation is new. Timoshenko´s beam theory can be transformed to an equivalent theory, if a specific shear-correction factor is used.

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