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Lectures Year : 2015

The Bending-Gradient theory for laminates and in-plane periodic plates

Arthur Lebée


The classical theory of plates, known also as Kirchhoff-Love plate theory is based on the assumption that the normal to the mid-plane of the plate remains normal after transformation. This theory is also the first order of the asymptotic expansion with respect to the thickness. Thus, it presents a good theoretical justification and was soundly extended to the case of periodic plates. It enables to have a first order estimate of the macroscopic deflection as well as local stress fields. In most applications the first order deflection is accurate enough. However, this theory does not capture the local effect of shear forces on the microstructure because shear forces are one higher-order derivative of the bending moment in equilibrium equations. Because shear forces are part of the macroscopic equilibrium of the plate, their effect is also of great interest for engineers when designing structures. However, modeling properly the action of shear forces is still a controversial issue. Revisiting the approach from Reissner directly with laminated plates, it appears that the transverse shear static variables which come out when the plate is heterogeneous are not shear forces but the full gradient of the bending moment. Using conventional variational tools, it is possible to derive a new plate theory, called Bending-Gradient theory. This new plate theory is considered as an extension of Reissner's theory to heterogeneous plates which preserves most of its simplicity. Originally designed for laminated plates, it is also extended to in-plane periodic plates using averaging considerations. The lecture will be illustrated with application to strongly heterogeneous plates such as cellular sandwich panels or periodic space frames.
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cel-01266716 , version 1 (03-02-2016)


  • HAL Id : cel-01266716 , version 1


Arthur Lebée. The Bending-Gradient theory for laminates and in-plane periodic plates. Doctoral. Arpino, Italy. 2015. ⟨cel-01266716⟩
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