Asymptotic post‐buckling analysis of rectangular plates by HC finite elements

Abstract

SUMMARYThe present paper extends the finite element perturbation approach already presented for pin-jointed and framed structuresL5 to rectangular thin plates. Koiter's asymptotic strategy' is coupled with a HighContinuity finite element discretization of the plate." The consistency of the discrete model is discussed from the kinematical and numerical points of view and several numerical tests are reported. It appears that use of the HC elements makes the perturbation algorithm insensitive to the locking phenomenon occurring in the evaluation of the postbuckling behaviour. It also allows the use of very fine discretization meshes at low computational cost.

3D beam element based on Saint Venànt’s rod theory

“…Note however that, while slender beams with compact cross-section can be generally treated in this way, thin walled beams can present a complex buckling behavior implying local in-plane distortions of the cross-section which are not captured by the Saint VenàntÕs solution. So a different, more complex, approach such as that proposed in [17], [18] could be required in this case.…”

“…The evaluation of H t , through Eqs. (30) and (20), however, requires the computation of the three scalar functions w j [x, y] implicitly defined by the differential problem (17). The latter, cannot be obtained in closed form, for generic sections, but have to be evaluated through numerical discretization.…”

“…associated with the differential problem (17). Stationary condition for functional (47) implies: X e q T e M e dq e À p e dq e…”

“…The BEM solution strategy is based on a rewriting of problem (17) in boundary integral form by exploiting SomiglianaÕs identity [6]. For the problem under consideration, the latter writes…”

A robust methodology for the simulation of postbuckling response of composite plates

“…In the second case study, the postbuckling response of a rectangular plate (a=b 3; h 0:1), from Lanzo et al (1995), was considered. They combined a high-continuity ®nite elements plate model with the Koiter's asymptotic strategy to solve for the buckling and postbuckling response of rectangular plates.…”