https://hal-enpc.archives-ouvertes.fr/hal-00987435Bleyer, JérémyJérémyBleyernavier umr 8205 - Laboratoire Navier - IFSTTAR - Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifiquede Buhan, PatrickPatrickde Buhanmulti-échelle - Modélisation et expérimentation multi-échelle pour les solides hétérogènes - navier umr 8205 - Laboratoire Navier - IFSTTAR - Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche ScientifiqueA computational homogenization approach for the yield design of periodic thin plates. Part I: Construction of the macroscopic strength criterionHAL CCSD2014 Yield design Limit analysis Homogenization theory Thin plate model Second-order cone programming Finite element method[PHYS.MECA.MSMECA] Physics [physics]/Mechanics [physics]/Materials and structures in mechanics [physics.class-ph][SPI.MECA.MSMECA] Engineering Sciences [physics]/Mechanics [physics.med-ph]/Materials and structures in mechanics [physics.class-ph]Bleyer, Jérémy2014-05-06 11:04:192022-01-15 03:49:572014-05-06 11:44:09enJournal articleshttps://hal-enpc.archives-ouvertes.fr/hal-00987435/document10.1016/j.ijsolstr.2014.03.018application/pdf1The purpose of this paper is to propose numerical methods to determine the macroscopic bending strength criterion of periodically heterogeneous thin plates in the framework of yield design (or limit analysis) theory. The macroscopic strength criterion of the heterogeneous plate is obtained by solving an auxiliary yield design problem formulated on the unit cell, that is the elementary domain reproducing the plate strength properties by periodicity. In the present work, it is assumed that the plate thickness is small compared to the unit cell characteristic length, so that the unit cell can still be considered as a thin plate itself. Yield design static and kinematic approaches for solving the auxiliary problem are, therefore, formulated with a Love-Kirchhoff plate model. Finite elements consistent with this model are proposed to solve both approaches and it is shown that the corresponding optimization problems belong to the class of second-order cone programming (SOCP), for which very efficient solvers are available. Macroscopic strength criteria are computed for different type of heterogeneous plates (reinforced, perforated plates,...) by comparing the results of the static and the kinematic approaches. Information on the unit cell failure modes can also be obtained by representing the optimal failure mechanisms. In a companion paper, the so-obtained homogenized strength criteria will be used to compute ultimate loads of global plate structures.