## Bridging plate theories and elasticity solutions

 dc.contributor Aalto-yliopisto fi dc.contributor Aalto University en dc.contributor.author Karttunen, Anssi dc.contributor.author von Hertzen, Raimo dc.contributor.author Reddy, JN dc.contributor.author Romanoff, Jani dc.contributor.department Department of Mechanical Engineering dc.contributor.department Texas A&M University dc.date.accessioned 2020-01-02T14:07:46Z dc.date.available 2020-01-02T14:07:46Z dc.date.embargo info:eu-repo/date/embargoEnd/2019-12-31 dc.date.issued 2017 dc.description.abstract In this work, we present an exact 3D plate solution in the conventional form of 2D plate theories without invoking any of the assumptions inherent to 2D plate formulations. We start by formulating a rectangular plate problem by employing Saint Venant’s principle so that edge effects do not appear in the plate. Then the exact general 3D elasticity solution to the formulated interior problem is examined. By expressing the solution in terms of mid-surface variables, exact 2D equations are obtained for the rectangular interior plate. It is found that the 2D presentation includes the Kirchhoff, Mindlin and Levinson plate theories and their general solutions as special cases. The key feature of the formulated interior plate problem is that the interior stresses of the plate act as surface tractions on the lateral plate edges and contribute to the total potential energy of the plate. We carry out a variational interior formulation of the Levinson plate theory and take into account, as a novel contribution, the virtual work due to the interior stresses along the plate edges. Remarkably, this way the resulting equilibrium equations become the same as in the case of a vectorial formulation. A gap in the conventional energy-based derivations of 2D engineering plate theories founded on interior kinematics is that the edge work due to the interior stresses is not properly accounted for. This leads to artificial edge effects through higher-order stress resultants. Finally, a variety of numerical examples are presented using the 3D elasticity solution. en dc.description.version Peer reviewed en dc.format.extent 251–263 dc.format.mimetype application/pdf dc.identifier.citation Karttunen , A , von Hertzen , R , Reddy , JN & Romanoff , J 2017 , ' Bridging plate theories and elasticity solutions ' , International Journal of Solids and Structures , vol. 106-107 , pp. 251–263 . https://doi.org/10.1016/j.ijsolstr.2016.09.037 en dc.identifier.doi 10.1016/j.ijsolstr.2016.09.037 dc.identifier.issn 0020-7683 dc.identifier.other PURE UUID: b8303918-c7d2-4f58-8063-1aa3b3232808 dc.identifier.other PURE ITEMURL: https://research.aalto.fi/en/publications/b8303918-c7d2-4f58-8063-1aa3b3232808 dc.identifier.other PURE FILEURL: https://research.aalto.fi/files/39749060/ENG_Karttunen_et_al_Bridging_plate_theories_and_elasticity_solutions_International_Journal_of_Solids_and_Structures.pdf dc.identifier.uri https://aaltodoc.aalto.fi/handle/123456789/42194 dc.identifier.urn URN:NBN:fi:aalto-202001021305 dc.language.iso en en dc.publisher PERGAMON-ELSEVIER SCIENCE LTD dc.relation.ispartofseries International Journal of Solids and Structures en dc.relation.ispartofseries Volume 106-107 en dc.rights openAccess en dc.title Bridging plate theories and elasticity solutions en dc.type A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä fi dc.type.version acceptedVersion