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General Multilayer Geometrically‐Exact Beams/1‐D Plates with Deformable Layer Thickness: Equations of Motion
Author(s) -
VuQuoc L.,
Ebcioğlu I.K.
Publication year - 2000
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/(sici)1521-4001(200002)80:2<113::aid-zamm113>3.0.co;2-k
Subject(s) - deformation (meteorology) , equations of motion , nonlinear system , layer (electronics) , motion (physics) , materials science , boundary value problem , shear (geology) , geometry , mechanics , classical mechanics , mathematical analysis , physics , mathematics , composite material , quantum mechanics
We formulate a theory of geometrically‐exact multilayer beams and one‐dimensional plates that account for the through‐the‐thickness deformation in each layer, in addition to shear deformation. The complete set of nonlinear equations of motion together with the appropriate boundary conditions are derived, and a linear constitutive law is postulated for the model. The number of layers is arbitrary and unlimited, with a reference layer arbitrarily chosen among the layers. The length and the thickness of each layer are also variable, making the modeling of multilayer structures with ply drop‐offs possible. The present theory reduces exactly to the case of multilayer structures without through‐the‐thickness deformation, and to the case of single‐layer structures. The formulation allows the description of large deformation and large overall motion in multilayer structures.