Journal
INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE
Volume 48, Issue 11, Pages 1507-1518Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.ijengsci.2010.09.020
Keywords
Bending; Classical theories; Nonlocal elasticity; Shear deformation theories; Virtual work principles; Von Karman nonlinearity
Categories
Funding
- Oscar S. Wyatt Endowed Chair
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The classical and shear deformation beam and plate theories are reformulated using the nonlocal differential constitutive relations of Eringen and the von Karman nonlinear strains. The equations of equilibrium of the nonlocal beam theories are derived, and virtual work statements in terms of the generalized displacements are presented for use with the finite element model development. The governing equilibrium equations of the classical and first-order shear deformation theories of plates with the von Karman nonlinearity are also formulated. The theoretical development presented herein should serve to obtain the finite element results and determine the effect of the geometric nonlinearity and nonlocal constitutive relations on bending response. (C) 2010 Elsevier Ltd. All rights reserved.
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