Nonlocal nonlinear formulations for bending of classical and shear deformation theories of beams and plates

abstract

• The classical and shear deformation beam and plate theories are reformulated using the nonlocal differential constitutive relations of Eringen and the von Krmn 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 Krmn 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. 2010 Elsevier Ltd. All rights reserved.

authors

• Reddy, Junuthula

published proceedings

• INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE

author list (cited authors)

• Reddy, J. N.

citation count

• 387

complete list of authors

• Reddy, JN

publication date

• November 2010

publisher

• Elsevier  Publisher

published in

• International Journal of Engineering Science  Journal

keywords

• Bending
• Classical Theories
• Nonlocal Elasticity
• Shear Deformation Theories
• Virtual Work Principles
• Von Karman Nonlinearity

Digital Object Identifier (DOI)

• 10.1016/j.ijengsci.2010.09.020

start page

• 1507

end page

• 1518

volume

• 48

issue

• 11

URL

• http://dx.doi.org/10.1016/j.ijengsci.2010.09.020