Nonlocal nonlinear formulations for bending of classical and shear deformation theories of beams and plates Academic Article uri icon


  • 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.

published proceedings


author list (cited authors)

  • Reddy, J. N.

citation count

  • 387

complete list of authors

  • Reddy, JN

publication date

  • November 2010