Geometrically nonlinear deformation range

This effect arises because the initially flat substrate does not deform into a developable surface, that as, a surface with zero Gaussian curvature. As a result, the substrate cannot deform into a spherical cap shape without stretching or compressing portions of its midplane. The substrate is very stiff in extension compared to bending, as noted above, and this coupling 

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Lee, H., Rosakis, A. J. and Freund, L. B. (2001), Full field optical measurement of curvatures in ultrathin film-substrate systems in the range of geometrically nonlinear deformations. Journal of Applied Physics 89, 6116-6129. 

A number of additional observations on film—substrate deformation in the geometrically nonlinear range can be made on the basis of modeling of the kind introduced here. Among these are ... 

This chapter deals with the transverse or out-of-plane deflection of a thin film, and it includes quantitative descriptions of the phenomena associated with the buckling, bulging or peeling of a film from its substrate. A common thread throughout the discussion is that system behavior extends beyond the range of geometrically linear deformation. Consequently, aspects of finite or nonlinear deformation must be incorporated to capture essential features of behavior. The progression of delamination associated with trans-... 

Even though the deformation is in the geometrically nonlinear range, the differential equation governing w x) is linear. This is a fortuitous outcome that follows naturally from the nonlinear von Karman plate theory. A solution of (5.5) is sought subject to the boundary conditions... 

When the displacement components of a member are small, a wide range of linear analysis tools, such as modal analysis, can be used, and some analytical results are possible. As these components become larger, the induced geometrical nonlinearities result in effects that are not observed in linear systems. When finite displacements are considered, the flexural-torsional dynamic analysis of beams becomes much more complicated, leading to the formulation of coupled and nonlinear flexural, torsional, and axial equations of motion. The analysis of these systems becomes even more complicated when shear deformation effect in flexure and secondary torsional moment deformation effect (STMDE) in torsion, which are significant in many cases (e.g., short beams, beams of box-shaped cross sections, folded structural members, beams made of materials weak in shear, etc.), are taken into account. 

Forced Vibrations or Beam of Hollow Rectangular Cross Section Under Biaxial Bending In order to examine the influence of shear deformation on the free vibrations of beams in the geometrically nonlinear range, a clamped beam... 

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