Vol. 8, No. 8-10, 2013

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ISSN: 1559-3959
Effects of transverse shear deformation on thermomechanical instabilities in patched structures with edge damage

Peinan Ge and William J. Bottega

Vol. 8 (2013), No. 8-10, 501–523
Abstract
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The problem of a patched structure under uniform thermal loading is studied, where geometric nonlinearity and shear deformation are considered. The formulation is based on the calculus of variations with propagating boundaries, and yields the governing equations, boundary conditions, matching conditions and transversality condition. Closed form analytical solutions are obtained in terms of an (unknown) membrane force parameter, the angle of rotation due to bending and the transverse displacement. Results of numerical simulations based on those solutions are presented and critical phenomena of the composite structure are unveiled. Results of the current work are compared with previously published results where transverse shear deformation was neglected. It is seen that shear deformation plays an important role in certain situations. In particular, the effects of shear deformation on the phenomena of “slingshot buckling” and “buckle trapping” are demonstrated and discussed. The influence of the relative size of the detached region and of the difference between the material properties of the base plate and of the patch (in particular, shear moduli) on the thermomechanical instabilities are elucidated.

Keywords
beam, buckle trapping, buckling, patch, patched structure, contact zone, plate, slingshot buckling, stability, temperature, thermal buckling, thermal load, transverse shear deformation
Milestones
Received: 16 July 2013
Revised: 26 September 2013
Accepted: 27 October 2013
Published: 30 December 2013
Authors
Peinan Ge
Department of Mechanical and Aerospace Engineering
Rutgers University
98 Brett Road
Piscatway, NJ 08854-8058
United States
William J. Bottega
Department of Mechanical and Aerospace Engineering
Rutgers University
Campus at New Brunswick, 98 Brett Road
Piscataway, NJ 08854-8058
United States