Abstract
A variational formulation of interaction problem is presented in this paper for the analysis of an elastic circular plate under axisymmetric vertical loading resting on an isotropic elastic half-space under the influence of surface energy. The Gurtin-Murdoch surface elasticity theory is adopted to take into account the surface energy effects. The contact surface between the plate and the half-space is assumed to be smooth, and the deflected shape of the plate is represented by a power series of the radial coordinate. The undetermined coefficients in the series are determined through the minimization of the total potential energy functional of the plate-half-space system. The accuracy of the present solution is verified by comparing with existing solutions, and selected numerical results are presented to portray the influence of surface energy effects on interaction between an elastic circular plate and an elastic half-space.
Highlights
Nano-scale materials are found to possess excellent mechanical properties when compared to conventional engineering materials
A variational solution scheme is presented in this paper to study the interaction problem between an elastic circular plate and an isotropic elastic half-space under the influence of surface energy by adopting Gurtin-Murdoch surface elasticity theory
The contact surface between the plate and the half-space is assumed to be smooth, and the deflection shape of the plate is represented by a power series of the radial coordinate
Summary
Nano-scale materials are found to possess excellent mechanical properties when compared to conventional engineering materials. To take into account the influence of surface energy, Gurtin and Murdoch [1,2] presented a mathematical framework based on continuum mechanics concepts In their model, the elastic surface is formed as an idealized layer of zero thickness perfectly bonded to the underlying bulk material without slipping. The present study is concerned with the analysis of interaction problem between a circular nano-plate of radius a under axisymmetric vertical loading resting on an isotropic elastic half-space as shown in Figure 1 with the consideration of surface energy effects. This interaction problem is studied by employing a variational approach and the Gurtin-Murdoch surface elasticity theory [1,2]. Selected numerical results for deflection and bending moment of the nano-plate are presented to demonstrate a significant influence of surface energy effects on the interaction problem
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