Harmonic shapes in isotropic laminated plates

Harmonic shapes are known to minimize stress disturbance when introduced into an elastic body as either holes or inclusions. This paper is concerned with the design of harmonic shapes in an isotropic laminated plate. Specifically, we require that the harmonic shape does not disturb the sum of the two normal membrane stress resultants and that of the two normal bending moments when inserted into a uniformly loaded laminated plate. Using complex variable methods, we demonstrate how a single harmonic shape (hole or rigid inclusion) and two interacting harmonic shapes can be successfully designed to meet our requirements. In our discussion, the two interacting harmonic shapes include (i) two interacting harmonic holes, (ii) two interacting harmonic rigid inclusions, and (iii) one harmonic hole interacting with another harmonic rigid inclusion.

Keywords

harmonic shape, stress concentration, inverse problem, isotropic laminated plate, conformal mapping

Milestones

Received: 13 March 2014

Accepted: 17 July 2014

Published: 26 August 2015

Authors

Xu Wang
School of Mechanical and Power Engineering East China University of Science and Technology 130 Meilong Road Shanghai, 200237 China

Peter Schiavone
Department of Mechanical Engineering University of Alberta 4-9 Mechanical Engineering Building Edmonton, AB T6G 2G8 Canada

Vol. 10, No. 3, 2015

Xu Wang and Peter Schiavone

Abstract

Keywords

Milestones

Authors