Vol. 10, No. 3, 2015

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Harmonic shapes in isotropic laminated plates

Xu Wang and Peter Schiavone

Vol. 10 (2015), No. 3, 433–445
DOI: 10.2140/jomms.2015.10.433

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.

harmonic shape, stress concentration, inverse problem, isotropic laminated plate, conformal mapping
Received: 13 March 2014
Accepted: 17 July 2014
Published: 26 August 2015
Xu Wang
School of Mechanical and Power Engineering
East China University of Science and Technology
130 Meilong Road
Shanghai, 200237
Peter Schiavone
Department of Mechanical Engineering
University of Alberta
4-9 Mechanical Engineering Building
Edmonton, AB T6G 2G8