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Simultaneous Recovery of Transverse Stresses at all Points in a Plate

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We address the challenging issue of simultaneously finding transverse shear and normal stresses at all points in a plate from a priori known values of the in-plane stresses at plate’s interior points. The principle of virtual work is employed to equate the work done by the transverse stresses to the difference between the work done by the external forces (applied surface tractions and body forces) and that by the in-plane stresses. The three transverse stresses and the virtual displacements are expressed in terms of polynomial (for example, those used in the finite element method) basis functions to deduce a system of simultaneous algebraic equations for the transverse stresses. The integrands for the right-hand side of these equations can be evaluated from the values of the in-plane stresses. The proposed scheme is advantageous over the current methods in economically evaluating accurate values of transverse stresses from the knowledge of the in-plane stresses at the Barlow points where they are most accurate. Since no spatial derivatives of the inplane stresses are needed, this technique provides excellent values of transverse stresses. Results for three example problems are provided to illustrate the methodology and the accuracy of computed transverse stresses.

Ref.  R.C. Batra, B. Alanbay, Simultaneous recovery of transverse stresses at all points in a plate, Int. J. Engineering Science, 169, Art. No. 103570, 2021.

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