The Equations of Motion of a Plate with Residual Stress |
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Authors: | Roberto Paroni |
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Affiliation: | (1) Dipartimento di Architettura e Pianificazione, Università degli Studi di Sassari, Palazzo del Pou Salit, Piazza Duomo, 07041 Alghero, Italy |
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Abstract: | We consider a three-dimensional body which is at rest in a cylindrical configuration of height 2ε. We assume that the material is residually stressed and that it responds elastically to deformations from the reference configuration. Under appropriate assumptions on the data, and using weak-convergence methods, we determine the limit, as ε goes to zero, of the elasto-dynamic problem. The plate problem obtained, as in the case without residual stress, splits into two problems: one governing the in-plane displacement and the other determining the out-of-plane motion. |
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Keywords: | Residual stress Equation of motion Elasto-dynamic problems Continuum mechanics |
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