Comparison of various linear plate theories in the light of a consistent second-order approximation

Abstract

The uniform-approximation technique in combination with the pseudo-reduction technique is applied in order to derive consistent theories for isotropic and anisotropic plates. The approach has already been used to assess and validate theories established in the literature, e.g., the theories of Reissner and Zhilin. In this contribution, we also present a comparison with the theories of Vekua, Ambartsumyan, Steigmann and Reddy’s third-order theory. The current paper is a corrected and extended version of the one originally published in Kienzler and Schneider (Comparison of various linear plate theories in the light of a consistent second-order approximation. In Pietraszkiewicz, W and Górski, J (eds), Shell Structures: Theory and Applications. London: Taylor & Francis Group, 2014, pp. 109–112). In addition we put special emphasis on the derivation and validation of Ambartsumyan’s general and simplified theories.