TY - JOUR

T1 - Two-Dimensional Model of Second-Order Accuracy for an Anisotropic Plate

AU - Tovstik, P. E.

N1 - Tovstik, P.E. Vestnik St.Petersb. Univ.Math. (2019) 52: 112. https://doi.org/10.3103/S1063454119010126

PY - 2019

Y1 - 2019

N2 - The deformation of a thin elastic anisotropic plate nonuniform in thickness is considered in a linear approximation. A two-dimensional model of second-order accuracy with respect to the small thickness parameter is constructed for a plate with general-type anisotropy (described by 21 elasticity moduli) via the asymptotic integration of the three-dimensional equations of elasticity theory. A system of differential equations describing the displacements of the middle layer with a differential order coinciding with the order of the Timoshenko-Reissner model is derived. The constructed model is suitable for studying the statics, dynamics, and stability of multilayered and functionally graded plates. The models of second-order accuracy for isotropic plates and plates with partial types of anisotropy were constructed earlier. This is the first time the model of second-order accuracy has been considered for general type anisotropy.

AB - The deformation of a thin elastic anisotropic plate nonuniform in thickness is considered in a linear approximation. A two-dimensional model of second-order accuracy with respect to the small thickness parameter is constructed for a plate with general-type anisotropy (described by 21 elasticity moduli) via the asymptotic integration of the three-dimensional equations of elasticity theory. A system of differential equations describing the displacements of the middle layer with a differential order coinciding with the order of the Timoshenko-Reissner model is derived. The constructed model is suitable for studying the statics, dynamics, and stability of multilayered and functionally graded plates. The models of second-order accuracy for isotropic plates and plates with partial types of anisotropy were constructed earlier. This is the first time the model of second-order accuracy has been considered for general type anisotropy.

KW - anisotropic heterogeneous plate

KW - model of second-order accuracy

UR - http://www.scopus.com/inward/record.url?scp=85064947227&partnerID=8YFLogxK

UR - https://link.springer.com/article/10.3103/S1063454119010126

U2 - 10.3103/S1063454119010126

DO - 10.3103/S1063454119010126

M3 - Article

AN - SCOPUS:85064947227

VL - 52

SP - 112

EP - 121

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 1

ER -