Applied Mathematics and Mechanics >
A theory for three-dimensional response of micropolar plates
Received date: 2024-03-14
Online published: 2024-07-31
Supported by
the National Natural Science Foundation of China(12072337);Project supported by the National Natural Science Foundation of China (No. 12072337)
Copyright
Through combined applications of the transfer-matrix method and asymptotic expansion technique, we formulate a theory to predict the three-dimensional response of micropolar plates. No ad hoc assumptions regarding through-thickness assumptions of the field variables are made, and the governing equations are two-dimensional, with the displacements and microrotations of the mid-plane as the unknowns. Once the deformation of the mid-plane is solved, a three-dimensional micropolar elastic field within the plate is generated, which is exact up to the second order except in the boundary region close to the plate edge. As an illustrative example, the bending of a clamped infinitely long plate caused by a uniformly distributed transverse force is analyzed and discussed in detail.
Dianwu HUANG, Linghui HE . A theory for three-dimensional response of micropolar plates[J]. Applied Mathematics and Mechanics, 2024 , 45(8) : 1403 -1414 . DOI: 10.1007/s10483-024-3128-7
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