Analytical Solution of the Bending Problem for Rectangular Orthotropic Plates with a Variable in-Plane Stiffness

The analytical solution of the bending problem for a clamped rectangular plate with a variable in-plane stiffness is found by using the method of superposition. The flexural rigidity of the plate varies across its width according to an exponential function. First, the analytical solution for a simpl...

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Bibliographic Details
Published in:Mechanics of composite materials 2021-03, Vol.57 (1), p.115-124
Main Authors: Yu, T. C., Nie, G. J., Zhong, Z., Chu, F. Y., Cao, X. J.
Format: Article
Language:English
Subjects:
Aspect ratio
Bending moments
Boundary conditions
Ceramics
Characterization and Evaluation of Materials
Chemistry and Materials Science
Clamping
Classical Mechanics
Composite materials
Composites
Exact solutions
Exponential functions
Glass
Materials Science
Mathematical analysis
Natural Materials
Orthotropic plates
Rectangular plates
Solid Mechanics
Stiffness
Transverse loads
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Summary:The analytical solution of the bending problem for a clamped rectangular plate with a variable in-plane stiffness is found by using the method of superposition. The flexural rigidity of the plate varies across its width according to an exponential function. First, the analytical solution for a simply supported rectangular plate with a variable in-plane stiffness is obtained, and then the bending problem for the plate clamped at its four edges is solved analytically by the superposition of one simply supported plate under the transverse load and two simply supported plates under pure bending. The influence of the variable in-plane stiffness, aspect ratio, and different boundary conditions on the deflection and bending moment is studied by numerical examples. The analytical solution presented here may be helpful for the design of rectangular plates with a variable in-plane stiffness.
ISSN:0191-5665
1573-8922
DOI:10.1007/s11029-021-09938-1