A discrete differential geometry-based approach to buckling and vibration analyses of inhomogeneous Reddy plates

• Published in: Applied Mathematical Modelling 2021-12, Vol.100, p.342-364
• Main Authors: Ruocco, E., Reddy, J.N.
• Format: Article
• Language: English
• Subjects: Buckling; Differential geometry; Discretized equations; Elastic deformation; Finite difference method; Formability; Free vibration; Inhomogeneous plates; Mathematical models; Numerical results; Partial differential equations; Plate theory; Rectangular plates; Reddy plate model; Shear deformation; Springs (elastic); Thick plates; Vibration
• ISSN: 0307-904X; 1088-8691; 0307-904X
• DOI: 10.1016/j.apm.2021.08.011

•A numerical procedure for buckling and vibration analyses of rectangular plates with non-uniform thickness is developed.•A finite number of rigid bars and lumped masses joined by elastic springs simulate both bending and shear deformation.•The analysis of thick plates is performed through the adoption of the Reddy’s third-order shear deformable plate theory.•The obtained results show both the versatility and the accuracy of the proposed approach. In this paper, a novel discrete differential geometry-based numerical procedure for buckling and vibration analyses of rectangular plates with non-uniform thickness is developed. In the proposed approach a plate is discretized using a finite number of rigid bars, lumped masses, and elastic rotational springs to simulate both bending and shear deformation responses, allowing the analysis of thick plates through the adoption of the Reddy’s third-order shear deformable plate theory. An interesting analogy between the proposed model and the central finite difference method for solving a set of partial differential equations is also highlighted, showing how the former can be seen as the physical model behind the mathematical representation of the latter. The numerical results presented show both the versatility and the accuracy of the proposed approach.