Geometrically nonlinear analysis of thick orthotropic plates with various geometries using simple HP-cloud method
Abstract
Purpose
The purpose of this paper is to present a simple HP-cloud method as an accurate meshless method for the geometrically nonlinear analysis of thick orthotropic plates of general shape. This method is used to investigate the effects of thickness, geometry of various shapes, boundary conditions and material properties on the large deformation analysis of Mindlin plates.
Design/methodology/approach
Nonlinear analysis of plates based on Mindlin theory is presented. The equations are derived by the Von-Karman assumption and total Lagrangian formulations. Newton-Raphson method is applied to achieve linear equations from nonlinear equations. Simple HP-cloud method is used for the construction of the shape functions based on Kronecker-δ properties, so the essential boundary conditions can be enforced directly. Shepard function is utilized for a partition of unity and complete polynomial is used as an enrichment function.
Findings
The suitability and efficiency of the simple HP-cloud method for the geometrically nonlinear analysis of thin and moderately thick plates is studied for the first time. Large displacement analysis of various shapes of plates, rectangular, skew, trapezoidal, circular, hexagonal and triangular with different boundary conditions subjected to distributed loading are considered.
Originality/value
This paper shows that the simple HP-cloud method is well suited for the large deformation analysis of Mindlin plates with various geometries, because it uses a set of a few arbitrary nodes placed in a plate of general shape. Moreover the convergence rate of the proposed method is high and the cost of solving equations is low.
Keywords
Citation
Jafari, N. and Azhari, M. (2016), "Geometrically nonlinear analysis of thick orthotropic plates with various geometries using simple HP-cloud method", Engineering Computations, Vol. 33 No. 5, pp. 1451-1471. https://doi.org/10.1108/EC-08-2015-0223
Publisher
:Emerald Group Publishing Limited
Copyright © 2016, Emerald Group Publishing Limited