Abstract
In this study, a new peridynamic Mindlin plate formulation is presented which is suitable for the analysis of functionally graded materials. The governing equations of peridynamic formulation are obtained by using Euler-Lagrange equations in conjunction with Taylor’s expansion. To validate the new formulation, three different numerical benchmark problems are considered for a Mindlin plate subjected to simply supported, fully clamped and mixed (clamped-simply supported) boundary conditions. Peridynamic results are compared against results from finite element analysis and a good agreement is observed between the two methods.
Highlights
As the manufacturing technology advances, it becomes possible to design materials that have better properties with respect to traditional materials including metals and fibre-reinforced composite materials
Fibre-reinforced composite materials are light, have good impact properties and corrosion resistance, they suffer from delamination damage occurring between neighbouring plies which significantly reduces the load carrying capacities of these materials
An alternative formulation is presented using peridynamics [9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29] to analyse functionally graded plates based on Mindlin plate theory by taking into account transverse shear deformation
Summary
As the manufacturing technology advances, it becomes possible to design materials that have better properties with respect to traditional materials including metals and fibre-reinforced composite materials. Ferreira et al [6] used meshless method and third-order shear deformation theory to analyse functionally graded plates. An alternative formulation is presented using peridynamics [9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29] to analyse functionally graded plates based on Mindlin plate theory by taking into account transverse shear deformation. To obtain governing equations of peridynamic Mindlin plate formulation for functionally graded materials Euler-Lagrange equations in conjunction with Taylor’s expansion are utilised. To validate the current formulation, several benchmark problems are considered and peridynamic results are compared against results from finite element analysis
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