Abstract
In this study, a new peridynamic formulation is presented for functionally graded Timoshenko beams. The governing equations of the peridynamic formulation are obtained by utilising Euler-Lagrange equation and Taylor’s expansion. The proposed formulation is validated by considering a Timoshenko beam subjected to different boundary conditions including pinned support-roller support, clamped-roller support and clamped-free boundary conditions. Results from peridynamics are compared against finite element analysis results. A very good agreement is obtained for transverse displacements, rotations and axial displacements along the beam.
Highlights
Peridynamics was introduced by Silling [1] to overcome the limitations of widely used classical continuum mechanics formulation especially for problems including discontinuities in the displacement field due to existence of cracks
To verify the validity of the PD formulation for functionally graded Timoshenko beams, the PD solutions are compared with the corresponding finite element (FE) analysis results
A new peridynamic formulation was presented for functionally graded Timoshenko beams
Summary
Peridynamics was introduced by Silling [1] to overcome the limitations of widely used classical continuum mechanics formulation especially for problems including discontinuities in the displacement field due to existence of cracks. The original formulation of peridynamics considers only translational degrees of freedom for material points and is capable of performing 3-dimensional analysis. This approach can be computationally expensive for certain geometries such as beam, plate and shell-type structures. To capture the correct deformation behaviour of such structures, additional rotational degrees of freedom may be necessary Such formulations are currently available in the literature. A new peridynamic formulation is presented suitable for analysis of functionally graded Timoshenko beams. To validate the current formulation, several benchmark problems are considered, and peridynamic results are compared against finite element analysis results
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