Abstract
In this study, a peridynamic model is presented for a Mindlin plate resting on a Winkler elastic foundation. In order to achieve static and quasi-static loading conditions, direct solution of the peridynamic equations is utilised by directly assigning inertia terms to zero rather than using widely adapted adaptive dynamic relaxation approach. The formulation is verified by comparing against a finite element solution for transverse loading condition without considering damage and comparing against a previous study for pure bending of a Mindlin plate with a central crack made of polymethyl methacrylate material having negligibly small elastic foundation stiffness. Finally, the fracture behaviour of a pre-cracked Mindlin plate rested on a Winkler foundation subjected to transverse loading representing a floating ice floe interacting with sloping structures. Similar fracture patterns observed in field observations were successfully captured by peridynamics.
Highlights
In many engineering applications including marine, civil and transport engineering, analysis of structures resting on an elastic foundation is an important problem of interest [1]
In this study, a peridynamic model is presented for a Mindlin plate resting on a Winkler elastic foundation
In order to achieve static and quasi-static loading conditions, direct solution of the peridynamic equations is utilised by directly assigning inertia terms to zero rather than using widely adapted adaptive dynamic relaxation approach
Summary
In many engineering applications including marine, civil and transport engineering, analysis of structures resting on an elastic foundation is an important problem of interest [1]. Farjoo et al [3] investigated rolling contact fatigue cracks in railway tracks and used a simplified finite element model (FEM) and extended finite element method (XFEM) They observed that the elastic foundation leads to an additional bending stress which increases the crack growth rate significantly. Nobili et al [4] presented a full-field solution for the linear elastostatic problem of a homogeneous infinite Kirchhoff plate with a semi-infinite rectilinear crack resting on a two-parameter elastic foundation. They calculated stress intensity factors for both symmetric and skew-symmetric loading conditions. An alternative approach, peridynamics [5], is used for the analysis of a Mindlin plate resting on a Winkler type elastic foundation. Several verification and demonstration cases including a Mindlin plate with or without an initial crack subjected to transverse loading or pure bending loading conditions are presented to validate the current formulation and demonstrate its capabilities
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