A Kirchhoff plate formulation in a state-based peridynamic framework

Abstract

In recent years, there has been rapid progress on peridynamics. It has been applied to many different material systems, used for coupled field analysis and is suitable for multi-scale analysis. This study mainly focuses on peridynamic analysis for plate-type structures. For this purpose, a new peridynamic Kirchhoff plate is developed. The new formulation is computationally efficient by having only one degree of freedom for each material point. Moreover, it is based on the state-based peridynamic formulation, which does not impose any limitation on material constants. After presenting how to impose simply supported and clamped boundary conditions in this new formulation, several numerical studies are considered to demonstrate the accuracy and capability of the proposed formulation.

Analysis of Functionally Graded Timoshenko Beams by Using Peridynamics

“…(7) can be written in nonlocal PD form for a particular material point k. To achieve this, it is necessary to transform all differential terms into equivalent PD forms in accordance with the form of PD strain energy density given in Eq. (17). As derived in Appendix 1, the strain energy density function of the material point k and its family member j can be expressed as:…”

Model order reduction of linear peridynamic systems using static condensation

“…However, the fact that the expansion of equation 20exactly gives the expression in equation (15) shows that this assumption does not affect the reduced stiffness matrix and the reduced force density vector. The condensed peridynamic equilibrium equations as represented by equation (14) yields the exact solution of the peridynamic model at the retained material points, as would be obtained if we used the detailed model.…”

“…Since its introduction [8], peridynamic theory has been successfully deployed to study a range of engineering systems [9][10][11][12][13][14][15]. However, the use of peridynamic theory in solving practical engineering problems implies dealing with systems with very large DoFs.…”

Derivation of dual-horizon state-based peridynamics formulation based on Euler–Lagrange equation

“…PD can also be used for fluid flow simulations [27,28]. Peridynamic formulations for simplified structures, including beams [29,30], plates [31] and shells [32], are also available in the literature. With the advancement of additive manufacturing technologies, fabrication of complex materials such as microstructured materials [33][34][35][36][37][38][39][40][41][42][43][44] is possible.…”