Locking alleviation technique for the peridynamic Reissner–Mindlin plate model: the developed reduced integration method

Peridynamics (PD) differs from classical continuum mechanics and other nonlocal theories that do not involve spatial derivatives of the displacement field. PD is based on the integral equation instead of differential equations to handle discontinuities and other singularities. In this paper, the sta...

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Bibliographic Details
Published inArchive of applied mechanics (1991) Vol. 93; no. 3; pp. 1167 - 1188
Main Authors Bai, Ruqing, Liang, Guan, Naceur, Hakim, Zhao, Jinglei, Yi, Jin, Luo, Jun, Wang, Li, Pu, Huayan
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.03.2023
Springer Nature B.V
Subjects
Classical Mechanics
Computing time
Continuum mechanics
Differential equations
Engineering
Integral equations
Kinematics
Locking
Mindlin plates
Original
Shear deformation
Theoretical and Applied Mechanics
Thick plates
Thin plates
Standard peridynamics (standard PD)
Reissner–Mindlin plate
Shear locking
Peridynamics (PD)
Reduced peridynamics (reduced PD)
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Summary:Peridynamics (PD) differs from classical continuum mechanics and other nonlocal theories that do not involve spatial derivatives of the displacement field. PD is based on the integral equation instead of differential equations to handle discontinuities and other singularities. In this paper, the standard peridynamic Reissner–Mindlin plate model (standard PD) accounting for the shear deformation is chosen to describe the thick plate kinematics. Unfortunately, when applied to very thin plate structures, the standard PD encounters shear locking phenomenon, leading to incorrect solutions. This shear locking can be successfully alleviated using the developed reduced or selective integration method. In particular, this technique has been implemented in the standard PD, which allows an accurate result for a wide range from very thin ( L / t > 10 3 ) to thick ( L / t ∼ 10 ) plate structures. It can also accelerate the computational time for particular dynamic problems using fewer neighboring integration particles. Several numerical examples are solved to demonstrate the effectiveness of the proposed method for modeling plate structures.
ISSN:0939-1533
1432-0681
DOI:10.1007/s00419-022-02320-0