Elastic large deflection analysis of plates subjected to uniaxial thrust using meshfree Mindlin-Reissner formulation
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A meshfree approach for plate buckling/post-buckling problems in the case of uniaxial thrust is presented. A geometrical nonlinear formulation is employed using reproducing kernel approximation and stabilized conforming nodal integration. The bending components are represented by Mindlin–Reissner plate theory. The formulation has a locking-free property in imposing the Kirchhoff mode reproducing condition. In addition, in-plane deformation components are approximated by reproducing kernels. The deformation components are coupled to solve the general plate bending problem with geometrical non-linearity. In buckling/post-buckling analysis of plates, the in-plane displacement of the edges in their perpendicular directions is assumed to be uniform by considering the continuity of plating, and periodic boundary conditions are considered in assuming the periodicity of structures. In such boundary condition enforcements, some node displacements/rotations should be synchronized with others. However, the enforcements introduce difficulties in the meshfree approach because the reproducing kernel function does not have the so-called Kronecker delta property. In this paper, the multiple point constraint technique is introduced to treat such boundary conditions as well as the essential boundary conditions. Numerical studies are performed to examine the accuracy of the multiple point constraint enforcements. As numerical examples, buckling/post-buckling analyses of a rectangular plate and stiffened plate structure are presented to validate the proposed approach.
KeywordsMeshfree method Reproducing kernel approximation Large deflection analysis Multiple point constraint
This research was partially supported by JKA through its promotion funds from KEIRIN RACE. A part of the present research conducted by Satoyuki Tanaka was financially supported by The Research Council of Norway (RCN) through the Yggdrasil mobility programme.
- 26.Liew KM, Peng LX, Kitipornchai S (2006) Buckling analysis of corrugated plates using a mesh-free Galerkin method based on the first-order shear deformation theory. Comput Mech 38: 61–75Google Scholar
- 35.Belyschko T, Organ D, Krongauz Y (1995) A coupled finite element—element free Galerkin method. Comput Mech 17: 186–195Google Scholar
- 41.Wu CT, Koishi M, Skinner G, Shimamoto H (2008) A meshfree procedure for the microscopic simulation and design of rubber compounds and its application to multi-scale simulation of tires. Proceedings of WCCM8 and ECCOMAS 2008, pp. 1–2Google Scholar
- 42.Noguchi H, Zhang Z (2007) Analysis of large deformation of rubber-filler structures under periodic boundary conditions using an enhanced meshfree method. Proc Comput Mech Conf 20: 661–662Google Scholar
- 43.Liu WK, Jun S, Li S, Adee J, Belytschko T (1995) Reproducing kernel particle methods for structural dynamics. Int J Numer Method Eng 38:1655–1679 Google Scholar
- 45.MSC.Marc 2005r3, User’s GuideGoogle Scholar