Meshfree flat-shell formulation for evaluating linear buckling loads and mode shapes of structural plates

Yoshida Ken-ichiro

Sadamoto Shota

Setoyama Yu

Tanaka Satoyuki

Bui Tinh Quoc

Murakami Chikahisa

Yanagihara Daisuke

Journal of Marine Science and Technology

We concentrate our attention on developing a meshfree flat-shell formulation for evaluating linear buckling loads and mode shapes (modes) of structural plates employing an eigen value analysis. A Galerkin-based shear deformable flat-shell formulation for that purpose is proposed. The in-plane and out-of-plane deformations are interpolated using the reproducing kernel particle method (RKPM), while the two membrane deformations, and the three deflection and rotational components are, respectively, approximated through a plane stress condition and Mindlin–Reissner plate theory. The meshfree discretization by which, as a consequence, constructs five degrees of freedom per node. A generalized eigenvalue problem for the solution of buckling loads and modes of the structural plates is then described. The stiffness matrices of the linear buckling analysis are numerically integrated based on the stabilized conforming nodal integration (SCNI) and sub-domain stabilized conforming integration (SSCI). The RKPM and SCNI/SSCI based on Galerkin meshfree formulation, i.e., stabilized meshfree Galerkin method, can overcome the shear locking problem by imposing the Kirchhoff mode reproducing condition. In addition, a singular kernel (SK) function is included in the meshfree interpolation functions to accurately impose the essential boundary conditions. The merits of the developed formulation are demonstrated through numerical buckling experiments of several examples of plates, by which the accuracy and performance of the proposed method are investigated and discussed in detail. It indicates from our numerical results of buckling loads and modes that the proposed meshfree formulation is accurate and useful in the simulation of buckling problems of structural stiffened plates.

Buckling

Meshfree

FEM

Stiffened plate

eng

Springer Nature

This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: https://doi.org/10.1007/s00773-017-0433-2

This is not the published version. Please cite only the published version.

この論文は出版社版ではありません。引用の際には出版社版をご確認、ご利用ください。

[DOI] https://doi.org/10.1007/s00773-017-0433-2 isVersionOf

日本学術振興会

Japan Society for the Promotion of Science

[Crossref Funder] https://doi.org/10.13039/501100001691

多軸応力影響と繰り返し載荷影響を考慮した船体桁の縦曲げ最終強度評価に関する研究 研究課題

Ultimate longitudinal bending strength of ship hull girder considering multi-axial stress and repeated loading effects Research Project

15H02328

日本学術振興会

Japan Society for the Promotion of Science

[Crossref Funder] https://doi.org/10.13039/501100001691

建造から品質・安全性・寿命まで評価可能な四次元可視化CAEシステムの開発 研究課題

Development of 4 Dimensional CAE Visualization System for Assessment of Quality and Safety of Structures through Life Time Starting from Production

15H04212

日本学術振興会

Japan Society for the Promotion of Science

[Crossref Funder] https://doi.org/10.13039/501100001691

き裂を有するパネルの圧壊挙動メカニズムの解明 研究課題

Collapse Behavior of Rectangular Panel with Crack Damage.

15K06632