Eigenvalue Analysis of Thin Plate With Complicated Shapes by a Novel Mesh-Free Method

Abstract

Further development of a novel mesh-free method for eigenvalue analysis of thin plate structures with complicated shapes is presented in this paper. A mesh-free method used the moving Kriging interpolation technique for constructing the shape functions, which possess the Kronecker's delta property, is formulated. Thus, it makes the present method efficient in enforcing the essential boundary conditions and none of any special techniques are required. The present plate theory followed the classical Kirchhoff's assumption and the deflection is in general approximated through the moving Kriging interpolation. Also, the mesh-free formulations for the vibration problem are formed in a simple way as finite element methods. The orthogonal transformation technique is used to implement the essential boundary conditions in the eigenvalue equation. A standard weak form is adopted to discrete the governing partial differential equation of plates. Some numerical examples are attempted to demonstrate the applicability, the effectiveness, and the accuracy of the method.

Moving Kriging reconstruction for high-order finite volume computation of compressible flows

“…This is very similar to the selection of the shape parameters for MLS reconstructions [21]. Recently, Bui and Nguyen [43] used a MK-based meshfree method for the eigenvalue analysis of Kirchhoff thin plate structures with complex geometric shapes. Improved mesh-free approximations were developed by Shaw et al [44] using a Kriging based errorreproducing and interpolating kernel method (ERIKM).…”

“…In order to overcome the difficulty of accurately imposing essential boundary conditions in element-free Galerkin (EFG) methods, Gu [36] proposed to build EFG shape functions using moving Kriging (MK) interpolation instead of MLS approximations for solving the weak form of the steady-state heat conduction problem. This approach was then deployed for various applications in solid mechanics [29,[37][38][39][40][41][42][43] including both static and dynamic structural analysis. Moving Kriging interpolation requires the choice of a correlation parameter which depends from the problem of interest.…”

A Reduced Order Model Based on Block Arnoldi Method for Aeroelastic System

“…To reduce the simulation cost and storage requirement, reduced-order models (ROMs) are needed to develop a simplified mathematical model that can captures the dominant dynamic of the original system. In structural dynamics field, eigenvalue analysis [Bui and Nguyen, 2011] and then mode superposition method are widely used in industry, in which a limited number of free vibration modes of the structure is used to represent the displacement pattern. However, there are some important points to note on the expansion procedures used in practice.…”