A three-dimensional element-free framework for coupled mechanical-diffusion induced nonlinear deformation of polymeric gels using the IMLS-Ritz method

2015 ◽  
Vol 296 ◽  
pp. 232-247 ◽  
Author(s):  
D.M. Li ◽  
L.W. Zhang ◽  
K.M. Liew
Keyword(s):  
Nonlinear Deformation ◽  
Ritz Method ◽  
Three Dimensional ◽  
Polymeric Gels ◽  
Mechanical Diffusion ◽  
Dimensional Element ◽  
Element Free

Free Vibrations of Thick, Complete Conical Shells of Revolution From a Three-Dimensional Theory

2005 ◽  
Vol 72 (5) ◽  
pp. 797-800 ◽  
Author(s):  
Jae-Hoon Kang ◽  
Arthur W. Leissa
Keyword(s):  
Ritz Method ◽  
Three Dimensional ◽  
Axial Direction ◽  
Free Vibrations ◽  
Mode Shapes ◽  
Vibration Frequencies ◽  
Shells Of Revolution ◽  
Dimensional Theory ◽  
Conical Shells ◽  
Cylindrical Coordinate

A three-dimensional (3D) method of analysis is presented for determining the free vibration frequencies and mode shapes of thick, complete (not truncated) conical shells of revolution in which the bottom edges are normal to the midsurface of the shells based upon the circular cylindrical coordinate system using the Ritz method. Comparisons are made between the frequencies and the corresponding mode shapes of the conical shells from the authors' former analysis with bottom edges parallel to the axial direction and the present analysis with the edges normal to shell midsurfaces.

ELEMENT-FREE METHODS VS. MESH-LESS CAE

2006 ◽  
Vol 03 (04) ◽  
pp. 445-464 ◽  
Author(s):  
HIDEYUKI SAKURAI
Keyword(s):  
Mesh Generation ◽  
Flow Analysis ◽  
Three Dimensional ◽  
Generation Task ◽  
3D Objects ◽  
Computer Aided ◽  
Analysis System ◽  
Mesh Less ◽  
Element Free ◽  
Cae System

Element-free methods (EFreeMs) are expected to eliminate the mesh generation task. However, a computer aided engineering (CAE) system by EFreeM for complex three-dimensional (3D) objects has not yet been developed. This paper discusses the obstacles to the CAE and way to solve them. A 3D groundwater flow analysis system with an EFreeM is presented as a practical CAE. In the system, instead of pursuing mesh-less CAE, a unique mesh is employed to achieve the practical CAE. Some 3D examples show the performance and usefulness of the system. Two serious drawbacks of the EFreeM are also discussed from the viewpoint of the practical CAE.

Three-Dimensional Vibration Analysis of Twisted Cylinder With Sectorial Cross Section

2013 ◽  
Vol 80 (2) ◽  
Author(s):  
D. Zhou ◽  
S. H. Lo
Keyword(s):  
Cross Section ◽  
Chebyshev Polynomial ◽  
Numerical Solutions ◽  
Twist Angle ◽  
Ritz Method ◽  
Three Dimensional ◽  
Cylindrical Domain ◽  
Linear Elasticity Theory ◽  
Boundary Functions ◽  
Polynomial Series

The three-dimensional (3D) free vibration of twisted cylinders with sectorial cross section or a radial crack through the height of the cylinder is studied by means of the Chebyshev–Ritz method. The analysis is based on the three-dimensional small strain linear elasticity theory. A simple coordinate transformation is applied to map the twisted cylindrical domain into a normal cylindrical domain. The product of a triplicate Chebyshev polynomial series along with properly defined boundary functions is selected as the admissible functions. An eigenvalue matrix equation can be conveniently derived through a minimization process by the Rayleigh–Ritz method. The boundary functions are devised in such a way that the geometric boundary conditions of the cylinder are automatically satisfied. The excellent property of Chebyshev polynomial series ensures robustness and rapid convergence of the numerical computations. The present study provides a full vibration spectrum for thick twisted cylinders with sectorial cross section, which could not be determined by 1D or 2D models. Highly accurate results presented for the first time are systematically produced, which can serve as a benchmark to calibrate other numerical solutions for twisted cylinders with sectorial cross section. The effects of height-to-radius ratio and twist angle on frequency parameters of cylinders with different subtended angles in the sectorial cross section are discussed in detail.

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