DESIGN OF ASYMMETRIC GEAR AND ACCURATE BENDING STRESS ANALYSIS USING THE ES-PIM WITH TRIANGULAR MESH

2011 ◽  
Vol 08 (04) ◽  
pp. 759-772 ◽  
Author(s):  
S. WANG ◽  
G. R. LIU ◽  
G. Y. ZHANG ◽  
L. CHEN
Keyword(s):  
Stress Analysis ◽  
Interpolation Method ◽  
Triangular Mesh ◽  
Bending Stress ◽  
Pressure Angle ◽  
Point Interpolation Method ◽  
Standard Pressure ◽  
Point Interpolation ◽  
Edge Based ◽  
Accurate Stress Analysis

This paper proposes a novel design of an asymmetric gear that applies a larger pressure angle in the drive side and a standard pressure angle in the coast side via accurate stress analysis using the edge-based smoothed point interpolation method with triangular mesh (ES-PIM-(T3)). An asymmetric rack cutter is first developed. Then, the governing equations of the tooth profiles cut by the rack cutter are derived. Finally, five sets of asymmetric gears with the pressure angles of 20° /20°, 25°/20°, 30°/20°, 35°/20°, and 40°/20° are established to quantitatively check the stress distributions at the fillet of the drive side of these teeth. The best point for applying force in a static bending stress analysis and the best pressure angle in the drive side for a gear design are suggested.

An Edge-Based Smoothed Point Interpolation Method for Material Discontinuity

2012 ◽  
Vol 19 (1-3) ◽  
pp. 3-17 ◽  
Author(s):  
G. R. Liu ◽  
Z. Wang ◽  
G. Y. Zhang ◽  
Z. Zong ◽  
S. Wang
Keyword(s):  
Interpolation Method ◽  
Point Interpolation Method ◽  
Point Interpolation ◽  
Edge Based

EDGE-BASED SMOOTHED POINT INTERPOLATION METHODS

2008 ◽  
Vol 05 (04) ◽  
pp. 621-646 ◽  
Author(s):  
G. R. LIU ◽  
G. Y. ZHANG
Keyword(s):  
Degrees Of Freedom ◽  
Solid Mechanics ◽  
Interpolation Method ◽  
Weak Form ◽  
Dirichlet Boundary Conditions ◽  
Triangular Meshes ◽  
Weak Formulation ◽  
Point Interpolation Method ◽  
Point Interpolation ◽  
Edge Based

This paper formulates an edge-based smoothed point interpolation method (ES-PIM) for solid mechanics using three-node triangular meshes. In the ES-PIM, displacement fields are construed using the point interpolation method (polynomial PIM or radial PIM), and hence the shape functions possess the Kronecker delta property, facilitates the enforcement of Dirichlet boundary conditions. Strains are obtained through smoothing operation over each smoothing domain associated with edges of the triangular background cells. The generalized smoothed Galerkin weak form is then used to create the discretized system equations and the formation is weakened weak formulation. Four schemes of selecting nodes for interpolation using the PIM have been introduced in detail and ES-PIM models using these four schemes have been developed. Numerical studies have demonstrated that the ES-PIM possesses the following good properties: (1) the ES-PIM models have a close-to-exact stiffness, which is much softer than for the overly-stiff FEM model and much stiffer than for the overly-soft node-based smoothed point interpolation method (NS-PIM) model; (2) results of ES-PIMs are generally of superconvergence and "ultra-accurate"; (3) no additional degrees of freedom are introduced, the implementation of the method is straightforward, and the method can achieve much better efficiency than the FEM using the same set of triangular meshes.

A NOVEL QUADRATIC EDGE-BASED SMOOTHED CONFORMING POINT INTERPOLATION METHOD (ES-CPIM) FOR ELASTICITY PROBLEMS

2012 ◽  
Vol 09 (02) ◽  
pp. 1240033 ◽  
Author(s):  
X. XU ◽  
G. R. LIU ◽  
Y. T. GU
Keyword(s):  
Displacement Field ◽  
Degrees Of Freedom ◽  
Solid Mechanics ◽  
Interpolation Method ◽  
Weak Form ◽  
Shape Functions ◽  
Point Interpolation Method ◽  
Elasticity Problems ◽  
Point Interpolation ◽  
Edge Based

This paper formulates an edge-based smoothed conforming point interpolation method (ES-CPIM) for solid mechanics using the triangular background cells. In the ES-CPIM, a technique for obtaining conforming PIM shape functions (CPIM) is used to create a continuous and piecewise quadratic displacement field over the whole problem domain. The smoothed strain field is then obtained through smoothing operation over each smoothing domain associated with edges of the triangular background cells. The generalized smoothed Galerkin weak form is then used to create the discretized system equations. Numerical studies have demonstrated that the ES-CPIM possesses the following good properties: (1) ES-CPIM creates conforming quadratic PIM shape functions, and can always pass the standard patch test; (2) ES-CPIM produces a quadratic displacement field without introducing any additional degrees of freedom; (3) The results of ES-CPIM are generally of very high accuracy.

Elastic-plastic analysis of multi-material structures using edge-based smoothed point interpolation method

2018 ◽  
Vol 233 (4) ◽  
pp. 1289-1298
Author(s):  
SZ Feng ◽  
YH Cheng ◽  
AM Li
Keyword(s):  
Interpolation Method ◽  
Shape Functions ◽  
Integral Domains ◽  
Elastic Plastic ◽  
Plastic Analysis ◽  
Point Interpolation Method ◽  
Point Interpolation ◽  
Triangular Elements ◽  
Standard Finite Element Method ◽  
Edge Based

An edge-based smoothed point interpolation method is formulated to deal with elastic-plastic analysis of multi-material structures. The problem domain is discretized using triangular elements and field functions are approximated using point interpolation method shape functions. Edge-based smoothing domains are constructed based on the edge of triangular cells and smoothing operations are then performed in these integral domains. Numerical examples with different kinds of material models are investigated to fully verify the validity of the present method. It is observed that all edge-based smoothed point interpolation method models can achieve much better accuracy and higher convergence rate than the standard finite element method, when dealing with elastic-plastic analysis of multi-material structures.

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