Numerical Analysis of Quasistatic Contact between Rubber Roller and Rigid Roller

2012 ◽  
Vol 479-481 ◽  
pp. 1446-1452
Author(s):  
Bing Wang ◽  
Zhao Wu Wang
Keyword(s):  
Boundary Condition ◽  
Normal Load ◽  
Meshfree Method ◽  
Contact Problems ◽  
Numerical Examples ◽  
Rubber Roller ◽  
Dual Series Equations ◽  
Point Interpolation ◽  
Stress And Deformation ◽  
Feed Unit

A quasistatic and steady state contact problems of rubber roller and rigid roller is modeled by using a stress function in the form of series. The model is derived from the paper feed unit of duplicating machine. The point interpolation meshfree method (PIM) is applied to obtain the solution of the dual series equations resulting from the boundary condition. Stress and deformation for the rubber roller are obtained based on elasticity theory. Effects of rubber thickness and normal load are observed through the numerical examples. The observation show that the contact zone is changing with the normal load F and the rubber thickness has effect on the stress distribution. In addition, the study shows that the PIM method is an efficient and promising method for simulating the problem.

MESHFREE CELL-BASED SMOOTHED POINT INTERPOLATION METHOD USING ISOPARAMETRIC PIM SHAPE FUNCTIONS AND CONDENSED RPIM SHAPE FUNCTIONS

2011 ◽  
Vol 08 (04) ◽  
pp. 705-730 ◽  
Author(s):  
G. Y. ZHANG ◽  
G. R. LIU
Keyword(s):  
Computational Efficiency ◽  
Interpolation Method ◽  
Shape Functions ◽  
Generalized Gradient ◽  
Singularity Problem ◽  
Numerical Examples ◽  
Point Interpolation Method ◽  
Point Interpolation ◽  
System Equations ◽  
Gradient Smoothing

This paper presents two novel and effective cell-based smoothed point interpolation methods (CS-PIM) using isoparametric PIM (PIM-Iso) shape functions and condensed radial PIM (RPIM-Cd) shape functions respectively. These two types of PIM shape functions can successfully overcome the singularity problem occurred in the process of creating PIM shape functions and make the constructed CS-PIM models work well with the three-node triangular meshes. Smoothed strains are obtained by performing the generalized gradient smoothing operation over each triangular background cells, because the nodal PIM shape functions can be discontinuous. The generalized smoothed Galerkin (GS-Galerkin) weakform is used to create the discretized system equations. Some numerical examples are studied to examine various properties of the present methods in terms of accuracy, convergence, and computational efficiency.

A three-dimensional fusion prediction model for fractal rough surfaces in the sliding contact process

2014 ◽  
Vol 66 (3) ◽  
pp. 459-467
Author(s):  
Yan Lu ◽  
Zuomin Liu
Keyword(s):  
Temperature Rise ◽  
Rough Surfaces ◽  
Normal Load ◽  
Contact Process ◽  
Three Dimensional ◽  
Contact Problems ◽  
Sliding Contact ◽  
Content Type ◽  
Solution Methods ◽  
Account Temperature

Purpose – The purpose of this manuscript is to analyze the fusion micro-zone generated by typical rough surfaces and investigate the factors of thermal effects on the tribological performance of surface asperities and its results verified by the experiment. Design/methodology/approach – A three-dimensional fractal rough surfaces sliding contact model has been developed, which takes into account temperature rise and distribution. The finite-element method, Green's function method, thermal conduct theory and contact mechanics are used as the solution methods. Findings – The results yield insights into the effects of the sliding velocity, thermal properties of the material, normal load and surface roughness on the temperature rise of the sliding contact surface. It allows the specification of working conductions' properties to reduce fusion. Originality/value – The model is developed and described by using the features of the contact between one flat surface and one rough surface with varied topographies. It can be easily applied for solving the sliding contact problems with different working conditions and specified for designing the surface accuracy in the severe working condition.

scholarly journals A Meshfree Method for Signorini Problems Using Boundary Integral Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Yanlin Ren ◽  
Xiaolin Li
Keyword(s):  
Integral Equations ◽  
Boundary Integral Equations ◽  
Inequality Constraints ◽  
Meshfree Method ◽  
Boundary Integral ◽  
Unknown Boundary ◽  
Nodal Data ◽  
Fixed Point Equation ◽  
Point Equation ◽  
Point Interpolation

This paper presents a meshfree method for the numerical solution of Signorini problems. In this method, a projection iterative algorithm is used to convert the boundary inequality constraints into a fixed point equation. Then, the boundary value problem is reformulated as boundary integral equations and the unknown boundary variables are interpolated by the point interpolation scheme. Thus, only a nodal data structure on the boundary of a domain is required, and boundary conditions can be implemented directly and easily. The convergence of this method is verified theoretically. Numerical examples involving groundwater flow and electropainting problems are also provided to illustrate the performance and usefulness of the method.

scholarly journals A High-Order Compact 2D FDFD Method for Waveguides

2012 ◽  
Vol 2012 ◽  
pp. 1-6
Author(s):  
Gang Zheng ◽  
Bing-Zhong Wang
Keyword(s):  
Boundary Condition ◽  
Finite Difference ◽  
Surface Impedance ◽  
Transverse Field ◽  
High Order ◽  
Impedance Boundary Condition ◽  
Two Dimensional ◽  
Dispersion Characteristics ◽  
Impedance Boundary ◽  
Numerical Examples

A high-order compact two-dimensional finite-difference frequency-domain (2D FDFD) method is proposed for the analysis of the dispersion characteristics of waveguides. A surface impedance boundary condition (SIBC) for the high-order compact 2D FDFD method is also given to model lossy metal waveguides. Four transverse field components are involved in the final eigenequation. Numerical examples are given, which show that this high-order compact 2D FDFD method is more efficient than the low-order compact 2D FDFD method and has a less storage cost.

scholarly journals RBF-Based Meshless Method for Large Deflection of Elastic Thin Rectangular Plates with Boundary Conditions Involving Free Edges

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Mohammed M. Hussein Al-Tholaia ◽  
Husain Jubran Al-Gahtani
Keyword(s):  
Boundary Condition ◽  
Basis Function ◽  
Meshless Method ◽  
Iterative Procedure ◽  
Large Deflection ◽  
Free Edge ◽  
Thin Plates ◽  
Rectangular Plates ◽  
Numerical Examples ◽  
Complex Boundary

An RBF-based meshless method is presented for the analysis of thin plates undergoing large deflection. The method is based on collocation with the multiquadric radial basis function (MQ-RBF). In the proposed method, the resulting coupled nonlinear equations are solved using an incremental-iterative procedure. The accuracy and efficiency of the method are verified through several numerical examples. The inclusion of the free edge boundary condition proves that this method is accurate and efficient in handling such complex boundary value problems.

Laplace-Weighted Residual Method For Problems with Semi-Infinite Domain

2016 ◽  
Vol 7 (2) ◽  
Author(s):  
Babatunde Sunday Ogundare
Keyword(s):  
Boundary Condition ◽  
Approximate Solution ◽  
Numerical Method ◽  
Laplace Transformation ◽  
Transformation Method ◽  
Weighted Residual Method ◽  
Infinite Domain ◽  
Numerical Examples ◽  
Residual Method ◽  
Laplace Transformation Method

This paper presents an efficient numerical method for the approximate solution of problems involving boundary condition at infinity. The whole idea of the method is based on the combination of Laplace transformation method and weighted residual method. Numerical examples are given to show the validity and applicability of the proposed method and the results obtained are compared with other methods in the literatures.

Mathematical Basis of G Spaces

2016 ◽  
Vol 13 (04) ◽  
pp. 1641007 ◽  
Author(s):  
Meng Chen ◽  
Ming Li ◽  
G. R. Liu
Keyword(s):  
Finite Element ◽  
Finite Element Methods ◽  
Weak Formulation ◽  
Mathematical Basis ◽  
Numerical Examples ◽  
Interpolation Methods ◽  
Point Interpolation ◽  
Theoretical Frame ◽  
Lower Boundedness ◽  
Numerical Approaches

This paper represents some basic mathematic theories for G[Formula: see text] spaces of functions that can be used for weakened weak (W2) formulations, upon which the smoothed finite element methods (S-FEMs) and the smoothed point interpolation methods (S-PIMs) are based for solving mechanics problems. We first introduce and prove properties of G[Formula: see text] spaces, such as the lower boundedness and convergence of the norms, which are in contrast with H1spaces. We then prove the equivalence of the Gsnorms and its corresponding semi-norms. These mathematic theories are important and essential for the establishment of theoretical frame and the development of relevant numerical approaches. Finally, numerical examples are presented by using typical S-FEM models known as the NS-FEM and [Formula: see text]S-FEM to examine the properties of a smoothed method based on Gsspaces, in comparison with the standard FEM with weak formulation.

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