Fast Fourier Transform Based Numerical Methods for Elasto-Plastic Contacts of Nominally Flat Surfaces

2008 ◽  
Vol 75 (1) ◽  
Author(s):  
W. Wayne Chen ◽  
Shuangbiao Liu ◽  
Q. Jane Wang
Keyword(s):  
Fourier Transform ◽  
Numerical Methods ◽  
Fast Fourier Transform ◽  
Analytical Solutions ◽  
Three Dimensional ◽  
Stress And Strain ◽  
Two Dimensional ◽  
Response Functions ◽  
Strain Fields ◽  
Flat Surfaces

This paper presents a three-dimensional numerical elasto-plastic model for the contact of nominally flat surfaces based on the periodic expandability of surface topography. This model is built on two algorithms: the continuous convolution and Fourier transform (CC-FT) and discrete convolution and fast Fourier transform (DC-FFT), modified with duplicated padding. This model considers the effect of asperity interactions and gives a detailed description of subsurface stress and strain fields caused by the contact of elasto-plastic solids with rough surfaces. Formulas of the frequency response functions (FRF) for elastic/plastic stresses and residual displacement are given in this paper. The model is verified by comparing the numerical results to several analytical solutions. The model is utilized to simulate the contacts involving a two-dimensional wavy surface and an engineering rough surface in order to examine its capability of evaluating the elasto-plastic contact behaviors of nominally flat surfaces.

On the Displacement of a Two-Dimensional Eshelby Inclusion of Elliptic Cylindrical Shape

2017 ◽  
Vol 84 (7) ◽  
Author(s):  
Xiaoqing Jin ◽  
Xiangning Zhang ◽  
Pu Li ◽  
Zheng Xu ◽  
Yumei Hu ◽  
...  
Keyword(s):  
Closed Form ◽  
Three Dimensional ◽  
Companion Paper ◽  
Stress And Strain ◽  
Cylindrical Shape ◽  
Two Dimensional ◽  
Elasticity Solution ◽  
Strain Fields ◽  
Closed Form Solutions ◽  
Eshelby Inclusion

In a companion paper, we have obtained the closed-form solutions to the stress and strain fields of a two-dimensional Eshelby inclusion. The current work is concerned with the complementary formulation of the displacement. All the formulae are derived in explicit closed-form, based on the degenerate case of a three-dimensional (3D) ellipsoidal inclusion. A benchmark example is provided to validate the present analytical solutions. In conjunction with our previous study, a complete elasticity solution to the classical elliptic cylindrical inclusion is hence documented in Cartesian coordinates for the convenience of engineering applications.

Three-Dimensional Non-Linear Shell Theory for Flexible Multibody Dynamics

2015 ◽  
Author(s):  
S. L. Han ◽  
O. A. Bauchau
Keyword(s):  
Shell Theory ◽  
Three Dimensional ◽  
Reduction Process ◽  
Flexible Multibody Dynamics ◽  
Stress And Strain ◽  
Two Dimensional ◽  
Governing Equations ◽  
Strain Fields ◽  
Flexible Multibody ◽  
Material Line

In flexible multibody systems, many components are approximated as shells. Classical shell theories, such as Kirchhoff or Reissner-Mindlin shell theory, form the basis of the analytical development for shell dynamics. While such approach is capable of capturing the kinetic energy of the system accurately, it cannot represent the strain energy adequately. For instance, it is well known from three-dimensional elasticity theory that the normal material line will warp under load for laminated composite shells, leading to three-dimensional deformations that generate complex stress states. To overcome this problem, a novel three-dimensional shell theory is proposed in this paper. Kinematically, the problem is decomposed into an arbitrarily large rigid-normal-material-line motion and a warping field. The sectional strains associated with the rigid-normal-material-line motion and the warping field are assumed to remain small. As a consequence of this kinematic decomposition, the governing equations of the problem fall into two distinct categories: the global equations describing geometrically exact shells and the local equations describing local deformations. The governing equations for geometrically exact shells are nonlinear, two-dimensional equations, whereas the local equations are linear, one dimensional, provide the detailed distribution of three-dimensional stress and strain fields. Based on a set of approximated solutions, the local equations is reduced to the corresponding global equations. In the reduction process, a 9 × 9 sectional stiffness matrix can be found, which takes into account the warping effects due to material heterogeneity. In the recovery process, three-dimensional stress and strain fields at any point in the shell can be recovered from the two-dimensional shell solution. The proposed method proposed is valid for anisotropic shells with arbitrarily complex through-the-thickness lay-up configuration.

A Fast Method for Solving Contact Plasticity in a Half Space

2011 ◽  
Author(s):  
Zhanjiang Wang ◽  
Xiaoqing Jin ◽  
Shuangbiao Liu ◽  
Leon M. Keer ◽  
Jian Cao ◽  
...  
Keyword(s):  
Fourier Transform ◽  
Residual Stresses ◽  
Fast Fourier Transform ◽  
Half Space ◽  
Three Dimensional ◽  
New Method ◽  
Fast Method ◽  
Discrete Convolution ◽  
Influence Coefficients ◽  
The One

This paper presents a new method of contact plasticity analysis based on Galerkin vectors to solve the eigenstresses due to eigenstrain. The influence coefficients relating eigenstrains to eigenstresses thus can be divided into four terms the one due to the eigenstrains in the full space, others due to the mirrored eigenstrains in the mirror half space. Each term can be solved fast and efficient by using the three-dimensional discrete convolution and fast Fourier transform (DC-FFT) or the three-dimensional discrete correlation and fast Fourier transform (DCR-FFT). The new method is used to analyze the contact plastic residual stresses in half space.

An Efficient Iterative Algorithm for Accurately Calculating Impulse Response Functions in Modal Testing

2011 ◽  
Vol 133 (6) ◽  
Author(s):  
J. M. Liu ◽  
W. D. Zhu ◽  
Q. H. Lu ◽  
G. X. Ren
Keyword(s):  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Iterative Algorithm ◽  
Impulse Response ◽  
Mimo Systems ◽  
Spectral Lines ◽  
Modal Testing ◽  
Impulse Response Functions ◽  
Response Functions ◽  
Modal Parameter

Impulse response functions (IRFs) and frequency response functions (FRFs) are bases for modal parameter identification of single-input, single-output (SISO) and multiple-input, multiple-out (MIMO) systems, and the two functions can be transformed from each other using the fast Fourier transform and the inverse fast Fourier transform. An efficient iterative algorithm is developed in this work to directly and accurately calculate the IRFs of SISO and MIMO systems in the time domain using relatively short input and output data series. The iterative algorithm can avoid the time-consuming inversion of a large matrix in the conventional least-square method for calculating an IRF, greatly reducing the computation time. In addition, a fitting index and an error energy decreasing coefficient are introduced to evaluate the accuracy in calculating an IRF and to provide the termination criterion for the iterative algorithm. A new coherence function is also introduced to evaluate the accuracy of calculated IRFs and FRFs at different spectral lines. Two examples are given to illustrate the effectiveness and efficiency of the methodology.

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