Member-only story

Method of Dimensionality Reduction in Contact Mechanics and Friction

Carlos Fuentes

·11.6k Followers· Follow

Published in 2015th Edition Kindle Edition

5 min read · 4 weeks before

1.2k View Claps

87 Respond

Save

Listen

Contact mechanics is the study of the interaction between two or more solid bodies. It is a fundamental topic in engineering, and has applications in a wide variety of fields, including mechanical engineering, civil engineering, and materials science.

Method of Dimensionality Reduction in Contact Mechanics and Friction

5 out of 5

Language	:	English
File size	:	11091 KB
Text-to-Speech	:	Enabled
Screen Reader	:	Supported
Enhanced typesetting	:	Enabled
Word Wise	:	Enabled
Print length	:	283 pages

Friction is a force that opposes the relative motion of two solid bodies in contact. It is a complex phenomenon that depends on a number of factors, including the surface roughness, the material properties, and the contact geometry.

The method of dimensionality reduction (MDR) is a powerful technique that can be used to reduce the computational cost of contact mechanics simulations by Free Downloads of magnitude. MDR is based on the idea that the contact between two bodies can be represented by a set of low-dimensional manifolds. These manifolds can be used to reduce the number of degrees of freedom in the simulation, which in turn reduces the computational cost.

Theoretical Foundations of MDR

The theoretical foundations of MDR are based on the work of Charles Connell and his colleagues. Connell showed that the contact between two bodies can be represented by a set of low-dimensional manifolds. These manifolds are called the contact manifolds.

The contact manifolds are defined by the following equations:

\mathbf{r}_1 - \mathbf{r}_2 = \mathbf{0}

\mathbf{n}_1 \cdot (\mathbf{r}_1 - \mathbf{r}_2) = 0

where:

* \(\mathbf{r}_1\) is the position vector of a point on the first body * \(\mathbf{r}_2\) is the position vector of a point on the second body * \(\mathbf{n}_1\) is the unit normal vector to the first body at the point of contact * \(\mathbf{n}_2\) is the unit normal vector to the second body at the point of contact

The first equation defines the geometric constraint that the two bodies are in contact. The second equation defines the kinematic constraint that the two bodies are not penetrating each other.

The contact manifolds can be used to reduce the number of degrees of freedom in a contact mechanics simulation. This is because the contact manifolds are a set of low-dimensional surfaces. The number of degrees of freedom in a simulation is equal to the number of independent variables that are needed to describe the system. Therefore, by reducing the number of dimensions of the contact manifolds, we can reduce the number of degrees of freedom in the simulation.

Implementation of MDR in Contact Mechanics Codes

MDR has been implemented in a number of contact mechanics codes. These codes include:

* Abaqus * ANSYS * LS-DYNA * PAM-CRASH * RADIOSS

The implementation of MDR in these codes varies. However, the general approach is the same. First, the contact manifolds are identified. Then, the number of degrees of freedom in the simulation is reduced by using the contact manifolds to constrain the motion of the bodies.

Examples of MDR Applications

MDR has been used to solve a wide variety of contact mechanics problems. These problems include:

* The contact of a wheel with a road surface * The contact of a gear with a gear tooth * The contact of a ball bearing with a raceway * The contact of a human foot with a shoe

MDR has been shown to significantly reduce the computational cost of these simulations. In some cases, MDR has reduced the computational cost by Free Downloads of magnitude.

MDR is a powerful technique that can be used to reduce the computational cost of contact mechanics simulations by Free Downloads of magnitude. MDR is based on the idea that the contact between two bodies can be represented by a set of low-dimensional manifolds. These manifolds can be used to reduce the number of degrees of freedom in the simulation, which in turn reduces the computational cost.

MDR has been implemented in a number of contact mechanics codes. These codes include Abaqus, ANSYS, LS-DYNA, PAM-CRASH, and RADIOSS. MDR has been used to solve a wide variety of contact mechanics problems, including the contact of a wheel with a road surface, the contact of a gear with a gear tooth, the contact of a ball bearing with a raceway, and the contact of a human foot with a shoe. MDR has been shown to significantly reduce the computational cost of these simulations. In some cases, MDR has reduced the computational cost by Free Downloads of magnitude.

Method of Dimensionality Reduction in Contact Mechanics and Friction

5 out of 5