Modeling and simulation of different and representative engineering problems using Network Simulation Method

Area of Science:

• Computational Engineering and Applied Mathematics
• Numerical Methods in Engineering
• Solid Mechanics and Tribology

Background:

• Engineering problems often involve complex, non-linear differential equations.
• Existing numerical methods may require simplifying assumptions like linearization.
• Accurate simulation of phenomena such as dry friction and moving fronts is crucial.

Purpose of the Study:

• To present a novel network method for solving a class of non-linear engineering problems.
• To demonstrate the application of this method to problems in atomic dry friction, moving fronts, and elastic/solid mechanics.
• To validate the reliability and accuracy of the network method against established techniques and experimental data.

Main Methods:

• Formulation of engineering problems as systems of non-linear, coupled or uncoupled differential equations.
• Numerical solution using the network method, implemented on standard electrical circuit simulation software.
• Analysis of model sensitivity to various parameter values without variable linearization.

Main Results:

• The network method successfully provides all problem variables for diverse engineering simulations.
• The model demonstrates high sensitivity to parameters, yet maintains accuracy without linearization.
• Results obtained via the network method show strong agreement with common numerical techniques and experimental data.

Conclusions:

• The network method offers a robust and reliable approach for simulating complex engineering problems.
• This simulation technique is versatile, applicable to friction, mechanics, and moving front problems.
• The use of standard circuit simulation software makes the method accessible and practical.