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Related Concept Videos

Three-Dimensional Force System:Problem Solving01:30

Three-Dimensional Force System:Problem Solving

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A three-dimensional force system refers to a scenario in which three forces act simultaneously in three different directions. This type of problem is commonly encountered in physics and engineering, where it is necessary to calculate the resultant force on the system, which can then be used to predict or analyze the behavior of the object or structure under consideration.
To solve a three-dimensional force system, first resolve each force into its respective scalar components. Do this using...
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Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
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In mechanical engineering, a three-dimensional force system is a system of forces acting in three dimensions, with forces applied along the x, y, and z coordinate axes. The three-dimensional force system is an important concept in mechanical engineering, as it allows engineers to understand and analyze the behavior of objects and structures in three dimensions. By understanding the forces acting on a system, engineers can design more efficient and effective mechanical systems that can withstand...
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A rigid body is said to be in dynamic equilibrium when both its linear and angular acceleration are zero, relative to an inertial frame of reference. This means that a body in equilibrium can be moving, but only when its linear and angular velocities are constant. A rigid body is said to be in static equilibrium when it is at rest in the selected frame of reference. The distinction between static equilibrium (e.g., a state of rest) and dynamic equilibrium (e.g, a state of uniform motion) is...
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Two-Dimensional Force System: Problem Solving01:29

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Solving problems related to two-dimensional force systems is an essential aspect of mechanics and engineering. By applying the principles of vector analysis and force equilibrium, one can determine the effect of multiple forces acting on an object in a two-dimensional space.
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Static equilibrium is a special case in mechanics that is very important in everyday life. It occurs when the net force and the net torque on an object or system are both zero. This means that both the linear and angular accelerations are zero. Thus, the object is at rest, or its center of mass is moving at a constant velocity. However, this does not mean that no forces are acting on the object within the system. In fact, there are very few scenarios on Earth in which no forces are acting upon...
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Computational Modeling of Retinal Neurons for Visual Prosthesis Research - Fundamental Approaches
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Deep learning-accelerated computational framework based on Physics Informed Neural Network for the solution of linear

Arunabha M Roy1, Rikhi Bose2, Veera Sundararaghavan3

  • 1Department of Materials Science and Engineering, Texas A&M University, 3003 TAMU, College Station, TX 77843, USA.

Neural Networks : the Official Journal of the International Neural Network Society
|March 26, 2023
PubMed
Summary
This summary is machine-generated.

This study introduces a deep learning (DL) framework using Physics Informed Neural Networks (PINNs) for elasticity problems. The novel approach achieves accurate and robust solutions, outperforming traditional methods with faster computation.

Keywords:
Artificial neural networks (ANNs)Bi-harmonic equationsDeep learningLinear elasticityPhysics Informed Neural Networks (PINNs)

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Area of Science:

  • Computational mechanics
  • Solid mechanics
  • Deep learning applications

Background:

  • Traditional computational methods for elasticity problems can be computationally intensive.
  • Physics Informed Neural Networks (PINNs) offer a data-driven approach to solve differential equations.

Purpose of the Study:

  • To develop an efficient and robust deep learning computational framework for linear continuum elasticity problems.
  • To integrate physical laws and data-driven insights for enhanced accuracy.

Main Methods:

  • Utilized Physics Informed Neural Networks (PINNs) with a multi-objective loss function.
  • Employed multiple independent Artificial Neural Networks (ANNs) to approximate field variables.
  • Incorporated residuals of governing PDEs, constitutive relations, boundary conditions, and data-driven fitting terms.

Main Results:

  • Successfully solved benchmark elasticity problems, including the Airy solution and Kirchhoff-Love plate problem.
  • Demonstrated superior accuracy and robustness compared to existing methods.
  • Achieved excellent agreement with analytical solutions.

Conclusions:

  • The proposed framework combines classical physics-based knowledge with deep learning capabilities.
  • The developed models offer significant computational speed-up with minimal parameters.
  • The framework is lightweight, accurate, robust, and adaptable to various computational platforms.