Related Experiment Video
Updated: Apr 22, 2026
11:00
Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section
Published on: July 19, 2016
10.3K
A remark on constrained von Kármán theories
1Institut für Angewandte Mathematik, Universität Bonn, Bonn, Germany.
Proceedings. Mathematical, Physical, and Engineering Sciences
|October 9, 2014
Summary
This study derives the Euler-Lagrange equation for non-Euclidean convex constrained von Kármán theories. These equations are crucial for analyzing complex mechanical behaviors in engineering applications.
Area of Science:
- Mechanical Engineering
- Theoretical Physics
- Applied Mathematics
Background:
- Von Kármán theories are fundamental in analyzing the behavior of thin structures.
- Non-Euclidean geometry and convex constraints introduce complexities not covered by standard theories.
Purpose of the Study:
- To derive the Euler-Lagrange equation for non-Euclidean convex constrained von Kármán theories.
- To provide a mathematical framework for analyzing advanced structural mechanics problems.
Main Methods:
- Application of the Euler-Lagrange formalism.
- Incorporation of non-Euclidean geometric principles.
- Inclusion of convex constraints within the variational framework.
Main Results:
- A novel Euler-Lagrange equation tailored for the specified theoretical framework.
- The derived equation accounts for both geometric non-Euclideanism and constraint conditions.
Conclusions:
- The derived Euler-Lagrange equation offers a powerful tool for researchers and engineers.
- This work advances the understanding of mechanics for complex, constrained systems.
Related Concept Videos
01:17Bernoulli's Principle: Applications
6.0K
There are many devices and situations in which fluid flows at a constant height and so can be analyzed using Bernoulli's principle. These devices include, but are not limited to, entrainment devices and fluid flow measuring devices.
Entrainment devices use a high fluid speed to create low pressures and, thus, entrain one fluid into another. Some examples of these devices are given below:
Entrainment devices use a high fluid speed to create low pressures and, thus, entrain one fluid into another. Some examples of these devices are given below:
6.0K
01:01Bernoulli's Principle
9.0K
Bernoulli's equation incorporates how fluid pressure changes across a static, incompressible fluid by equating the kinetic energy contribution to zero. It is also helpful in analyzing horizontal flows in which the gravitational energy density is constant throughout. The latter equation is so useful that it is called Bernoulli's principle. According to Bernoulli's principle, the fluid pressure drops if the speed increases and vice versa.
Bernoulli's principle has several...
Bernoulli's principle has several...
9.0K
00:59Bernoulli's Equation
11.5K
In the middle of the nineteenth century, it was observed that two trains passing each other at a high relative speed get pulled towards each other. The same occurs when two cars pass each other at a high relative speed. The reason is that the fluid pressure drops in the region where the fluid speeds up. As the air between the trains or the cars increases in speed, its pressure reduces. The pressure on the outer parts of the vehicles is still the atmospheric pressure, while the resultant...
11.5K
01:16Energy Conservation and Bernoulli's Equation
7.1K
Applying the conservation of energy principle or the work-energy theorem to an incompressible, inviscid fluid in laminar, steady, irrotational flow leads to Bernoulli's equation. It states that the sum of the fluid pressure, potential, and kinetic energy per unit volume is constant along a streamline.
All the terms in the equation have the dimension of energy per unit volume. The kinetic energy per unit volume is called the kinetic energy density, and the potential energy per unit volume is...
All the terms in the equation have the dimension of energy per unit volume. The kinetic energy per unit volume is called the kinetic energy density, and the potential energy per unit volume is...
7.1K
01:16Bernoulli's Equation for Flow Normal to a Streamline
1.2K
Bernoulli's equation for flow normal to a streamline explains how pressure varies across curved streamlines due to the outward centrifugal forces induced by the fluid's curvature. The pressure is higher on the inner side of the curve, near the center of curvature, and decreases outward to balance these centrifugal forces.
The pressure difference depends on the fluid's velocity and radius of curvature. The pressure variation is minimal in flows with nearly straight streamlines. However, the...
The pressure difference depends on the fluid's velocity and radius of curvature. The pressure variation is minimal in flows with nearly straight streamlines. However, the...
1.2K
01:30Bernoulli's Equation for Flow Along a Streamline
1.6K
Bernoulli's equation relates the energy conservation in a fluid moving along a streamline. The equation applies to incompressible and inviscid fluids under steady flow. For such a flow, Newton's second law is applied to a small fluid element, which experiences forces due to pressure differences, gravity, and velocity variations. The force balance leads to the following form of Bernoulli's equation:
1.6K