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Temperature Dependent Deformation

Temperature Dependent Deformation

In a nonhomogeneous rod made up of steel and brass, restrained at both ends and subjected to a temperature change, several steps are involved in calculating the stress and compressive load. Due to the problem's static indeterminacy, one end support is disconnected, allowing the rod to experience the temperature change freely. Next, an unknown force is applied at the free end, triggering deformations in the rod's steel and brass portions. These deformations are then calculated and added together...

Thermal Strain

Thermal Strain

Thermal strain is a concept that arises when we consider how temperature changes affect structures. Unlike the conventional assumption that structures remain constant under load, real-world scenarios often involve temperature fluctuations that can significantly impact these structures. Consider a homogeneous rod with a uniform cross-section resting freely on a flat horizontal surface. If the rod's temperature increases, the rod elongates. This elongation is proportional to the temperature...

Thermal Stress

Thermal Stress

If the temperature of an object is changed while it is prevented from expanding or contracting, the object is subjected to stress. The stress is compressive if the object expands in the absence of constraint and tensile if it contracts. This stress resulting from temperature change is known as thermal stress. It can be quite large and can cause damage. To avoid this stress, engineers may design components so they can expand and contract freely. For instance, on highways, gaps are deliberately...

Bending of Curved Members - Neutral Surface

Bending of Curved Members - Neutral Surface

In curved beams, unlike straight beams, the stress distribution across the cross-section is not uniform due to the beam's curvature. This non-uniformity arises because the neutral axis, where stress is zero, does not align with the centroid of the section. In a curved beam, the strain varies along the section as a function of the distance from the neutral axis.
Consider the curved member described in the previous lesson. According to Hooke's law, which relates stress to strain within the...

Internal Loadings in Structural Members: Problem Solving

Internal Loadings in Structural Members: Problem Solving

When designing or analyzing a structural member, it is important to consider the internal loadings developed within the member. These internal loadings include normal force, shear force, and bending moment. Engineers can ensure that the structural member can support the applied external forces by calculating these internal loadings.
To illustrate this, let's consider a beam OC of 5 kN, inclined at an angle of 53.13° with the horizontal and supported at both ends. Determine the internal loadings...

Shear on the Horizontal Face of a Beam Element

Shear on the Horizontal Face of a Beam Element

To understand shear on the flat side of a prismatic beam element, consider the vertical and horizontal shearing forces, and the normal forces, acting on the element. The element's upper (U) and lower (L) sections, which are divided by the beam's neutral axis, are examined. The equilibrium of these forces is determined by applying the equilibrium equation, which helps identify the horizontal shearing force. This force is directly related to the bending moments and the cross-section's first...

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Related Experiment Video

Updated: May 26, 2026

Easy and Accurate Mechano-profiling on Micropost Arrays

Easy and Accurate Mechano-profiling on Micropost Arrays

Published on: November 17, 2015

Negative Knudsen force on heated microbeams.

Taishan Zhu¹, Wenjing Ye, Jun Zhang

¹Department of Mechanical Engineering, The Hong Kong University of Science and Technology, Hong Kong.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|December 21, 2011

Summary

This summary is machine-generated.

This study confirms the existence of negative Knudsen forces in rarefied gases, a phenomenon previously unobserved. These forces, arising from thermal gradients, have potential applications in microscale sensing and actuation.

Related Experiment Videos

Last Updated: May 26, 2026

Easy and Accurate Mechano-profiling on Micropost Arrays

Easy and Accurate Mechano-profiling on Micropost Arrays

Published on: November 17, 2015

Area of Science:

Physics
Mechanical Engineering
Fluid Dynamics

Background:

Knudsen force arises from unbalanced thermal gradients in rarefied gases.
The force typically directs towards lower thermal gradients and diminishes at continuum and free-molecule limits.
Previous studies reported conflicting experimental and numerical results regarding negative Knudsen forces.

Purpose of the Study:

To confirm the existence of negative Knudsen forces using numerical simulation and theoretical analysis.
To analyze the asymptotic behavior of the Knudsen force near the collisionless limit.
To propose methods for enhancing negative Knudsen forces.

Main Methods:

Numerical simulation of Knudsen force.
Theoretical analysis of thermal gradients and force behavior.
Asymptotic analysis near the collisionless limit.

Main Results:

Confirmed the existence of negative Knudsen forces in specific rarefied gas conditions.
Provided an analytical expression for the leading term of the Knudsen force near the collisionless limit.
Identified approaches to enhance negative Knudsen forces.

Conclusions:

The negative Knudsen force phenomenon is validated through rigorous analysis.
Understanding this force opens avenues for novel microscale pressure sensing and actuation mechanisms.
Further research can optimize conditions for harnessing negative Knudsen forces.