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Related Concept Videos

Temperature Dependent Deformation01:12

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...
Deformations in a Transverse Cross Section01:21

Deformations in a Transverse Cross Section

When a material is subjected to uniaxial stress, it elongates or contracts in the direction of the applied force, and also undergoes changes in the perpendicular directions. This behavior is crucial for understanding how materials behave under stress and is governed by mechanical properties such as Poisson's ratio v, which measures the ratio of transverse strain to axial strain.
As the material stretches, it expands or contracts in orthogonal directions to the load. This phenomenon varies...
Thermal Strain01:19

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 Stress01:09

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...
Deformations in a Symmetric Member in Bending01:18

Deformations in a Symmetric Member in Bending

When analyzing the deformation of a symmetric prismatic member subjected to bending by equal and opposite couples, it becomes clear that as the member bends, the originally straight lines on its wider faces curve into circular arcs, with a constant radius centered at a point known as Point C. This phenomenon helps to understand the stress and strain distribution within the member more clearly.
When the member is segmented into tiny cubic elements, it is observed that the primary stress...
Plastic Deformation in Circular Shafts01:20

Plastic Deformation in Circular Shafts

When materials are subjected to forces that surpass their yield strength, they undergo a process known as plastic deformation. This results in a permanent alteration or strain in their structure. This concept can be specifically applied to circular shafts, where the deformation leads to a change in its shape. The precise evaluation of this plastic deformation requires understanding the stress distribution within the circular shaft, which is achieved by calculating the maximum shearing stress in...

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The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry
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Published on: August 12, 2013

Thermal deformations of solid mirrors.

A J Malvick

    Applied Optics
    |January 23, 2010
    PubMed
    Summary
    This summary is machine-generated.

    This study presents tensor equations for elasticity with temperature effects in nonorthogonal coordinates, suitable for dynamic relaxation methods. Results are computed for various circular mirror and lens configurations under different temperature distributions.

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    Area of Science:

    • Solid mechanics
    • Thermal stress analysis
    • Computational mechanics

    Background:

    • Elasticity equations are fundamental in solid mechanics.
    • Incorporating thermal effects is crucial for accurate structural analysis.
    • Nonorthogonal coordinate systems are necessary for complex geometries like circular mirrors.

    Purpose of the Study:

    • To present tensor equations of elasticity including temperature terms in nonorthogonal coordinates.
    • To adapt these equations for the dynamic relaxation method.
    • To analyze structures with circular solid mirrors or lenses.

    Main Methods:

    • Formulation of tensor equations for elasticity with thermal considerations.
    • Adaptation of equations for the dynamic relaxation numerical technique.
    • Application to a nonorthogonal coordinate system accommodating circular geometries.

    Main Results:

    • The developed equations are suitable for dynamic relaxation analysis.
    • A coordinate system for circular mirrors/lenses is described.
    • Computed results for several prescribed temperature distributions are provided.

    Conclusions:

    • The presented method effectively handles thermal stresses in complex geometries.
    • Dynamic relaxation is a viable approach for solving these elasticity problems.
    • The study provides a framework for analyzing optical components under thermal loads.