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PDE top 20 songs of 2024 – at number 19
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PDE top 20 songs of 2024 – at number 20
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Equations of motion explained
The equations of motion describe the mathematical relationship between the motion of an object and the forces acting on it. They are fundamental in physics and engineering, providing a framework to analyse how objects move under various conditions. 1. Newton’s Second Law (General Form) This is the foundation of the equations of motion:Where: It states…
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Stress concentrations explained
Stress concentrations occur when stress in a material is increased due to the presence of geometrical irregularities like holes, notches, or sharp corners. These irregularities cause localised “hot spots” where stress is much higher than in the surrounding material, which can lead to failure. Stress concentrations are especially critical in engineering design since they can…
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Plasticity explained
Plasticity is the property of a material that allows it to undergo permanent deformation under an applied load, beyond its elastic limit, without fracture. It is a crucial concept in solid mechanics, particularly in materials that can endure large deformations, like metals. 1. Elastic vs. Plastic Deformation 2. Yield Criteria To determine when a material begins to…
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Hertzian contact explained
Hertzian contact stresses describe the localised stress distribution that occurs when two curved surfaces (e.g., spheres, cylinders, gears) are pressed against each other. This theory, developed by Heinrich Hertz in the late 19th century, is used to predict the behaviour of materials under compressive loads where contact is made over a small area, like in…
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Eccentric column buckling
When the geometrical centre of area (centroid) of a column does not correspond to the load path, the situation introduces eccentric loading, which can lead to additional bending moments along with axial compression. Here’s how you can approach the buckling analysis in this case: 1. Determine Eccentricity (e): 2. Calculate the Total Stress: Where: 3. Account for Buckling Using…
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What are response surface models?
Response Surface Models (RSM) are a set of statistical and mathematical techniques used for modeling and analysing problems where a response of interest is influenced by several variables. The primary purpose of RSM is to optimise this response, often referred to as the output, by adjusting the input variables. Here are the key aspects of…
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How to use Paris’ law
Paris’ Law describes the rate of fatigue crack growth in materials under cyclic loading. The law is expressed with the following equation: Where: Detailed Explanation Experimental Determination To determine the constants and , fatigue crack growth tests are conducted on samples made of the material of interest. The tests involve: The resulting plot is typically…
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Elasticity basics
Stress and strain are fundamental concepts used to describe how materials deform under applied forces and subsequently return to their original shape when the forces are removed. Stress Stress () is a measure of the internal forces that develop within a material when an external force is applied. It is defined as the force () applied per unit cross-sectional…