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Related Concept Videos

Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity01:15

Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity

326
Deformation occurs in axial and transverse directions when an axial load is applied to a slender bar. This deformation impacts the cubic element within the bar, transforming it into either a rectangular parallelepiped or a rhombus, contingent on its orientation. This transformation process induces shearing strain. Axial loading elicits both shearing and normal strains. Applying an axial load instigates equal normal and shearing stresses on elements oriented at a 45° angle to the load axis.
326
Bending of Members Made of Several Materials01:08

Bending of Members Made of Several Materials

261
In analyzing a structural member composed of two different materials with identical cross-sectional areas, it is crucial to understand how their distinct elastic properties affect the member's response under load. The analysis involves assessing stress and strain distributions using the transformed section concept, which accounts for variations in material properties.
Hooke's Law determines stress in each material, stating that stress is proportional to strain but varies due to each...
261
Distribution of Stresses in a Narrow Rectangular Beam01:11

Distribution of Stresses in a Narrow Rectangular Beam

239
In studying beam stress distribution, examining an elemental section is essential. To determine the average shearing stress on this face, the calculated shear is divided by the surface area. Importantly, shearing stresses on the beam's transverse and horizontal planes mirror each other, indicating a consistent stress distribution along the upper region of the beam. Notably, shearing stresses are absent at the beam's upper and lower surfaces due to the absence of applied forces in these...
239
Unsymmetric Loading of Thin-Walled Members: Problem Solving01:07

Unsymmetric Loading of Thin-Walled Members: Problem Solving

165
The shear center of a channel section with uniform thickness, height, and width, is determined by computing the shear force in the member and calculating the moments of inertia of the sections.
To compute the shear forces, find the shear flow at a specific distance from the endpoint using the vertical shear and the moment of inertia values. The total shear force on the flange is calculated by integrating the shear flow from one end of the flange to the other.
Next, calculate the moments of...
165
Residual Stresses in Circular Shafts01:10

Residual Stresses in Circular Shafts

235
In materials that exhibit elastic and plastic behavior, known as elastoplastic materials, residual stresses can accumulate when these materials experience plastic deformation. This deformation arises from either high levels of shearing stress or significant strains. Residual stresses are internal stresses that persist within a material after removing the external force causing deformation. This phenomenon is demonstrated when observing the behavior of a shaft under torque; notably, the...
235
Temperature Dependent Deformation01:12

Temperature Dependent Deformation

192
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...
192

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Related Experiment Video

Updated: Sep 11, 2025

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Stiffness and Density Relationships in Additively Manufactured Structures: A Virial Theorem-Based Approach.

Tomáš Stejskal1, Silvia Maláková1, Marcela Lascsáková2

  • 1Department of Engineeringfor Design of Machines and Transport Equipment, Faculty of Mechanical Engineering, Technical University of Kosice, Letna No. 9, 042 00 Kosice, Slovakia.

Materials (Basel, Switzerland)
|August 14, 2025
PubMed
Summary

This study introduces a new virial-based model to predict stiffness-density relationships in 3D printed structures. This framework enhances materials characterization for topological optimization and advanced manufacturing.

Keywords:
additive production technologiesmaterials modelingsignal energystructure stiffnessvirial stability

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Area of Science:

  • Materials Science
  • Mechanical Engineering
  • Computational Modeling

Background:

  • Topological optimization aims for maximum stiffness with minimum weight, respecting stress limits.
  • This process yields complex structures with variable densities, where stiffness correlates with density, often linked to the golden ratio.

Purpose of the Study:

  • To introduce a mathematical theory based on the virial theorem for predicting stiffness-density relationships.
  • To provide a predictive framework for materials characterization in additively manufactured structures.

Main Methods:

  • Defining virial stability based on kinetic and potential energy components of random signals.
  • Developing a virial-based model to analyze stiffness-density correlations.

Main Results:

  • Established a theoretical link between virial stability and stiffness-density relationships.
  • Demonstrated the model's applicability to additively manufactured materials.

Conclusions:

  • The proposed virial-based model offers a generalizable tool for materials characterization.
  • This framework has broad applications in topological optimization, materials science, and advanced manufacturing.