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Related Concept Videos

Temperature Dependent Deformation01:12

Temperature Dependent Deformation

203
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...
203
Deformation of Member under Multiple Loadings01:11

Deformation of Member under Multiple Loadings

228
When a rod is made of different materials or has various cross-sections, it must be divided into parts that meet the necessary conditions for determining the deformation. These parts are each characterized by their internal force, cross-sectional area, length, and modulus of elasticity. These parameters are then used to compute the deformation of the entire rod.
In the case of a member with a variable cross-section, the strain is not constant but depends on the position. The deformation of an...
228
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

340
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.
340
Statically Indeterminate Problem Solving01:16

Statically Indeterminate Problem Solving

511
Statically indeterminate problems are those where statics alone can not determine the internal forces or reactions. Consider a structure comprising two cylindrical rods made of steel and brass. These rods are joined at point B and restrained by rigid supports at points A and C. Now, the reactions at points A and C and the deflection at point B are to be determined. This rod structure is classified as statically indeterminate as the structure has more supports than are necessary for maintaining...
511
Bending of Members Made of Several Materials01:08

Bending of Members Made of Several Materials

299
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...
299
Impact Loading01:19

Impact Loading

306
Impact loading occurs when a moving object collides with a stationary structure, such as a rod with a uniform cross-sectional area fixed at one end. Under these conditions, the rod absorbs the kinetic energy from the striking object, leading to deformation and subsequent stress development. As the rod returns to its original position and reaches maximum stress, the absorbed energy, initially manifested as kinetic energy, transforms entirely into strain energy.
In cases of elastic deformation,...
306

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Updated: Sep 26, 2025

Finite Element Modeling for the Simulation of the Quasi-Static Compression of Corrugated Tapered Tubes
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Modelling of Longitudinal Elastic Wave Propagation in a Steel Rod Using the Discrete Element Method.

Magdalena Knak1, Michał Nitka2, Erwin Wojtczak1

  • 1Department of Mechanics of Materials and Structures, Faculty of Civil and Environmental Engineering, Gdansk University of Technology, Narutowicza 11/12, 80-233 Gdansk, Poland.

Materials (Basel, Switzerland)
|April 23, 2022
PubMed
Summary
This summary is machine-generated.

The discrete element method (DEM) effectively models elastic wave propagation in rods. This study developed a novel DEM algorithm, validated experimentally and theoretically, proving its suitability for structural analysis.

Keywords:
discrete element methoddispersion curvesfinite element methodguided waveslongitudinal wavenumerical modelling

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Area of Science:

  • Computational Mechanics
  • Solid Mechanics
  • Wave Propagation

Background:

  • Accurate modeling of elastic wave propagation is crucial for structural health monitoring and design.
  • The discrete element method (DEM) offers a promising alternative to traditional methods for complex wave phenomena.

Purpose of the Study:

  • To develop and validate a novel algorithm for modeling elastic wave propagation using DEM.
  • To compare DEM simulations with experimental data and finite element method (FEM) calculations.
  • To determine the optimal DEM model parameters for accurate wave propagation analysis in rods.

Main Methods:

  • Development of a complex DEM algorithm for wave propagation simulation.
  • Creation of multiple DEM models with varying discretization and material properties.
  • Comparison of DEM results with experimental data and theoretical predictions (Pochhammer-Chree theory).
  • Inclusion of finite element method (FEM) calculations for comparative analysis.

Main Results:

  • A novel DEM algorithm for elastic wave propagation was successfully developed.
  • DEM models were systematically evaluated against experimental waveforms and theoretical dispersion curves.
  • The study identified the most suitable DEM model configuration based on correlation and theoretical agreement.
  • DEM simulations demonstrated strong agreement with experimental and theoretical results.

Conclusions:

  • The discrete element method (DEM) is a viable and effective tool for modeling elastic wave propagation in structural rods.
  • The developed DEM algorithm provides accurate predictions comparable to experimental and theoretical benchmarks.
  • This research validates DEM's application in analyzing wave dynamics within structural components.