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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

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.
Equation of the Elastic Curve01:23

Equation of the Elastic Curve

The concept of curvature in plane curves, crucial in structural engineering, defines how sharply a beam bends under load. This curvature is determined using the curve's first and second derivatives.
Consider a cantilever beam with a point load at its free end (for instance, a diving board). When analyzing beam deflection with small slopes, the shape of the beam's elastic curve becomes key. The governing equation for this analysis involves the bending moment and the beam's flexural rigidity,...
Elasticity in Concrete01:20

Elasticity in Concrete

Upon subjecting concrete to moderate or high uniaxial compressive or tensile stresses, the strain response is non-linear relative to the stress applied. As the stress is removed, the resulting stress-strain curve deviates from the original path traced during loading, creating a hysteresis loop, indicative of the concrete's non-linear and non-elastic properties. Typically, a material's modulus of elasticity, which is a measure of the material's stiffness, is inferred from the linear portion of...
Generalized Hooke's Law01:22

Generalized Hooke's Law

The generalized Hooke's Law is a broadened version of Hooke's Law, which extends to all types of stress and in every direction. Consider an isotropic material shaped into a cube subjected to multiaxial loading. In this scenario, normal stresses are exerted along the three coordinate axes. As a result of these stresses, the cubic shape deforms into a rectangular parallelepiped. Despite this deformation, the new shape maintains equal sides, and there is a normal strain in the direction of the...
Euler's Formula to Columns: Problem Solving01:23

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Euler's formula is used in structural engineering to determine the buckling load of columns under various conditions. However, when dealing with systems that incorporate both rigid elements and elastic components, such as springs, the analysis requires a finer approach to determine the critical load. The problem described involves two rigid bars connected at a pivot point with a spring attached and a vertical load applied at one end.
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Euler's Formula for Pin-Ended Columns01:21

Euler's Formula for Pin-Ended Columns

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Shear Assay Protocol for the Determination of Single-Cell Material Properties
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Published on: May 19, 2023

A Numerical Method for Solving Elasticity Equations with Interfaces.

Songming Hou1, Zhilin Li, Liqun Wang

  • 1Department of Mathematics and Statistics, Louisiana Tech University, Ruston, LA, 71272, USA.

Communications in Computational Physics
|June 19, 2012
PubMed
Summary
This summary is machine-generated.

A novel finite element method efficiently solves elasticity equations with interfaces using non-body-fitting grids. This accurate approach achieves second-order accuracy for smooth solutions and higher for singular ones.

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Area of Science:

  • Computational Mechanics
  • Applied Mathematics
  • Numerical Analysis

Background:

  • Solving elasticity equations with interfaces is crucial in engineering and science but poses significant challenges for conventional numerical methods.
  • Existing techniques often struggle with accuracy and efficiency when dealing with complex interface geometries.

Purpose of the Study:

  • To propose an efficient and accurate non-traditional finite element method (FEM) for solving elasticity equations with interfaces.
  • To utilize non-body-fitting grids, simplifying mesh generation for complex geometries.

Main Methods:

  • Employs a non-traditional FEM approach with non-body-fitting grids.
  • Utilizes standard finite element basis functions for test functions, independent of the interface.
  • Constructs solution basis functions as piecewise linear, enforcing interface jump conditions.

Main Results:

  • The developed linear system of equations is proven to be positive definite under specific assumptions.
  • Numerical experiments demonstrate second-order accuracy in the L(∞) norm for piecewise smooth solutions.
  • Achieves over 1.5th order accuracy for solutions with singularities at sharp-edged interface corners.

Conclusions:

  • The proposed non-traditional FEM offers an accurate and efficient solution for elasticity problems with interfaces.
  • The method's ability to handle non-body-fitting grids and singular solutions makes it broadly applicable in computational engineering and science.