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Related Concept Videos

Deformation of Member under Multiple Loadings01:11

Deformation of Member under Multiple Loadings

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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...
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Temperature Dependent Deformation01:12

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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...
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Statically Indeterminate Problem Solving01:16

Statically Indeterminate Problem Solving

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

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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.
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Stability of structures01:14

Stability of structures

347
In mechanical engineering, the stability of systems under various forces is critical for designing durable and efficient structures. One fundamental way to explore these concepts is by analyzing systems like two rods connected at a pivot point, O, with a torsional spring of spring constant k at the pivot point. This system is similar in appearance to a scissor jack used to change tires on a car. In this case, the arms of the linkage (equivalent to the rods in this system) are entirely vertical,...
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The study of solid circular shafts under stress shows that within the elastic limit, stress increases directly to the distance from the shaft's center. This relationship holds until the shaft reaches a critical point of stress, beyond which it begins to yield, marking the transition from elastic to plastic deformation. At this crucial juncture, the maximum torque the shaft can endure without permanent deformation is determined, signifying the limit of its elastic behavior.
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Related Experiment Video

Updated: Nov 26, 2025

Subject-specific Musculoskeletal Model for Studying Bone Strain During Dynamic Motion
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A constrained spline dynamics (CSD) method for interactive simulation of elastic rods.

Karthikeyan Panneerselvam1,2, Rahul1, Suvranu De1,2

  • 1Center for Modeling, Simulation, and Imaging in Medicine, Rensselaer Polytechnic Institute, Troy, NY, USA.

Computational Mechanics
|December 14, 2020
PubMed
Summary
This summary is machine-generated.

Constrained Spline Dynamics (CSD) offers a unified framework for simulating elastic rods with constraints at interactive speeds. This method accurately models bending, twisting, and coupled behaviors using B-splines and Hamilton

Keywords:
B-splinesElastic rodsarc-length parametrizationinextensibilityshape functionsthread simulation

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Area of Science:

  • Computational physics
  • Mechanical engineering
  • Applied mathematics

Background:

  • Simulating elastic rods with constraints is computationally intensive.
  • Existing methods struggle with interactive rates and complex bend-twist coupling.

Purpose of the Study:

  • Introduce Constrained Spline Dynamics (CSD) as a unified framework.
  • Enable real-time elastodynamic simulation of constrained elastic rods.
  • Accurately model bend-twist coupling without rotational director frames.

Main Methods:

  • Discretize rod geometry and kinematics using B-spline functions.
  • Formulate dynamics from Hamilton's principle with compliant constraints for energies.
  • Utilize holonomy of curves for bend-twist coupling and uniform arc-length parametrization.

Main Results:

  • CSD achieves interactive simulation rates for constrained elastic rods.
  • The formulation accurately captures bending, twisting, and bend-twist coupled behaviors.
  • Numerical examples demonstrate convergence, accuracy, and computational efficiency.

Conclusions:

  • CSD provides an efficient and accurate unified framework for elastodynamic rod simulation.
  • The method effectively handles constraints and complex material behaviors.
  • This approach is suitable for real-time applications requiring high fidelity.