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Deformation of Member under Multiple Loadings

Deformation of Member under Multiple Loadings

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...

Deformation in a Circular Shaft

Deformation in a Circular Shaft

One of the distinctive characteristics of circular shafts is their ability to maintain their cross-sectional integrity under torsion. In other words, each cross-section continues to exist as a flat, unaltered entity, simply rotating like a solid, rigid slab. To understand the distribution of shearing stress within such a shaft, consider a cylindrical section inside this circular shaft. This section has a length of L and a radius of R, with one end fixed. The radius of the cylindrical section is...

Deformations in a Transverse Cross Section

Deformations in a Transverse Cross Section

When a material is subjected to uniaxial stress, it elongates or contracts in the direction of the applied force, and also undergoes changes in the perpendicular directions. This behavior is crucial for understanding how materials behave under stress and is governed by mechanical properties such as Poisson's ratio v, which measures the ratio of transverse strain to axial strain.
As the material stretches, it expands or contracts in orthogonal directions to the load. This phenomenon varies...

Plastic Deformation in Circular Shafts

Plastic Deformation in Circular Shafts

When materials are subjected to forces that surpass their yield strength, they undergo a process known as plastic deformation. This results in a permanent alteration or strain in their structure. This concept can be specifically applied to circular shafts, where the deformation leads to a change in its shape. The precise evaluation of this plastic deformation requires understanding the stress distribution within the circular shaft, which is achieved by calculating the maximum shearing stress in...

Three-Dimensional Force System:Problem Solving

Three-Dimensional Force System:Problem Solving

A three-dimensional force system refers to a scenario in which three forces act simultaneously in three different directions. This type of problem is commonly encountered in physics and engineering, where it is necessary to calculate the resultant force on the system, which can then be used to predict or analyze the behavior of the object or structure under consideration.
To solve a three-dimensional force system, first resolve each force into its respective scalar components. Do this using...

Deformations in a Symmetric Member in Bending

Deformations in a Symmetric Member in Bending

When analyzing the deformation of a symmetric prismatic member subjected to bending by equal and opposite couples, it becomes clear that as the member bends, the originally straight lines on its wider faces curve into circular arcs, with a constant radius centered at a point known as Point C. This phenomenon helps to understand the stress and strain distribution within the member more clearly.
When the member is segmented into tiny cubic elements, it is observed that the primary stress...

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Related Experiment Video

Updated: May 23, 2026

Subject-specific Musculoskeletal Model for Studying Bone Strain During Dynamic Motion

Subject-specific Musculoskeletal Model for Studying Bone Strain During Dynamic Motion

Published on: April 11, 2018

Dynamic cylindrical free-form deformation for interactive simulation of tool-tissue interaction.

Woojin Ahn¹, Doo Yong Lee

¹Rensselaer Polytechnic Institute, Troy, NY, USA.

The International Journal of Medical Robotics + Computer Assisted Surgery : MRCAS

|April 5, 2012

Summary

This study introduces an enhanced free-form deformation (FFD) method for simulating complex object deformations with precise tool contact. The technique enables real-time, accurate simulations for applications like colonoscopic polypectomy.

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Subject-specific Musculoskeletal Model for Studying Bone Strain During Dynamic Motion

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Published on: April 11, 2018

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A Novel Stretching Platform for Applications in Cell and Tissue Mechanobiology

A Novel Stretching Platform for Applications in Cell and Tissue Mechanobiology

Published on: June 3, 2014

Area of Science:

Computer Graphics and Simulation
Medical Simulation
Geometric Modeling

Background:

Dynamic lattice-based free-form deformation (FFD) enables efficient global deformation simulation of complex objects.
Directly imposing position constraints for tool contact in FFD is challenging due to over-determined problems.

Purpose of the Study:

To extend FFD for direct imposition of position constraints in embedded objects.
To enable accurate simulation of tool-tissue interaction in complex geometric deformation.

Main Methods:

Objects are embedded in (rounded) cylindrical lattice structures.
Position constraints are applied via local deformation along the near-normal surface direction.

Main Results:

Computational time for local deformation is independent of the number of constrained points.
The method achieves real-time performance, exceeding 60 Hz in colonoscopic polypectomy simulations.

Conclusions:

The proposed method efficiently simulates global and local deformations of complex geometric objects.
It achieves accurate, realistic, and robust tool-tissue interaction for medical simulations.