Columbia University

Technology Ventures

Computer aided rigid-body stress analysis using a defect free, four-node finite-element technique for two-dimensional bodies

Technology #ms96-05-15

Lead Inventor: Gautam Dasgupta, Ph.D.

Tech Ventures Reference: IR MS96/05/15

Current finite-element techniques for stress analysis use triangles and/or quadrilateral shaped finite elements. These shapes introduce error when analyzing bending bodies and add artificial “stiffening,” or additional zero-energy modes other than rigid-body responses. This technology is an improved computer aided stress-analysis technique for two-dimensional bodies of uniform thickness. It uses quadrilaterals, free of these modeling errors, to improve computational accuracy and increase design efficiency. It can be used for determining stress, strain, and/or deformation of two-dimensional bodies under compression, stretching, shearing, and/or bending by algebraically generating a “defect-free” nodal force-displacement relationship.

Using defect-free quadrilateral finite-elements avoids modeling errors which introduce non-rigid body effects into models of two-dimensional bodies

Finite-element stress-analysis techniques solve complex two-dimensional solid-body modeling problems through numerical approximation. This technology dynamically determines defect-free quadrilateral elements for each rigid body under study using four-node rigid body analysis and a neural-network solution technique.

The increased accuracy of the technology has been demonstrated using a Mathematica-based program called Tessellica.


* Aids in the manufacturing and design of load bearing structures such as buildings, bridges, dams, automobiles, ships, and aircraft
* Aids in the analysis and design of hard and soft tissue in bioengineering applications
* Allows for the determination of stress, strain, and/or deformation of two-dimensional bodies of uniform thickness


* Greater modeling accuracy compared to existing two-dimensional finite elements
* Accurate analyses and designs lead to material savings during manufacturing
* Avoids modeling errors introduced by using triangular shaped finite-elements
* Automatically determines defect-free finite-element shapes using neural-network solution strategy

Patent information: ~ see link below.

Patent Issued (US 6,101,450)

Licensing Status: Available for licensing and sponsored research support

Related Publications:

* None