This innovation unifies an earlier innovation and a new solution method based on finite differences to simulate structural dynamic phenomena over time-varying grids in generalized curvilinear coordinates. The methodology is based on physics-based first principles partial differential equations of elastodynamics in the space-time domain. It provides a powerful, yet simple methodology to compute structural dynamic variables of interest such as stresses over an entire grid mapped over or inside a given body of interest directly in the time domain. The grid can be allowed to deform in time as the solution evolves. The simulation (deforming grids and stresses) can be visualized as the solution proceeds in time; the simulation can be suspended at any point in time based on the visualization of the state of the system, and the simulation can be resumed/terminated altogether as the evolving solution proceeds within/outside the expectation bounds dictated by physics. The attractiveness of the innovation lies in the intuitiveness of the approach where the physical variables such as stresses and the displacements can be visualized directly in space and time as the simulation proceeds.

This Gear Cross-Section shows a tooth region with reduced rigidity. Structural dynamic variables that can be computed include stresses over an entire grid mapped over or inside a body of interest.
The need to know the state of a structural system during its operation in terms of the physical output variables such as stresses and the geometric configuration of the system itself is essential for monitoring the system health. Such systems can be tested, prior to launching them in their operational domain, in a laboratory or through relatively inexpensive computational simulations. Such systems, when subjected to space and time-varying loads during their operation, can throw the system into unsafe states from the system’s health perspective. It is therefore essential to have a prior knowledge of such system states before the systems are commissioned. An innovative and intuitive method to do this has been invented that can compute the system health as it passes through different states in time by solving elastodynamic equations over deforming grids representing the system geometry. Another objective of this innovation is to enhance the state-of-the-art structural design methodology.

This simulation technology incorporates an innovative elliptic grid generation methodology that automatically updates the grid during the finite difference simulation of a given structural system directly in the time domain. The structural simulation over such a geometry using elastodynamic partial differential equations is itself innovative, and it gives results directly in the time domain.

This work was done by Upender K. Kaul of Ames Research Center.

NASA invites companies to inquire about partnering opportunities. Contact the Ames Technology Partnerships Office at 1-855-627-2249 or This email address is being protected from spambots. You need JavaScript enabled to view it.. Refer to ARC-15462-1.

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This article first appeared in the September, 2014 issue of Software Tech Briefs Magazine.

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