November 22, 2010
School of Engineering, Coimbatore
 

A stitch in time saves nine. This familiar proverb tells us that we should rectify minor faults, otherwise these may snowball and assume catastrophic proportions.
 

Any structural or mechanical device may have invisible internal defects. These could lead to in–homogeneity of materials, causing the device to behave in unpredictable ways. Eventually this may result in fracture, thereby causing failure of the device. The key to preventing this from happening is to detect minute defects at an early stage.
 

A monograph published by Dr. Arun C. O., Assistant Professor, Amrita School of Engineering, titled Stochastic Meshfree Method for Elasto-Plastic Damage Analysis details a new method to analyze such initial damage and defects in structural and mechanical systems.
 

“The presence of the initial damage always has uncertainty surrounding it, primarily due to the uncertainties associated with the material manufacturing and processing,” explained Dr. Arun. “Structural and mechanical systems thus exhibit complex random variations in their properties. This requires the use of stochastic (probability-based) tools for damage analysis.”
 

The most commonly used tool for this purpose is the Stochastic Finite Element Method (SFEM). SFEM requires a mesh-based analysis to map the material domain under consideration. This is a cumbersome method; the effectiveness of the analysis depends heavily on the accuracy of the meshing.
 

How can one describe meshing?
 

“The discretization of a continuous domain into a set of discrete sub-domains, usually called elements, in order to perform an accurate analysis is what is known as meshing,” explained Dr. Arun.
 

Meshing is cumbersome for surfaces that have moving boundaries, crack growth, etc. Thus there is considerable interest towards using methods that do not require a structured mesh.
 

“Our monograph details a novel mesh-free method for elasto-plastic damage analysis,” elaborated Dr. Arun, whose research interests include Computational Mechanics, Finite Element Analysis, Meshfree Methods, Stochastic Meshfree Methods, Structural Mechanics and Damage Mechanics.
 

The new method is presented as an attractive alternative for stochastic analysis. Numerical examples validate the proposed method.
 

“We believe that this method will be much simpler, yet more efficient mesh-free alternative to existing methods of damage analysis,” commented Dr. Arun.
 

Abstract:

Arun C. O, B. N. Rao, S. M. Srinivasan, Stochastic Meshfree Method for Elasto-Plastic Damage Analysis , LAP Lambert Academic Publishing GmbH &CO.KG, Germany, 2010.

This monograph presents a stochastic element free Galerkin method for elasto–plastic damage analysis. First and second order perturbation methods are presented to predict the mean and covariance properties of stochastic responses in conjunction with shape function method and Karhunen–Loève expansion method for random field discretization. A novel stochastic state update procedure is presented to solve for the statistics of state variables. Numerical examples are solved to validate the proposed stochastic element free Galerkin method when uncertainty associated with the initial damage is considered. A study also has been carried out in this monograph using the deterministic EFGM to understand the effect of initial damage and its growth on structural response of single and bi–material problems. The newly proposed scaled transformation method developed during course of this research is adopted for the essential boundary and material discontinuity treatment in EFGM. The monograph focuses on the work carried by the first author at Indian Institute of Technology Madras, India.