Paper presentation by Users and developers in the User's Meet 2020

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Workshops On FEAST have been conducted in

MITS, Madanapalli;

BAIT Bangalore;

KIT Kolhapur;

VJTI Mumbai;

MIT Aurangabad;

RIT Islampur

and many more other colleges all over India.

FEAST (Finite Element Analysis of STructures) is a structural analysis software based on Finite Element Method. FEAST is ISRO’s structural analysis software based on finite element method realized by Structural Engineering Entity of Vikram Sarabhai Space Centre (VSSC)/Indian Space Research Organisation (ISRO). The software was primarily developed for solving ISRO’s launch vehicle and satellite structural engineering problems.

PreWin is the graphical user interface based pre /post processor of FEAST. It provides state of the art features for geometric modelling, mesh generation, model editing and results visualization. FEAST solver is seamlessly integrated with PreWin as a single application. Sub structured and Multi-Threaded (SMT) implementation of the solver ensures high performance by exploiting multi-core architecture of modern computing platforms. With advanced solution algorithms the solver is able to handle large order problems of structural engineering. FEAST-SMT is a completely new solver implemented using C++ with OO technology. The solution to system’s governing differential equations is obtained at discrete locations by FEAST-SMT solver by Sub-structured and Multi-Threaded (SMT) techniques. This has resulted in considerable reduction of solution time, which is comparable with industry standard software. The fundamental architecture of SMT can be easily extended to parallel processing of large order problems. PreWin, the GUI for FEAST is bestowed with command line, menu driven and tree-based control/ model manipulation options. Models on the screen can be visualised in 3D, with rich rendering choices. Geometry representation in STEP and IGES format is supported in PreWin. PreWin is designed for intuitive interaction to reduce learning time and improved efficiency and features context sensitive help. Hence, this software can be utilised not only in aerospace/ aeronautical engineering domains but also other fields where structural and heat transfer problems need to be simulated.

The Structures entity at VSSC is involved in design, analysis, testing and delivery of launch vehicle structures for the Indian Space Research Organization. The development of these mission critical and high-performance structures, demands high end tools at every stage. In addition to several design data and semi-empirical expressions available at the disposal of the designer for configuring the structures, numerical methods have become indispensable during design and analysis phase. Among the numerical methods available the finite element method is most popular owing to its ease of implementation and use in digital computers. Due to affordable computational cost, it is possible to simulate and characterize the structural behaviour by numerous iterations. These predictive computations minimize the overall development expenditure by bringing down the number of prohibitively expensive
testing that needs to be conducted to establish the reliability and robustness of the
design. Numerical methods are utilized to solve large dimension (variables, not
geometric proportions) problems that in most cases belong to elliptic, parabolic and
hyperbolic class of partial differential equations encountered in the field of solid
mechanics, which is the theoretical basis for structural engineering. Several
proprietary finite element software packages are available that are vended by
multinational corporations. Dominating commercial considerations result in high
pricing of these tools, which limit the number of licenses for acquisition. In view of the above, VSSC initiated the indigenous development of finite element software capability since 1977, which still continues. Over the years several scientists have greatly contributed in understanding this complex technology and have periodically brought out working software versions and upgrades for solving practical aerospace structural engineering problems of our community. The objective of the development activity is for competency building and capability enhancement in this discipline. The earlier working code was developed using FORTRAN 77. The computer hardware technology since late seventies of last century has galloped in terms speed and revolutionary architectures to the present times. Naturally, the software technologies have to be in tandem with the changes occurring in the areas of hardware for high end performances. To this end, the present version of in-house code was developed using Substructure and Multithreading (SMT) concept since 2005, which suits our requirements. This concept is extendable to large scale parallelization, which is one of the objectives of this developmental work.

Finite element method is a very popular numerical method that has found use in finding practical solutions to field problems in solid mechanics, electro-magnetics, thermal engineering etc. Earlier, solving real-life problems involved time and hence, technologies used to evolve at its own ‘natural’ pace. The contemporary developments in finite element method and technological breakthroughs in digital computers has complemented each other’s growth and has led to revolutionary innovations in many fields of science and technology. The sophistication and user friendliness in the modern finite element software has popularized this method but has led many uninitiated users to think the results from it as the final verdict for their problem in hand. This is due to lack of discretion on their part. If asked “What is finite element method?” to many users of the software, the answer would in most of the cases describe the steps involved in operating one of the much available software. Analogously, one may ask why a person should know the combustion cycle or mechanisms of power steering of an automobile while owning it for transportation needs. Well, the question is legitimate in case of an automobile ownership, not so for the high-end users like scientists, engineers and technologists using finite element software. This is because they should have the overall grasp of the problem, the solutions, validity/applicability and complete understanding of methods used to arrive at the solution, be it analytical, test or numerical. Rigour should dominate heuristics while comprehending the nature of the problem. If not, the blind choice will result is disastrous consequences in terms of resources, time and at times life.

Although, finite element method can make a good engineer better, it can make a poor engineer more dangerous. The mathematical foundations of this method are to be dwelled into for making rational conclusions while interpreting results. There are several textbooks and peer reviewed scientific publications that are available on the finite element method covering various aspects. These literatures are mathematically formidable but they are not impossible to understand. It is ironic to come across the comments that these tomes of math are “impractical” as these form the very foundations from where any finite element software is built and designed.

Before we try to understand what finite element method is, let us appreciate how modern science works in first place.

We observe several phenomena in nature and try to comprehend it by relating principal quantities involved to the net effect. In other words, the qualitative observations are translated to quantitative mathematical statements. These statements take the form of polynomial expressions, differential equations (ordinary or partial), integro-partial differential equations etc. These expressions are formulated based on some rational hypothesis, which concentrates on the cardinal influencing factors on what is being sought. Example is the Euler-Bernoulli beam. This is based on small deflection hypothesis that essentially means that the differential equation represents/captures linear behaviour and this model should seldom be used to estimate large deflection of beams.

It is important to remember that the mathematical models are only an approximation to reality. If it is possible to measure a physical quantity of interest directly, then all the convoluted mathematics and rational arguments for approximations can be gleefully abandoned. This is the reason why there is no substitute for experimental or test based results. The prohibitive cost is the drawback of tests, which may have its own pitfalls. Verifying mathematical models against real physical behaviour, from either laboratory-based experiments or in-situ observations, is an essential part of the design process.

Finding solution to these mathematical models is the next logical step. Constraints are identified before resorting to solution finding. Wherever or whenever it is possible, closed form solution is the preferred option. Analytical solutions based on variational principles are the resorted to when closed form solutions are impossible. This is true in many situations. But variational methods have their own limitations as it can give solutions only over simple domains. Numerical methods are used for finding solutions when closed form or analytical solutions are inadequate. It has to be remembered that finite element method is a numerical method for solving partial differential equations and basically is piece-wise application of variational methods such as Rayleigh-Ritz or Galerkin method.

When standard commercial packages are used for the analysis, we implicitly accept the element solution without considering the consequences of the choice. Before zeroing into a particular element (solution) the analyst/designer should carefully read the documentation on underlying theories and assumptions that has gone into the element definition. If the chosen element doesn’t meet the requirement, then special purpose code has to be developed or shopped for. This process will help the analyst/designer achieve solution to the required degree of confidence.

The theoretical manual primarily dwells on:

- Mathematical principles, which is precursor to the governing relations
- Solution of eigen value and steady state problems
- Element library
- Constraints
- Material constitutive laws
- Solvers and their algorithms

The solver is supported by a rich graphic user interface based pre/post processor to create numerical models and map the results. It takes years to master the use of any finite element software for achieving intended objectives of an analyst.

FEAST-SMT is validated using standard NAFEMS (National Agency for Finite Element Methods and Standards) benchmark problems. In addition to this, the development team has solved many of ISRO’s structural engineering problems using PreWin/ FEAST-SMT as test cases. The results obtained using the present software is comparable with those obtained from industry standard proprietary software.

- FEAST Capabilities
- Linear Static Analysis
- Free-Vibration Analysis
- Buckling Analysis
- Visco-Elastic Analysis
- Thermo-elasticity
- Heat Transfer
- Transient Response
- Frequency Response
- Random Response
- Shock response spectra / shock response
- Fluid-structure interaction and

Base excitation analyses with metallic and composite material models. - Electro-static
- Electro-Magnetic
- XFEM based Fracture mechanics