Journal of Minerals & Materials Characterization & Engineering, Vol. 8, No.2, pp 107-114, 2009 Printed in the USA. All rights reserved
Modeling and Simulation Perspective
O. Oluwole
Mechanical Engineering Department, University of Ibadan, Ibadan.
Tel: +234(0)8033899701
Engineering research is a sine-qua-non for development of new products, new production
processes, hence production lines in the quest for self reliance in any economy. Modeling and
simulation is a veritable tool for such research and development. This paper presents the
multifaceted use of modeling and simulation as decision tools for engineering facet of an
economy drawing examples from two different engineering disciplines- Metallurgic al and Civil.
Key words: Modeling; Simulation; R&D; Self-reliance.
Modeling and simulation in the foundry industry is now an integral part in economical
production of new designs (Chen et al, 1994; Chen and Hwang, 1996). The casting engineer is
assisted through modeling and simulation in trans l a t ing paper designs into manufacturing
designs. The engineer is able to determine among other things th e co rr ec t p la ce ment of risers,
gatings, chills and paddings. He is able to simulate the solidification process, locating the solidus
and liquidus, the temperature at different points in the casting as the solidification progresses and
thus be able to make intelligent decisions as to possible defect formation in the casting (Cheng et
al, 1992; Fackeldy et al, 1996; Ehlen et al, 2000). Resulting microstructures can be s i mulated
(Fackeldy et al, 1996; Ludwig, 2001). Heat-treatment microstructures and grain growth can be
simulated as well.
108 O. Oluwole Vol.8, No.2
The use of computers in civil and structural engine ering is well established. Behaviour of novel
designs cannot be ascertained without subjection of designs to simulations of behaviour in true-
life situations using mathematical models. Stress-strain behaviour and hence mode of possible
shear could be simulated in concrete stru ctur es-b uild ing s, brid ges, houses, dams etc.
2.1 Simulation Software Development
The mathematical representation of many physical processes like the solidification process and
elasticity problems in building structures have been understood for long. The development of
digital computers has stimulated research in the areas of modeling and simulation of these
processes. Early work (Marron et al, 1970 and Pelke and Kirt, 1973) had utilized the finite
difference method. The implicit method with Gauss –Seidel iteration permitted the use of the
finite difference method for irregular shapes. However, the finite element method with its
flexibility of meshing with irregular or complex shapes has found wide usage in process and
engineering simulati ons . R esul tin g fr om the multifaceted research into this area, different
software have been produced both private and commercial for prediction of many engineering
processes ( Oluwole et al, 2007b). Some multipurpose software for engineering modeling and
simulation are:
(i) Ansys by Swanson Analysis Systems of Philadelphia
(ii) Nastran by McNeal Schwender Corporation of Los Angeles
(iii) Matlab by the Math Works Inc, USA.
Specialised commercial s o f t w a r e f or s olidification are also available, e.g.,
(i) Magmasoft by Magma of Alsdorf, Germany
(ii) Solstar by Foseco Inc.
(iii) Procast by Universal Energy Systems, USA
(iv) Swift by JML research, USA
(v) Phoenics by CHAM of North America
(vi) Simulor by Aluminium Pechiney of France
What makes the above software stand out is the graphics user interface (GUI) making results
translated into visual display in seconds (Figs 1-4). Simplicity of use, accuracy of results and
justifiable cost of software acquisition are other attractive points.
2.2 Geometric Representation
In both the finite difference and finite element methods, geometry of interest is divided into
elements which are simple geometric shapes. These are usually triangles and /or quadrilaterals
for two-dimensional ob jects and tetrahedrons for 3-dimensional objects.
Vol.8, No.2 Engineering Research 109
Mesh generation could be by automatic generation or by manual generation. Generating meshes
involve understanding of the casting requirement and the numerical method being used.
Experience is needed to h ave an accurate representation of the geometry of interest. Automated
meshing needs a graphic int e grated user interphase for geometric modeling.
2.3 Flexibility of Program
General purpose programs prove to be very unwieldy and lack d epth and it is better when
programs are focused on specific problem areas such as solidification (Fig. 5), elasticity,
structures, etc., rather than lumping all together in one software package.
2.4 Graphics Interphase
Interactive graphic user interphase (GUI) using programs like the C++ builder, Visual Basic and
MatlabR make programs user friendly. However, many real life programs in 3-dimensions still
have to be connected to plotters for graphic displays.
2.5 Accuracy of Results
Accuracy of results is affected by the accuracy of the numerical method and the fineness of the
meshing. The best way in evaluating the degree of error is by comparison with experimental
results (validation).
2.6 Stability of Numerical Method
The explicit finite diffe rence and the finite element methods are known to introduce oscillations
in the results when the time step is too large. For solidification proble ms using the explic i t finite
difference method, the time step
≤Δ for 1-D problems
≤Δ for 2-D problems and
≤Δ for 3-D problems.
For the finite element method,
≥Δ . steptimet
spacinggridx −=Δ ydiffusivitthermal −=
2.7 Complexity Systems
Complexity problems are dynamical systems at the edge of chaos. Modeling using finite
elements is not feasib le f or t h es e sy stems. Dynamical systems model time –dependent
phenomena in which the next state is computable from the current state (Kroc, 1999). Many
110 O. Oluwole Vol.8, No.2
physical systems are modeled as dynamical systems. However, cellular automaton (CA)
becomes very useful in modeling dynamical systems that are spatially and locally dynamic as it
is itself a temporarily and spatially discrete dynamical system. The updating of the system is
spatially localized making it very useful tool in modeling and simulation of chaos, fractals,
randomness, complexity and particles which numerical approximation methods cannot handle.
Thus it finds usefulness in modeling and simulation of recrystallization and phase
transformations in materials. In CA, all cells behave identically and have some connectivity.
Thus, there is parallelism (individual cells a r e u p dated independently of each other); ther e i s
localization (a cells update is based on its old state and that of its neighbours) and there is
homogeneity (same rules apply to all cell updates). These rules make it easy in simulating phase
transformation as cells modeled using voronoi tessellation can be updated with transformed
phases in each cell. Same rule applies to recrystallization since it’s a dynamical system itself.
Fig.1: Grain size modeling with voronoi tessellation using Matlab C (author’s unpublished work)
Vol.8, No.2 Engineering Research 111
Fig.2: Modeling strains in reinforced concrete structures using Matlab Pdetool (author’s
unpublished work)
Fig.3: Modeling displacement in ductile iron using MatlabR Pdetool (Oluwole and Olorunniwo,
112 O. Oluwole Vol.8, No.2
Fig.4: Solidification simulation using Matlab Pdetool (Oluwole et al, 2007a)
Fig.5: Riser effect in solidification simulation using author’s solidification software and Matlab’s
contour plotting cabability (Oluwole et al, 2007b)
There is the need to deve l op a strong modeling and simulation capacity among engineers with
expertise in software de ve lop ment. This will be p ossible when engineers acquire extensive
programming and mathematical skills. Software programming in modern programming
languages such as C+ +, Java, Power Fortran, Tcl/tk etc are essential. Experience has shown that
Vol.8, No.2 Engineering Research 113
only engineers can better understand the nitty-gritty of the problem under study and write
algorithms for the software. Computer programmers often lack depth of understanding of the
problem and/or mathematical skills to express such.
In the light of this d i sclosure, some of our curriculum at the undergraduate and postgraduate
levels need revisiting to take into consideration the highlighted points. At least one object
oriented programming language and a c o u r s e i n m o de l i n g an d s i mulation need to be introduced
at the undergraduate level. At the postgraduate level emphasis will now shift to application of
modeling and simulation.
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