Salim P.M.1, Seshadri Sekhar T.2
1Research Scholar, GITAM School of Technology, Hyderabad-502329, Telengana, India
2 Professor and Dean NICMAR, Hyderabad-500084, Telengana, India
Optimisation is the controlling factor in every sort of manufacturing process for better productivity with minimal usage of labour, materials and power .In this context structural optimisation is a challenging task for the engineering fields connected with manufacturing. With the introduction of computers in the process of structural analysis, structural optimisation also underwent drastic developments. It is alarming that the natural resources are exhausting at a high rate due to the industrialisation and the higher per capita usage of different metallic and non metallic substances. So the materials should be utilized with minimum usage and maximum efficiency for the conservation of nature and to cater for the future needs. The advancement in structural optimisation is the only remedy resorted for the efficient utilization of the resources in a scientific way. Compared to other engineering fields the developments in structural optimisation in civil engineering field is still far behind. So a collaborative effort from the various experts in different specialisation in civil engineering is resorted to the effective utilisation of this method to the advancement of cost effective utilisation of various resources.
The high living standard of modern man is the sole output of the research and developmental activities of science and technology. When the standard of living increases the per capital consumption of materials are also increased. This will lead to depletion of useful materials from the universe. For the conservation of natural resources efficient use of the materials without wastage is necessary. Now optimisation is the controlling factor in every sort of manufacturing process for better productivity with minimal usage of labour, materials and power. The structural optimisation is much concerned about the minimal use of materials without compromising structural strength. The structural optimisation finds extensive applications in agriculture, automobile, aeronautical, space, mechanical and civil engineering fields. The present day process of structural optimisation is invariably connected with the wider applications of different softwares.
HISTORY OF STRUCTURAL OPTIMISATION:
The first work on structural optimisation is by Maxell(1869).Then came Mitchell(1904).Development of finite element analysis using electronic computers started way back to 1950’s.Later several papers were published with the pioneering work by Schmitt(1960).In 1984 Schmitt stated that “Historically the desire to reduce structural weight while preserving structural integrity, particularly in aero space applications has been a strong driving force behind the development of structural optimisation methods. Today the need for energy conservation in transportation systems via weight reduction provides further motivation for the structural optimisation methods. The growing use of fibre composite materials in structures is likely to increase the demand for modern analytical tools that will make it possible to fully exploit the design potential offered by these new materials”. It is worth to note that the structural optimisation methods have the widest applications in aero space engineering with the introduction of variety of fibre composite materials.
A structure in mechanics is defined as any assemblage of materials which is intended to sustain loads. Optimization means making things the best. Thus, structural optimization is the subject of making an assemblage of materials sustains loads in the best way. Mathematically optimization is the process of obtaining conditions, which give the maximum or minimum magnitude of a function.
Due to the complexity in the process of mathematical modeling for structural optimization problems by manual means is not at all feasible. So the development of the structural optimization is in very slow pace before the introduction of electronic computing facilities. After the introduction of electronic computers in the process of structural analysis, structural optimization also underwent drastic changes.
Mathematical modelling of structural optimisation problem:
· Objective function: Objective function is the unique function used to designate the design problem. It is denoted by”f”. For every possible design, f returns a value which indicates the effectiveness of the design. Usually in structural optimisation we choose f such that a small value is better than a large one such as a minimization problem. Frequently f measures weight, displacement in a given direction, effective stress or cost of production etc.
· Design variable (x): A function or vector that describes the design, and which can be changed during optimisation. It may represent geometry or choice of material. When it describes geometry, it may relate to a sophisticated interpolation of shape or it may simply be the area of a bar, or the thickness of a sheet.
· State variable (y): For a given structure, i.e., for a given design x, y is a function or vector that represents displacement, stress, strain or force.
A general structural optimisation problem is in the form:
Where behavioural constraints are constraints on state variable y usually written as g(y) ≤ 0, where g is a function which represents, e.g., a displacement in a certain direction.
Design constraints are similar constraints involving the design variable x.
Equilibrium constraint is in the form K(x) u = F(x)
Where K(x) is the stiffness matrix of the structure, which generally is a function of the design, u is the displacement vector and F(x) is the force vector which may also depend on the design
Classification of structural optimisation:
Structural optimisations are typically classified according to the following three viewpoints:
· The type of analysis used (e.g. linear static stress/displacement analysis, natural frequencies and normal modes analysis, buckling analysis, etc
· Area of application (e.g. mechanical engineering, civil engineering, automotive engineering, etc.)
· Objectives of the optimisation effort (e.g. geometry parameterization and optimisation, development of optimisation algorithms, etc.).
Types of structural optimisation problems:
There are three types of structural optimisation problems viz.
· mass or size optimisation
· shape optimisation
· topology optimisation
A. Mass or Size Optimisation :
Size optimisation defines ideal component parameters, such as material values, cross-section dimensions and thicknesses. It is used to determine the ideal thickness of a material based on the performance goals and the forces expected to be placed on the component during its life.
Figure 1.Size optimisation
The purpose of performing size optimisation is to minimise the material being used in a product while reducing its overall weight without compromising on performance. The technology can be applied to meet weight targets and performance challenges for structures or products concerned.
B. Shape Optimisation:
The purpose of structural shaping optimisation analysis is to find the best use of material for a body. Typically, this involves optimising the distribution of material, such that a structure will have the maximum stiffness for a defined set of loads.
Figure 2. Shape optimization
Many different objective functions need to be considered simultaneously for different load conditions and constraints to produce an optimum geometry. In addition, the optimum shape may change based on the material selection process.
C. Topology Optimisation:
Topology optimisation is a mathematical approach that optimises material layout within a given design space, for a given set of loads and boundary conditions such that the resulting layout meets a prescribed set of performance targets. Using topology optimisation, design engineers can find the best concept design that meets the design requirements.
Figure 3. Topology optimisation
Topology optimisation has been implemented widely through the use of finite element analysis, and optimisation techniques based on the method of moving asymptotes, genetic algorithms, optimality criteria method, level sets, and topological derivatives. Topology optimisation is used at the concept level of the design process to arrive at a conceptual design proposal that is then finetuned for performance and manufacturability. This replaces time consuming and costly design iterations and hence reduces design development time and overall cost while improving design performance. In some cases, proposals from a topology optimisation, although optimal, may be infeasible to manufacture due to high cost. These types of situations can be overcome through the use of manufacturing constraints in the topology optimisation problem formulation. Using manufacturing constraints, the optimisation yields engineering designs that would satisfy practical manufacturing requirements. An experimental study of a subsoiler, used for deep tillage in agricultural fields, was carried out to determine its maximum draft force by Mehmet Topakci et.al (2010). In this study the working conditions of the subsoiler were simulated three-dimensionally. The simulation showed that a structural optimisation can be generated on a subsoiler frame work body for reducing the weight . M. Grujicic et.al (2008) illustrated how geometrical-modelling, topology, size and shape optimization and manufacturing-process modeling methods and tools may be used in the design of body-in-white (BIW) load bearing polymer/metal hybrid components .
structural optimisation flow chart:
Figure 4. General flow chart of structural optimization
Applications in Mechanical Engineering:
Since the inception, structural optimisation has been widely used in mechanical, automobile and aeronautical engineering fields. Some of them are
· Optimum design of axles, cams, gears, machine tools, and other mechanical components.
· Minimising the weight for aircrafts and its components
· Minimising the weight for automobile components
· Design of pumps, turbines etc.
· Design of space craft components
Desirability function analysis and ANOVA can also be used for the optimisation of the parameters concerned with the various operations in mechanical engineering. N. Naresh and P. Vijaya Bhaskara Reddy (2014) presented desirability function analysis (DFA) and Analysis of Variance (ANOVA) for the Optimisation of Machining Parameters for Turning EN16 Steel 
Applications in civil Engineering field:
The largest consumption of materials among all engineering field take place in the civil engineering field .It is alarming that the natural resources are exhausting at a high rate due to the industrialisation and the higher per capita usage of different metallic and non metallic substances. So the materials should be utilized with minimum usage and maximum efficiency for the conservation of nature and to cater for the future needs. The advancement in structural optimisation is the only remedy resorted for the efficient utilization of the resources in a scientific way .In this context Structural Optimisation can be effectively utilised in various civil engineering applications like
· Portal frames
· Roof trusses
· Water tanks
· Shell structures
· Retaining walls etc.etc.
Problems on implementation of optimised models in civil engineering:
Apart from other fields of engineering the products are not machined to its final shape in civil engineering. There are several process of temporary staging and shuttering etc. for the construction of a civil engineering structure. When we go for optimisation there may be reduction in the quantity of materials. But at the same time the cost of shuttering and other arrangements may increase. When mechanisation and advanced construction methods are not implemented in most cases the optimised models will not be an optimised one in a true sense. There may be some time constraints in implementing the optimised model. So a broad approach is necessary in the development of structural optimisation for civil engineering applications considering every possible constraint.
The applications of structural optimisation in mechanical, automobile and aeronautical fields are developing in a very faster pace. But in the case of civil engineering the wide spread use of structural optimisation is still a dream. As we know the majority of consumption of materials is in civil engineering or its relative field. This reminds the civil engineers as a whole, the consumption of the materials should be in a scientific way to minimise the cost and to reduce other environmental impact problems.
In most of the cases in civil engineering the self weight of the structure is many times more than the live loads as in the case of bridges etc...This also relevant in case of building structures also. So by applying structural optimisation techniques we will be able to reduce the self weight of the structure without compromising on the overall performance and keeping the structural integrity intact.
Structural Engineers can do a lot in this field for adopting new methodology and technique for promoting the structural optimisation along with the structural design.
As stated by Bulent N. Alemdar et.al (2013) an optimal design solution is a very challenging task to achieve in structural engineering and is often a rigorous iterative process to produce the best solution in terms of the prescribed engineering criteria or objective while satisfying the design constraints and optimization. So structural analysis tools can be effectively used together to provide supplemental design information for structural engineers .
Normally the material required to construct taller buildings is disproportionately greater than for low-rise construction due to the increased bracing requirements. Tsavaridis K D et.al(2014) pointed out that topology optimisation may be a useful design tool in civil/structural engineering in order to overcome the frontiers between civil engineers and other engineers from other disciplines. In this context structural optimisation can be used for analysing building structures for different loading conditions. Zakhama, et al. (2007, 2010) investigated the topology optimisation of two and three dimensional structures subject to dead and wind loading for finding the optimum topology of the structures.
Johannes Lundgren, Christopher Palmqvist (2012) showed that structural optimisation is useful for structures, where simple linear material models are sufficient to represent the behaviour of the structure . And for civil engineering structures, the optimisation methods have yet to be further developed for truly becoming useful in practice, mainly due to the lack of proper material models for the behaviour of concrete in the available optimisation software’s. Another futuristic application of structural optimisation is in the crack repair of patches. Jiwu Tang (2011) investigated the topological optimisation for patch repair of structures with crack and stated the optimised bonded patch repair is more cost effective than its counter mechanical fasteners with improved fatigue life reduced corrosion and in situ application . Tsavaridis K D et.al (2015) investigated the application of structural topology optimisation to perforated steel beams and showed that optimised beam over performed in terms of load carrying capacities, deformations and stress intensities .
With the advancement in computing facilities the application of structural optimisation techniques are widely used in other engineering fields for variety of innovative applications. However its application in civil engineering is still in nascent stage. Even though civil engineering is the fore runner and the largest consumer of the natural resources, compared to other engineering fields the developments in structural optimisation in civil engineering field is still far behind. Numerous possibilities are opened for structural engineers in this regard. It is high time that a collaborative effort from the various experts in different specialisation in civil engineering is resorted to the effective utilisation of this method to the advancement of cost effective utilisation of various resources. So a collective effort has been initiated to implement the structural optimisation methods to the academia and researchers and the industry for the efficient utilization of resources so as to protect the environment and save the natural resources for the generations to come.
The authors wish to acknowledge their deep gratitude to the management and faculty of GITAM University, Hyderabad and NICMAR, Hyderabad for their constant support and encouragement rendered for research work.
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11 Johannes Lundgren, Christopher Palmqvist (2012)” Structural form optimization Methods of numerical optimization and applications on civil engineering structures” Master of Science Thesis, Chalmers University of Technology, Goteborg, Sweden.
12 Jiwu Tang, (2011), Developing Evolutionary Structural Optimisation Techniques for Civil Engineering Applications, Ph. D Thesis, RMIT University
13 Tsavaridis. KD, Kingman JJ and Toropov VV (2015),”Application of structural topology optimization to perforated steel beams “Science Direct, Computers and Science, Volume-158, October 2015 PP108-123
Received on 05.11.2015 Accepted on 06.12.2015
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Int. J. Tech. 5(2): July-Dec., 2015; Page 251-256