Abstract: In Finite Element Technique nodal stresses are calculated through displacement as nodes. In this process, the displacement calculated at nodes is sufficiently good enough but stresses calculated at nodes are not sufficiently accurate. Therefore, the accuracy in the stress computation in FEM models based on the displacement technique is obviously matter of concern for computational time in shape optimization of engineering problems. In the present work same is focused to find out unique points within the element as well as the boundary of the element so, that good accuracy in stress computation can be achieved. Generally, major optimal stress points are located in domain of the element some points have been also located at boundary of the element where stresses are fairly accurate as compared to nodal values. Then, it is subsequently concluded that there is an existence of unique points within the element, where stresses have higher accuracy than other points in the elements. Therefore, it is main aim is to evolve a generalized procedure for the determination of the optimal stress location inside the element as well as at the boundaries of the element and verify the same with results from numerical experimentation. The results of quadratic 9 noded serendipity elements are presented and the location of distinct optimal stress points is determined inside the element, as well as at the boundaries. The theoretical results indicate various optimal stress locations are in local coordinates at origin and at a distance of 0.577 in both directions from origin. Also, at the boundaries optimal stress locations are at the midpoints of the element boundary and the locations are at a distance of 0.577 from the origin in both directions. The above findings were verified through experimentation and findings were authenticated. For numerical experimentation five engineering problems were identified and the numerical results of 9-noded element were compared to those obtained by using the same order of 25-noded quadratic Lagrangian elements, which are considered as standard. Then root mean square errors are plotted with respect to various locations within the elements as well as the boundaries and conclusions were drawn. After numerical verification it is noted that in a 9-noded element, origin and locations at a distance of 0.577 from origin in both directions are the best sampling points for the stresses. It was also noted that stresses calculated within line at boundary enclosed by 0.577 midpoints are also very good and the error found is very less. When sampling points move away from these points, then it causes line zone error to increase rapidly. Thus, it is established that there are unique points at boundary of element where stresses are accurate, which can be utilized in solving various engineering problems and are also useful in shape optimizations.
Abstract: In this paper a 3-D finite element (FE) investigation of soil-blade interaction is described. The effects of blade’s shape and rake angle are examined both numerically and experimentally. The soil is considered as an elastic-plastic granular material with non-associated Drucker-Prager material model. Contact elements with different properties are used to mimic soil-blade sliding and soil-soil cutting phenomena. A separation criterion is presented and a procedure to evaluate the forces acting on the blade is given and discussed in detail. Experimental results were derived from tests using soil bin facility and instruments at the University of Saskatchewan. During motion of the blade, load cells collect data and send them to a computer. The measured forces using load cells had noisy signals which are needed to be filtered. The FE results are compared with experimental results for verification. This technique can be used in blade shape optimization and design of more complicated blade’s shape.
Abstract: In Electric Power Steering (EPS), spoke type
Brushless AC (BLAC) motors offer distinct advantages over other
electric motor types in terms torque smoothness, reliability and
efficiency. This paper deals with the shape optimization of spoke
type BLAC motor, in order to reduce cogging torque. This paper
examines 3 steps skewing rotor angle, optimizing rotor core edge and
rotor overlap length for reducing cogging torque in spoke type BLAC
motor. The methods were applied to existing machine designs and
their performance was calculated using finite- element analysis
(FEA). Prototypes of the machine designs were constructed and
experimental results obtained. It is shown that the FEA predicted the
cogging torque to be nearly reduce using those methods.
Abstract: Non-linear FEM calculations are indispensable when
important technical information like operating performance of a
rubber component is desired. For example rubber bumpers built into
air-spring structures may undergo large deformations under load,
which in itself shows non-linear behavior. The changing contact
range between the parts and the incompressibility of the rubber
increases this non-linear behavior further. The material
characterization of an elastomeric component is also a demanding
engineering task.
The shape optimization problem of rubber parts led to the study of
FEM based calculation processes. This type of problems was posed
and investigated by several authors. In this paper the time demand of
certain calculation methods are studied and the possibilities of time
reduction is presented.
Abstract: The present environmental issues have made aircraft jet noise reduction a crucial problem in aero-acoustics research. Acoustic studies reveal that addition of chevrons to the nozzle reduces the sound pressure level reasonably with acceptable reduction in performance. In this paper comprehensive numerical studies on acoustic characteristics of different types of chevron nozzles have been carried out with non-reacting flows for the shape optimization of chevrons in supersonic nozzles for aerospace applications. The numerical studies have been carried out using a validated steady 3D density based, k-ε turbulence model. In this paper chevron with sharp edge, flat edge, round edge and U-type edge are selected for the jet acoustic characterization of supersonic nozzles. We observed that compared to the base model a case with round-shaped chevron nozzle could reduce 4.13% acoustic level with 0.6% thrust loss. We concluded that the prudent selection of the chevron shape will enable an appreciable reduction of the aircraft jet noise without compromising its overall performance. It is evident from the present numerical simulations that k-ε model can predict reasonably well the acoustic level of chevron supersonic nozzles for its shape optimization.
Abstract: Non-linear FEM calculations are indispensable when important technical information like operating performance of a rubber component is desired. Rubber bumpers built into air-spring structures may undergo large deformations under load, which in itself shows non-linear behavior. The changing contact range between the parts and the incompressibility of the rubber increases this non-linear behavior further. The material characterization of an elastomeric component is also a demanding engineering task. In this paper a comprehensive investigation is introduced including laboratory measurements, mesh density analysis and complex finite element simulations to obtain the load-displacement curve of the chosen rubber bumper. Contact and friction effects are also taken into consideration. The aim of this research is to elaborate a FEM model which is accurate and competitive for a future shape optimization task.
Abstract: Unmanned aerial vehicles (UAVs) performing their
operations for a long time have been attracting much attention in
military and civil aviation industries for the past decade. The
applicable field of UAV is changing from the military purpose only to
the civil one. Because of their low operation cost, high reliability and
the necessity of various application areas, numerous development
programs have been initiated around the world. To obtain the optimal
solutions of the design variable (i.e., sectional airfoil profile, wing
taper ratio and sweep) for high performance of UAVs, both the lift and
lift-to-drag ratio are maximized whereas the pitching moment should
be minimized, simultaneously. It is found that the lift force and
lift-to-drag ratio are linearly dependent and a unique and dominant
solution are existed. However, a trade-off phenomenon is observed
between the lift-to-drag ratio and pitching moment. As the result of
optimization, sixty-five (65) non-dominated Pareto individuals at the
cutting edge of design spaces that are decided by airfoil shapes can be
obtained.
Abstract: A strategy is implemented to find the improved configuration design of an existing aircraft structure by executing topology and shape optimizations. Structural analysis of the Initial Design Space is performed in ANSYS under the loads pertinent to operating and ground conditions. By using the FEA results and data, an initial optimized layout configuration is attained by exploiting nonparametric topology optimization in TOSCA software. Topological optimized surfaces are then smoothened and imported in ANSYS to develop the geometrical features. Nodes at the critical locations of resulting voids are selected for sketching rough profiles. Rough profiles are further refined and CAD feasible geometric features are generated. The modified model is then analyzed under the same loadings and constraints as defined for topology optimization. Shape at the peak stress concentration areas are further optimized by exploiting the shape optimization in TOSCA.shape module. The harmonized stressed model with the modified surfaces is then imported in CATIA to develop the final design.
Abstract: The purpose of this study is to derive optimal shapes of
a body located in viscous flows by the finite element method using the
acoustic velocity and the four-step explicit scheme. The formulation
is based on an optimal control theory in which a performance function
of the fluid force is introduced. The performance function should be
minimized satisfying the state equation. This problem can be transformed
into the minimization problem without constraint conditions
by using the adjoint equation with adjoint variables corresponding to
the state equation. The performance function is defined by the drag
and lift forces acting on the body. The weighted gradient method
is applied as a minimization technique, the Galerkin finite element
method is used as a spatial discretization and the four-step explicit
scheme is used as a temporal discretization to solve the state equation
and the adjoint equation. As the interpolation, the orthogonal basis
bubble function for velocity and the linear function for pressure
are employed. In case that the orthogonal basis bubble function is
used, the mass matrix can be diagonalized without any artificial
centralization. The shape optimization is performed by the presented
method.
Abstract: Numerical design optimization is a powerful tool that
can be used by engineers during any stage of the design process.
There are many different applications for structural optimization. A
specific application that will be discussed in the following paper is
experimental data matching. Data obtained through tests on a physical
structure will be matched with data from a numerical model of that
same structure. The data of interest will be the dynamic characteristics
of an antenna structure focusing on the mode shapes and modal
frequencies. The structure used was a scaled and simplified model of
the Karoo Array Telescope-7 (KAT-7) antenna structure.
This kind of data matching is a complex and difficult task. This
paper discusses how optimization can assist an engineer during the
process of correlating a finite element model with vibration test data.
Abstract: Shape optimization of the airfoil with high aspect ratio
of long endurance unmanned aerial vehicle (UAV) is performed by the
multi-objective optimization technology coupled with computational
fluid dynamics (CFD). For predicting the aerodynamic characteristics
around the airfoil the high-fidelity Navier-Stokes solver is employed
and SMOGA (Simple Multi-Objective Genetic Algorithm), which is
developed by authors, is used for solving the multi-objective
optimization problem. To obtain the optimal solutions of the design
variable (i.e., sectional airfoil profile, wing taper ratio and sweep) for
high performance of UAVs, both the lift and lift-to-drag ratio are
maximized whereas the pitching moment should be minimized,
simultaneously. It is found that the lift force and lift-to-drag ratio are
linearly dependent and a unique and dominant solution are existed.
However, a trade-off phenomenon is observed between the lift-to-drag
ratio and pitching moment. As the result of optimization, sixty-five
(65) non-dominated Pareto individuals at the cutting edge of design
spaces that is decided by airfoil shapes can be obtained.
Abstract: Predictions of flow and heat transfer characteristics and shape optimization in internally finned circular tubes have been performed on three-dimensional periodically fully developed turbulent flow and thermal fields. For a trapezoidal fin profile, the effects of fin height h, upper fin widths d1, lower fin widths d2, and helix angle of fin ? on transport phenomena are investigated for the condition of fin number of N = 30. The CFD and mathematical optimization technique are coupled in order to optimize the shape of internally finned tube. The optimal solutions of the design variables (i.e., upper and lower fin widths, fin height and helix angle) are numerically obtained by minimizing the pressure loss and maximizing the heat transfer rate, simultaneously, for the limiting conditions of d1 = 0.5~1.5 mm, d2 = 0.5~1.5 mm, h= 0.5~1.5mm, ? = 10~30 degrees. The fully developed flow and thermal fields are predicted using the finite volume method and the optimization is carried out by means of the multi-objective genetic algorithm that is widely used in the constrained nonlinear optimization problem.
Abstract: This research is to design and implement a new kind
of agitators called differential agitator. The Differential Agitator is an
electro- mechanic set consists of two shafts. The first shaft is the
bearing axis while the second shaft is the axis of the quartet upper
bearing impellers group and the triple lower group which are called
as agitating group. The agitating group is located inside a cylindrical
container equipped especially to contain square directors for the
liquid entrance and square directors called fixing group for the liquid
exit. The fixing group is installed containing the agitating group
inside any tank whether from upper or lower position. The agitating
process occurs through the agitating group bearing causing a lower
pressure over the upper group leading to withdrawing the liquid from
the square directors of the liquid entering and consequently the liquid
moves to the denser place under the quartet upper group. Then, the
liquid moves to the so high pressure area under the agitating group
causing the liquid to exit from the square directors in the bottom of
the container. For improving efficiency, parametric study and shape
optimization has been carried out. A numerical analysis,
manufacturing and laboratory experiments were conducted to design
and implement the differential agitator. Knowing the material
prosperities and the loading conditions, the FEM using ANSYS11
was used to get the optimum design of the geometrical parameters of
the differential agitator elements while the experimental test was
performed to validate the advantages of the differential agitators to
give a high agitation performance of lime in the water as an example.
In addition, the experimental work has been done to express the
internal container shape in the agitation efficiency. The study ended
up with conclusions to maximize agitator performance and optimize
the geometrical parameters to be used for manufacturing the
differential agitator
Abstract: A novel methodology has been used to design an
evaporator coil of a refrigerant. The methodology used is through a
complete Computer Aided Design /Computer Aided Engineering
approach, by means of a Computational Fluid Dynamic/Finite
Element Analysis model which is executed many times for the
thermal-fluid exploration of several designs' configuration by an
commercial optimizer. Hence the design is carried out automatically
by parallel computations, with an optimization package taking the
decisions rather than the design engineer. The engineer instead takes
decision regarding the physical settings and initializing of the
computational models to employ, the number and the extension of the
geometrical parameters of the coil fins and the optimization tools to
be employed. The final design of the coil geometry found to be better
than the initial design.
Abstract: In this paper, a tooth shape optimization method for
cogging torque reduction in Permanent Magnet (PM) motors is
developed by using the Reduced Basis Technique (RBT) coupled by
Finite Element Analysis (FEA) and Design of Experiments (DOE)
methods. The primary objective of the method is to reduce the
enormous number of design variables required to define the tooth
shape. RBT is a weighted combination of several basis shapes. The
aim of the method is to find the best combination using the weights
for each tooth shape as the design variables. A multi-level design
process is developed to find suitable basis shapes or trial shapes at
each level that can be used in the reduced basis technique. Each level
is treated as a separated optimization problem until the required
objective – minimum cogging torque – is achieved. The process is
started with geometrically simple basis shapes that are defined by
their shape co-ordinates. The experimental design of Taguchi method
is used to build the approximation model and to perform
optimization. This method is demonstrated on the tooth shape
optimization of a 8-poles/12-slots PM motor.
Abstract: The Prediction of aerodynamic characteristics and
shape optimization of airfoil under the ground effect have been carried
out by integration of computational fluid dynamics and the multiobjective
Pareto-based genetic algorithm. The main flow
characteristics around an airfoil of WIG craft are lift force, lift-to-drag
ratio and static height stability (H.S). However, they show a strong
trade-off phenomenon so that it is not easy to satisfy the design
requirements simultaneously. This difficulty can be resolved by the
optimal design. The above mentioned three characteristics are chosen
as the objective functions and NACA0015 airfoil is considered as a
baseline model in the present study. The profile of airfoil is
constructed by Bezier curves with fourteen control points and these
control points are adopted as the design variables. For multi-objective
optimization problems, the optimal solutions are not unique but a set
of non-dominated optima and they are called Pareto frontiers or Pareto
sets. As the results of optimization, forty numbers of non- dominated
Pareto optima can be obtained at thirty evolutions.
Abstract: This paper describes the shape optimization of impeller
blades for a anti-heeling bidirectional axial flow pump used in ships.
In general, a bidirectional axial pump has an efficiency much lower
than the classical unidirectional pump because of the symmetry of the
blade type. In this paper, by focusing on a pump impeller, the shape of
blades is redesigned to reach a higher efficiency in a bidirectional axial
pump. The commercial code employed in this simulation is CFX v.13.
CFD result of pump torque, head, and hydraulic efficiency was
compared. The orthogonal array (OA) and analysis of variance
(ANOVA) techniques and surrogate model based optimization using
orthogonal polynomial, are employed to determine the main effects
and their optimal design variables. According to the optimal design,
we confirm an effective design variable in impeller blades and explain
the optimal solution, the usefulness for satisfying the constraints of
pump torque and head.
Abstract: A finite element analysis (FEA) computer software HyperWorks is utilized in re-designing an automotive component to reduce its mass. Reduction of components mass contributes towards environmental sustainability by saving world-s valuable metal resources and by reducing carbon emission through improved overall vehicle fuel efficiency. A shape optimization analysis was performed on a rear spindle component. Pre-processing and solving procedures were performed using HyperMesh and RADIOSS respectively. Shape variables were defined using HyperMorph. Then optimization solver OptiStruct was utilized with fatigue life set as a design constraint. Since Stress-Number of Cycle (S-N) theory deals with uni-axial stress, the Signed von Misses stress on the component was used for looking up damage on S-N curve, and Gerber criterion for mean stress corrections. The optimization analysis resulted in mass reduction of 24% of the original mass. The study proved that the adopted approach has high potential use for environmental sustainability.