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Multidisciplinary design optimization (MDO) is a field of engineering that uses optimization methods to solve design problems incorporating a number of disciplines. It is also known as multidisciplinary optimization and multidisciplinary system design optimization (MSDO). Engineering is the application of scientific and technical knowledge to solve human problems. ...
In mathematics, the term optimization refers to the study of problems that have the form Given: a function f : A R from some set A to the real numbers Sought: an element x0 in A such that f(x0) ≤ f(x) for all x in A (minimization) or such that...
Usually considered in the context of the applied arts, engineering, architecture, and other such creative endeavours, design is used as both a noun and a verb. ...
MDO allows designers to incorporate all relevant disciplines simultaneously. The optimum of the simultaneous problem is superior to the design found by optimizing each discipline sequentially, since it can exploit the interactions between the disciplines. However, including all disciplines simultaneously significantly increases the complexity of the problem. In computer science, computational complexity theory is the branch of the theory of computation that studies the resources, or cost, of the computation required to solve a given problem. ...
These techniques have been used in a number of fields, including automobile design, naval architecture, electronics, computers, and electricity distribution. However, the largest number of applications have been in the field of aerospace engineering, such as aircraft and spacecraft design. For example, the proposed Boeing blended wing body (BWB) aircraft concept has used MDO extensively in the conceptual and preliminary design stages. The disciplines considered in the BWB design are aerodynamics, structural analysis, propulsion, control theory, and economics. This article or section does not cite its references or sources. ...
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The field of electronics is the study and use of systems that operate by controlling the flow of electrons (or other charge carriers) in devices such as thermionic valves and semiconductors. ...
A Lego RCX Computer is an example of an embedded computer used to control mechanical devices. ...
The examples and perspective in this article or section may not represent a worldwide view. ...
Aerospace engineering is the branch of engineering that concerns aircraft, spacecraft and related topics. ...
Airbus A380 An aircraft is any machine capable of atmospheric flight. ...
A spacecraft is designed to leave Earths atmosphere and operate beyond the surface of the Earth in outer space. ...
The Boeing Company (NYSE: BA, TYO: 7661 ) is the world’s largest aircraft manufacturer. ...
Categories: Possible copyright violations ...
This article is about the branch of Physics. ...
Structural analysis is the computation of deformations, deflections, and internal forces or stresses (Stress Eqiuivalents) within structures, either for design or for performance evaluation of existing structures. ...
Propulsion method may refer to a number of different articles: For a list of space propulsion methods, see spacecraft propulsion. ...
In engineering and mathematics, control theory deals with the behavior of dynamical systems. ...
Buyers bargain for good prices while sellers put forth their best front in Chichicastenango Market, Guatemala. ...
History
Traditional engineering design has normally been performed by teams, each with expertise in a specific discipline, such as aerodynamics or structures. Each team would use its members experience and judgement to develop a workable design, usually sequentially. For example, the aerodynamics experts would outline the shape of the body, and the structural experts would be expected to fit their design within the shape specified. The goals of the teams were generally performance-related, such as maximum speed, minimum drag, or minimum structural weight. An object falling through a gas or liquid experiences a force in direction opposite to its motion. ...
Between 1970 and 1990, two major developments in the aircraft industry changed the approach of aircraft design engineers to their design problems. The first was computer-aided design, which allowed designers to quickly modify and analyse their designs. The second was changes in the procurement policy of most airlines and military organizations, particularly the military of the United States, from a performance-centred approach to one that emphasized lifecycle cost issues. This led to an increased concentration on economic factors and the attributes known as the "ilities": manufacturability, reliability, maintainability, etc. CAD is a TLA that may stand for: Cadiz Railroad (AAR reporting mark CAD) Canadian dollar – ISO 4217-code Capital Adequacy Directive Card Acceptance Device Children of the Anachronistic Dynasty Computer-aided design Computer-aided detection (medical) Computer-aided diagnosis (medical) Computer-assisted dispatch Computer-assisted drafting Coronary artery disease...
A Boeing 747-400 belonging to Virgin Atlantic Airways, one of the UKs largest airlines. ...
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Since 1990, the techniques have expanded to other industries. Globalization has resulted in more distributed, decentralized design teams. The high-performance personal computer has largely replaced the centralized supercomputer and the Internet and local area networks have facilitated sharing of design information. Disciplinary design software in many disciplines (such as NASTRAN, a finite element analysis program for structural design) have become very mature. In addition, many optimization algorithms, in particular the population-based algorithms, have advanced significantly. A supercomputer is a computer that leads the world in terms of processing capacity, particularly speed of calculation, at the time of its introduction. ...
A local area network (LAN) is a computer network covering a small local area, like a home, office, or small group of buildings such as a home, office, or college. ...
Visualization of how a car deforms in an asymmetrical crash using finite element analysis. ...
Problem formulation Problem formulation is normally the most difficult part of the process. It is the selection of design variables, constraints, objectives, and models of the disciplines. A further consideration is the strength and breadth of the interdisciplinary coupling in the problem.
Design variables A design variable is a numeric value that is controllable, from the point of view of the designer. For instance, the thickness of a structural member can be considered a design variable. Design variables can be continuous (such as a wing span), discrete (such as the number of ribs in a wing), or boolean (such as whether to build a monoplane or a biplane). Design problems with continuous variables are normally solved more easily. Hs123 biplane. ...
Design variables are often bounded, that is, they often have maximum and minimum values. Depending on the solution method, these bounds can be treated as constraints or separately.
Constraints A constraint is a condition that must be satisfied in order for the design to be feasible. An example of a constraint in aircraft design is that the lift generated by a wing must be equal to the weight of the aircraft. In addition to physical laws, constraints can reflect resource limitations, user requirements, or bounds on the validity of the analysis models. Constraints can be used explicitly by the solution algorithm or can be incorporated into the objective using Lagrange multipliers. Lift consists of the sum of all the fluid dynamic forces on a body perpendicular to the direction of the external flow approaching that body. ...
In mathematical optimization problems, Lagrange multipliers are a method for dealing with constraints. ...
Objectives An objective is a numerical value that is to be maximized or minimized. For example, a designer may wish to maximize profit or minimize weight. Many solution methods work only with single objectives. When using these methods, the designer normally weights the various objectives and sums them to form a single objective. Other methods allow multiobjective optimization, such as the calculation of a Pareto front. Pareto efficiency, or Pareto optimality, is an important notion in economics with broad applications in game theory, engineering and the social sciences. ...
Models The designer must also choose models to relate the constraints and the objectives to the design variables. These models are dependent on the discipline involved. They may be empirical models, such as a regression analysis of aircraft prices, theoretical models, such as from computational fluid dynamics, or reduced-order models of either of these. In choosing the models the designer must trade off fidelity with analysis time. Generally, regression is a move backwards; It is the opposite of progress. ...
Computational fluid dynamics (CFD) is the use of computers to analyze problems in fluid dynamics. ...
The multidisciplinary nature of most design problems complicates model choice and implementation. Often several iterations are necessary between the disciplines in order to find the values of the objectives and constraints. As an example, the aerodynamic loads on a wing affect the structural deformation of the wing. The structural deformation in turn changes the shape of the wing and the aerodynamic loads. Therefore, in analysing a wing, the aerodynamic and structural analyses must be run a number of times in turn until the loads and deformation converge.
Standard form Once the design variables, constraints, objectives, and the relationships between them have been chosen, the problem can be expressed in the following form: - find
 that minimizes  subject to  and  where J is an objective, is a vector of design variables,  is a vector of constraints, and  and  are vectors of lower and upper bounds on the design variables. Maximization problems can be converted to minimization problems by multiplying the objective by -1. Constraints can be reversed in a similar manner. Equality constraints can be replaced by two inequality constraints. In physics and in vector calculus, a spatial vector is a concept characterized by a magnitude, which is a scalar, and a direction (which can be defined in a 3-dimensional space by the Euler angles). ...
Problem solution The problem is normally solved using appropriate techniques from the field of optimization. These include gradient-based algorithms, population-based algorithms, or others. Very simple problems can sometimes be expressed linearly; in that case the techniques of linear programming are applicable. In the above two images, the scalar field is in black and white, black representing higher values, and its corresponding gradient is represented by blue arrows. ...
In mathematics, linear programming (LP) problems are optimization problems in which the objective function and the constraints are all linear. ...
Gradient-based methods In numerical analysis, Newtons method (or the Newton-Raphson method) is an efficient algorithm for finding approximations to the zeros (or roots) of a real-valued function. ...
Gradient descent is an optimization algorithm that approaches a local maximum of a function by taking steps proportional to the gradient (or the approximate gradient) of the function at the current point. ...
In mathematics, the conjugate gradient method is an algorithm for the numerical solution of particular systems of linear equations, namely those whose matrix is symmetric and positive definite. ...
Population-based methods A genetic algorithm (GA) is a search technique used in computer science to find approximate solutions to optimization and search problems. ...
Particle swarm optimization (PSO) is form of swarm intelligence. ...
Other methods Most of these techniques require large numbers of evaluations of the objectives and the constraints. The disciplinary models are often very complex and can take significant amounts of time for a single evaluation. The solution can therefore be extremely time-consuming. Many of the optimization techniques are adaptable to parallel computing. Much current research is focused on methods of decreasing the required time. Simulated annealing (SA) is a generic probabilistic meta-algorithm for the global optimization problem, namely locating a good approximation to the global optimum of a given function in a large search space. ...
Parallel computing is the simultaneous execution of the same task (split up and specially adapted) on multiple processors in order to obtain results faster. ...
Also, no existing solution method is guaranteed to find the global optimum of a general problem. Gradient-based methods find local optima with high reliability but are normally unable to escape a local optimum. Stochastic methods, like simulated annealing and genetic algorithms, will find a good solution with high probability, but very little can be said about the mathematical properties of the solution. It is not guaranteed to even be a local optimum. These methods often find a different design each time they are run. Global optimization is a branch of applied mathematics and numerical analysis that deals with the optimization of a function or a set of functions to some criteria. ...
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