Inverse Design Problem Research Articles

Topological and Architectural Designs for Pre-ISDN Integration of Fiber Optic Voice and Data Networks

Several inter-LATA carriers in the United States are implementing fiber optic networks. The geographic coverage of these networks coupled with the bias to choose fiber as backbone links via traditional data network design yields an opportunity for pre-ISDN integration of voice and data. This paper presents three transitional models for pre-ISDN integration of voice and data. The impact of incorporating a fiber optic network in the traditional data design formulation is demonstrated. Based upon the theoretical considerations of fiber optic incorporation, data routing, delay, throughput, and reliability are redefined, yielding an inverse design problem formulation for data. Practical considerations are presented with each transitional model.

An Inverse (Design) Problem Solution Method for the Blade Cascade Flow on Streamsurface of Revolution

On the basis of the fundamental equations of aerothermodynamics a method for solving the inverse (design) problem of blade cascade flow on the blade-to-blade streamsurface of revolution is suggested in the present paper. For this kind of inverse problem the inlet and outlet flow angles, the aerothermodynamic parameters at the inlet, and the other constraint conditions are given. Two approaches are proposed in the present paper: the suction-pressure-surface alternative calculation method (SSAC) and the prescribed streamline method (PSLM). In the first method the metric tensor (blade channel width) is obtained by alternately fixing either the suction or pressure side and by revising the geometric form of the other side from one iteration to the next. The first step of the second method is to give the geometric form of one of the streamlines. The velocity distribution or the mass flow rate per unit area on that given streamline is estimated approximately by satisfying the blade thickness distribution requirement. The stream function in the blade cascade channel is calculated by assuming initial suction and pressure surfaces and solving the governing differential equations. Then, the distribution of metric tensor on the given streamline is specified by the stream function definition. It is evident that the square root of the metric tensor is a circumferential width of the blade cascade channel for the special nonorthogonal coordinate system adopted in the present paper. The iteration procedure for calculating the stream function is repeated until the convergence criterion of the metric tensor is reached. A comparison between the solutions with and without consideration of viscous effects is also made in the present paper.

Direct and inverse problem in supersonic axisymmetric flow

Introduction SUPERSONIC inviscid flow can generally be solved by the i^method of characteristics or by shock-capturing methods. The method of characteristics computes the flow along characteristics and uses the Rankine-Hugoniot conditions at the shock. This method has the advantage of accuracy, but is regarded as complex and computationally inefficient, especially in regions of near coalescence of the two sets of characteristics.' In shock-capturing methods the shock is smeared over several grid points, where oscillations can occur and the scheme loses accuracy. However, due to their directness and computational ease, shock-capturing methods have been preferred in recent years. In this Note, we develop an efficient method using the characteristics and streamlines of a flow. These are used as coordinates and the flow quantities are expressed in terms of Riemann functions. A scheme is obtained which is significantly more efficient and accurate than shock-capturing methods for flow over axisymmetric bodies. Since streamlines form one of the coordinates, we naturally obtain a body-fit system. It is also a truly shock-fit coordinate system. Not only are the Rankine-Hugoniot conditions used, but the shock lies exactly on grid points also. The success of the present method in the two-dimensional case rests on the discovery of an accurate and simple approximation. In the axisymmetric case, a similarly accurate and simple approximation has eluded us. The approximation presented herein is simple, but generally not as accurate as that for the two-dimensional case. A better iterative procedure has been developed to compensate for this weakness. As was the case for the two-dimensional flow, our method is well suited for the inverse design problem (i.e., given M0>1 and the pressure distribution on the body, find the shape of the body and the flow everywhere).

The design of transonic aerofoils by a well‐posed inverse method

AbstractThis paper describes a numerical method for designing closed aerofoils that correspond to given surface speed distributions including flows with shock waves. The prescribed surface speed distribution in general contains three parameters whose values are found as part of the solution. The inverse aerofoil design problem is not well posed unless the prescribed speed satisfies three constraints that can be used to fix the value of the three adjustable parameters. The computational method is based on the numerical solution of the full potential equation in conservation form by an approximate factorization–multigrid scheme. The nature of the constraints and several strategies for introducing the necessary freedom in the prescribed speed are discussed along with typical solutions illustrating the method.

An engineering approach to the inverse transonic wing design problem

Communications in Applied Numerical MethodsVolume 2, Issue 1 p. 47-56 Article An engineering approach to the inverse transonic wing design problem E. Greff, E. Greff MBB-UT, Department of Aerodynamics, TE 21, Hünefeldstr. 1–5, 2800 Bremen, FRG Research Scientist, Project Coordinator Theoretical and Applied Aerodynamics.Search for more papers by this authorJ. Mantel, J. Mantel MBB-UT, Department of Aerodynamics, TE 21, Hünefeldstr. 1–5, 2800 Bremen, FRG Research Engineer, Aerodynamic Design.Search for more papers by this author E. Greff, E. Greff MBB-UT, Department of Aerodynamics, TE 21, Hünefeldstr. 1–5, 2800 Bremen, FRG Research Scientist, Project Coordinator Theoretical and Applied Aerodynamics.Search for more papers by this authorJ. Mantel, J. Mantel MBB-UT, Department of Aerodynamics, TE 21, Hünefeldstr. 1–5, 2800 Bremen, FRG Research Engineer, Aerodynamic Design.Search for more papers by this author First published: January/February 1986 https://doi.org/10.1002/cnm.1630020108Citations: 5 AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Citing Literature Volume2, Issue1January/February 1986Pages 47-56 RelatedInformation

A Simple Method for Solving Three-Dimensional Inverse Problems of Turbomachine Flow and the Annular Constraint Condition

In 1950, Wu [1] suggested that the three-dimensional inverse (design) problem of turbomachine flow may be solved approximately by a Taylor series expansion in the circumferential direction based on the known flow variation over an S2 stream surface in the midchannel of the blade passage. This idea has been realized recently. A new coordinate transformation has been developed. The coordinate surfaces are coincident with the S2 stream surfaces. This transformation leads to a new method to calculate the aerodynamic equations of three-dimensional flow. By the use of this transformation, a high-order expansion is realized to determine the shape of the blade surfaces from the fluid state on the S2m stream surface directly. Computation in this manner soon leads to the discovery that theoretically the distribution of flow parameter (usually Vθr) on S2m prescribed by the designer should satisfy a constraint condition, which guarantees that the S1 stream surfaces along the hub and shroud obtained from circumferential extension of the S2m surface are surfaces of revolution. An approximate method is suggested to meet this condition.

Soft elastic shells undergoing large deformations

Soft shells made of elastomers and undergoing large deformations under load are studied. The inverse design problem, non-linear under large deformations, is solved. The results obtained are illustrated on a two-parameter shell of revolution fabricated from a two-constant material. The problems of coupling the biaxial and uniaxial zones of the shell and of designing the composite shell are clarified. Amongst the papers dealing with the theory of soft shells and, generally, under small deformations, /1–7/ merit attention.

Harmonic Shape and Optimum Design

The harmonic condition and strategy for the inverse design problem in elasticity is examined. The analogy to membrane shapes and free-surface potential flow problems due to the irrotational character of the perturbations introduced by harmonic shapes is highlighted. Basic equations for the interior problem for holes and inclusions are derived using the complex variable formulation. They are than applied to determine the harmonic shape for a rigid inclusion in a biaxial field which is shown to be optimum giving the minimum possible stress concentration.

Free Boundary Problem for the Laplace Equation With Application to ECM Tool Design

The tool design problem of electrochemical machining (ECM) is formulated by the inverted approach in which the spatial coordinates are treated as the dependent variables on the plane of the complex potential. A general solution of this free boundary problem by analytic continuation provides the basis for a series approximation with correct asymptotic behavior using the method of weighted residues. The procedure is used to determine the noninsulated or partially insulated tool shapes which can be used to machine a prescribed workpiece geometry. The method is generally applicable to inverse (design) problems of potential theory which involve a given equipotential (or streamline) boundary along which a Neumann boundary condition is also prescribed as occurs in heat conduction, ideal flow, and electrostatics. The inverted approach not only eliminates the need for trial-and-error design procedures but also provides the advantage of adjustment in geometry by superposition.

Nonlinear regulator theory and an inverse optimal control problem

Nonlinear optimal regulators are discussed, and some useful properties are isolated. An inverse problem of nonlinear regulator design is posed and solved.

Pure Design Method for Aerofoils in Cascade

An extension of Martensen's method is described which permits an exact solution of the inverse or blade design problem. An equation is derived for the normal velocity distributed about a given contour when a given tangential velocity is imposed about the contour and from this normal velocity an initial arbitrarily chosen blade shape may be successively modified until a blade is found having a desired surface velocity distribution. Five examples of the method are given.