THE DESIGN AND ANALYSIS OF EXPERIMENTS. By Oscar Kempthorne. New York, John Wiley and Sons, Inc., 1952. 631 pp. $8.50. This book by a teacher of statistics (as well as a consultant for \"experimenters\") is a comprehensive study of the philosophical background for the statistical design of experiment. It is necessary to have some facility with algebraic notation and manipulation to be able to use the volume intelligently. The problems are presented from the theoretical point of view, without such practical examples as would be helpful for those not acquainted with mathematics. The mathematical justification for the techniques is given. As a somewhat advanced treatment of the design and analysis of experiments, this volume will be interesting and helpful for many who approach statistics theoretically as well as practically. With emphasis on the \"why,\" and with description given broadly, the author relates the subject matter to the general theory of statistics and to the general problem of experimental inference. MARGARET J. ROBERTSON

The Design and Analysis of Experiments

The Personal Interview

The boundary layer equations for plane, incompressible, and steady flow are 

$$\matrix{ {u{{\partial u} \over {\partial x}} + v{{\partial u} \over {\partial y}} = - {1 \over \varrho }{{\partial p} \over {\partial x}} + v{{{\partial ^2}u} \over {\partial {y^2}}},} \cr {0 = {{\partial p} \over {\partial y}},} \cr {{{\partial u} \over {\partial x}} + {{\partial v} \over {\partial y}} = 0.} \cr }$$

Boundary Layer Theory

Topology optimization is the process of determining the optimal layout of material and connectivity inside a design domain. This paper surveys topology optimization of continuum structures from the year 2000 to 2012. It focuses on new developments, improvements, and applications of finite element-based topology optimization, which include a maturation of classical methods, a broadening in the scope of the field, and the introduction of new methods for multiphysics problems. Four different types of topology optimization are reviewed: (1) density-based methods, which include the popular Solid Isotropic Material with Penalization (SIMP) technique, (2) hard-kill methods, including Evolutionary Structural Optimization (ESO), (3) boundary variation methods (level set and phase field), and (4) a new biologically inspired method based on cellular division rules. We hope that this survey will provide an update of the recent advances and novel applications of popular methods, provide exposure to lesser known, yet promising, techniques, and serve as a resource for those new to the field. The presentation of each method's focuses on new developments and novel applications.

/pdf/a-survey-of-structural-and-multidisciplinary-continuum-3lbeegkisv.pdf

A survey of structural and multidisciplinary continuum topology optimization: post 2000

A new method for performing a balanced reduction of a high-order linear system is presented. The technique combines the proper orthogonal decomposition and concepts from balanced realization theory. The method of snapshotsisused to obtainlow-rank,reduced-rangeapproximationsto thesystemcontrollability and observability grammiansineitherthetimeorfrequencydomain.Theapproximationsarethenusedtoobtainabalancedreducedorder model. The method is particularly effective when a small number of outputs is of interest. It is demonstrated for a linearized high-order system that models unsteady motion of a two-dimensional airfoil. Computation of the exact grammians would be impractical for such a large system. For this problem, very accurate reducedorder models are obtained that capture the required dynamics with just three states. The new models exhibit far superiorperformancethanthosederived using a conventionalproperorthogonal decomposition. Although further development is necessary, the concept also extends to nonlinear systems.

/pdf/balanced-model-reduction-via-the-proper-orthogonal-5c77iwc45j.pdf

Balanced Model Reduction via the Proper Orthogonal Decomposition

https://ntrs.nasa.gov/api/citations/20010018414/downloads/20010018414.pdf

Reduced-order modeling: new approaches for computational physics

111 this paper, we rcvicw the deve lo l~n~e~~ t of new reducecl-orcler ~ r ~ o t l e l i ~ ~ g tecl~niques ant1 tliscuss their applicalrility to variolts prol)len~s in co~ril)utatior~ul pl~ysics. Eu~pllasis is gi~.cn to r~~ctho(ls basetl 011 j'olterra series re l ) rese~~ta t io~~s and thr proper ortllogo11a1 deco~~~position. Results are reported for cliffcre~~t 11ol11i11ear systct~l~s to 1)rovidc clear cxan~ples of the cor~struc.tio~~ a11t1 usc of recluc~cd-orcler llod(>ls, p;lrtic.ularly ill the 1l11tlti-cliscil)li11:1ry field of c o ~ ~ ~ l ) u t a t i o ~ ~ a l aeroelasticity. U~~s t eady aerodj,nan~ic and aeroelast,ic behaviors of two-di~nrnsional and three-dinle~~sional geo~~~e t r i e s arc. tlcscri1)etl. Large illcreases in co1111)utational efficie~~c,y are ol~t,:ii~lccl thruugl~ the use of rcducetl-order ~r~otlc!ls! thcrebj. justifying the izlitial c.onlputatio11a1 esl)c:~~se of constructing th(:sr r~~oticls and ~ ~ ~ o t i v a t i r ~ g tl~eirusc for ~~~ult i-disc, i[)I i~la~>. design analysis.

/pdf/reduced-order-modeling-new-approaches-for-computational-3fpt7e0ddd.pdf

Reduced-order modeling - New approaches for computational physics

https://digitalcommons.unl.edu/cgi/viewcontent.cgi?article=1080&context=usafresearch

State-space representation of the unsteady aerodynamics of flapping flight

Numerical solutions of viscous, swirling flows through circular pipes of constant radius and circular pipes with throats have been obtained. Solutions were computed for several values of vortex circulation, Reynolds number and throat/inlet area ratio, under the assumptions of steady flow, rotational symmetry and frictionless flow at the pipe wall. When the Reynolds number is sufficiently large, vortex breakdown occurs abruptly with increased circulation as a result of the existence of non-unique solutions. Solution paths for Reynolds numbers exceeding approximately 1000 are characterized by an ensemble of three inviscid flow types: columnar (for pipes of constant radius), soliton and wavetrain. Flows that are quasi-cylindrical and which do not exhibit vortex breakdown exist below a critical circulation, dependent on the Reynolds number and the throat/inlet area ratio. Wavetrain solutions are observed over a small range of circulation below the critical circulation, while above the critical value, wave solutions with large regions of reversed flow are found that are primarily solitary in nature. The quasi-cylindrical (QC) equations first fail near the critical value, in support of Hall's theory of vortex breakdown (1967). However, the QC equations are not found to be effective in predicting the spatial position of the breakdown structure.

/pdf/the-role-of-non-uniqueness-in-the-development-of-vortex-2ai3ry55o5.pdf

The role of non-uniqueness in the development of vortex breakdown in tubes

This work considers the design optimization of a flapping wing in forward flight with active shape morphing, aimed at maximizing propulsive efficiency under lift and thrust constraints. This is done with an inviscid three-dimensional unsteady vortex lattice method, whose lack of fidelity is offset by a relatively inexpensive computational cost. The design is performed with a gradient-based optimization, where gradients are computed with an analytical sensitivity analysis. Wake terms provide the only connection between the forces generated at disparate time steps, and must be included to compute the derivative of the aerodynamic state at a time step with respect to the wing shape at all previous steps. The cyclic wing morphing, superimposed upon the flapping motions, is defined by a series of spatial and temporal approximations. The generalized coordinates of a finite number of twisting and bending modes are approximated by cubic splines. The amplitudes at the control points provide design variables; increasing the number of variables (providing the wing morphing with a greater degree of spatial and temporal freedom) is seen to provide increasingly superior designs, with little increase in computational cost. I. Introduction HE design and optimization of artificial flapping wing flyers presents considerable difficulties in terms of computational cost: the complex physical phenomena associated with the flight (unsteady low Reynolds number vortical flows in conjunction with a nonlinear elastic wing surface undergoing large prescribed rotations and translations) may require a high-fidelity computational tool. Furthermore, the search optimization process typically requires many function evaluations to converge to a relevant optimum. Lower fidelity numerical tools may help alleviate the burden, either used during the search process in conjunction with a higher-fidelity model 1

Philip S. Beran

Papers

Reduced-order modeling: new approaches for computational physics

Reduced-order modeling - New approaches for computational physics

State-space representation of the unsteady aerodynamics of flapping flight

The role of non-uniqueness in the development of vortex breakdown in tubes

Analytical Sensitivity Analysis of an Unsteady Vortex Lattice Method for Flapping Wing Optimization