Mikael Langthjem

Optimum design of cantilevered columns under the combined action of conservative and nonconservative loads: Part I: The undamped case

Abstract This paper considers stability optimization of undamped cantilevered columns subjected to the simultaneous action of a conservative (‘dead’) load and a nonconservative (‘follower’) load at their free ends. The load combination is characterized by a ‘nonconservativeness parameter’ η, where η=0 corresponds to a purely conservative load (an Euler column) and η=1 to a pure follower load (Beck’s column). The optimization problem is considered in the form of volume minimization by constant critical load and is solved numerically by using finite elements and sequential linear optimization. It is shown that the minimum volume design for constant critical load is equivalent to the maximum critical load design for constant volume; for any design and any load combination, critical load/(volume of column)2 = constant. Optimum designs are determined for η=0.0, 0.2, 0.4, 0.5, 0.6, 0.8 and 1.0. For the uniform column, stability is lost by divergence for η 0.5. For the optimal columns, divergence occurs only in the case η=0.0; for the other η-values considered, stability is lost by flutter. The largest benefit of optimization is obtained in the case η=0.4; here the critical load for the optimal column is more than ten times larger than for the uniform column. The stability of the optimal columns for other types of loads than the design-load is thoroughly investigated and illustrated by diagrams.

Multifidelity Response Surface Approximations for the Optimum Design of Diffuser Flows

Response surface methods use least-squares regression analysis to fit low-order polynomials to a set of experimental data. It is becoming increasingly more popular to apply response surface approximations for the purpose of engineering design optimization based on computer simulations. However, the substantial expense involved in obtaining enough data to build quadratic response approximations seriously limits the practical size of problems. Multifidelity techniques, which combine cheap low-fidelity analyses with more accurate but expensive high-fidelity solutions, offer means by which the prohibitive computational cost can be reduced. Two optimum design problems are considered, both pertaining to the fluid flow in diffusers. In both cases, the high-fidelity analyses consist of solutions to the full Navier-Stokes equations, whereas the low-fidelity analyses are either simple empirical formulas or flow solutions to the Navier-Stokes equations achieved using coarse computational meshes. The multifidelity strategy includes the construction of two separate response surfaces: a quadratic approximation based on the low-fidelity data, and a linear correction response surface that approximates the ratio of high-and low-fidelity function evaluations. The paper demonstrates that this approach may yield major computational savings.

Modal expansion of the perturbation velocity potential for a cantilevered fluid-conveying cylindrical shell

The subject of this paper is the application of the method of separation of variables and the Galerkin method for discretization of the equations of motion for a cantilevered cylindrical fluid-conveying shell. The perturbation velocity potential is expressed in terms of a series of orthonormal beam modal functions. The final Galerkin generalized fluid force coefficients are simple, compact, and easy to evaluate numerically. To validate the method, comparisons with results obtained from the Fourier transform method are made. Mismatch between the actual axial fluid modes and the assumed modes affects the Galerkin coefficients to some extent, but the unstable eigenvalue branch is only affected slightly over a wide range of system parameters, and critical flow speeds predicted by the two methods generally agree well.

Optimum design of Beck's column with a constraint on the static buckling load

The paper is concerned with optimization of a damped column subjected to a follower load. The aim is to determine the colum of least volume which has the same critical load as a uniform reference column. The stability analysis is based on the finite element method. The optimization problem is solved by sequential linear programming. By only including a constraint on the flutter load in the volume minimization, a very large volume reduction is possible but the static buckling load (by a pure conservative loading) becomes very small.In applications, it may be important that the optimal column also is capable of supporting a conservative load. Consequently, the volume is minimized with constraints on both the flutter load and the static buckling load. The constraint on the buckling loadpb has the formpbopt≥cpb0, 0≤c≤1, where the upper index “opt” refers to the optimal design while the upper index “0” refers to the uniform initial design. It is found that, as the constantc approaches 1, the optimal column approaches the optimal Euler column of Tadjbakhsh and Keller (1962).

Analysis and Minimization of Flow Noise in a Centrifugal Pump

In a recent review article on noise from centrifugal pumps, Rzentkowski [1] concludes by the words, “At the present stage of knowledge, one can hardly claim that the process of noise generation within centrifugal pumps is understood. This is rather surprising, given the industrial importance of the problem.” The present work attempts to give a contribution to a better understanding through a numerical study. Another purpose is to develop a numerical tool for minimization of the noise generation.