On the influence of damping in a problem of dynamic stability optimization

A non-uniform, elastic cantilever, with Kelvin-Voigt internal damping and viscous external damping, subjected to a follower load at its free end, is considered. The mass/stiffness distribution of the column is described by a limited number of orthogonal design functions. For different values of internal and external damping, the mass distribution maximizing the critical load is found. The design improvements are based on analytical sensitivity analysis and the optimal linear combination of the design functions is found by sequential linear programming. Interaction of eigenvalues and the transference of the instability branch during optimization are discussed. Finally, the energy relations for the critical modes are considered.     

Shape optimization of cantilevered columns subjected to a rocket-based follower force and its experimental verification

Intended aims of the paper are, firstly to conduct a realistic structural optimization of a nonconservative system, and secondly to give an experimental verification of the theoretically predicted stabilizing effect of shape optimization of cantilevered columns subjected to a rocket-based follower force. Flutter of a cantilevered column having a small solid rocket motor at its free end is considered in this paper. The shape optimization for maximum flutter load was conducted computationally with the design constraint that the width of the column should not be less than half of the initial width, in order to keep test-pieces elastic during compressive loading. The theory predicts that the flutter parameter of the shape optimized column with constant volume can be 1.2 times higher than that of the uniform column. Then the corresponding experiment was conducted. The mean thrust produced by the rocket motor was assumed constant during firing. As the applied load in the experiment was constant the free parameter for loading was the length of the columns. The mean thrust was 580?N and the burnout time was 3.2?s. Five test runs were conducted to find the experimental critical length of the uniform test columns. Following this, two runs were made with optimum columns having the same lengths as the corresponding uniform test columns. As the outcome, an experimental verification was given to structural optimization of cantilevered columns subjected to a rocket-based follower force.     

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.     

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 loadp _b has the formp _b ^opt cp _b ⁰ , 0c1, 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).Notation c slack parameter on the constraint on the static buckling load; defined by (9) - c _int,c _ext dimensionless internal and external damping parameters defined by (3) - d _j eigenvalue margin defined by (9) - d vector of time-independent nodal displacements and rotations - _e length of thee-th finite element - L total length of the column - vector of element lengths defined by (11) - m, m(x) mass distribution function - m _i design variables; the mass distribution function evaluated at the nodal points - upper and lower bounds on the design parameters - m design vector with elementsm _i - M mass matrix - N _e the number of finite elements used - p load parameter - Q load matrix - S stiffness matrix - t time - x distance along the column, measured from the clamped end - y lateral deflection of the column - y vector of nodal displacements and rotations - complex eigenvalue - b refers to buckling (static instability by conservative loading) - d refers to divergence (static instability by nonconservative loading) - f refers to flutter (dynamic instability by nonconservative loading)