Shape sensitivity analysis of flutter characteristics of a low aspect ratio supersonic wing using analytical method

Shape sensitivities of flutter characteristics can predict the moving of flutter boundary as wing shape varies. The nonlinear relationship between mass, stiffness and damping matrices of aeroelastic systems and shape variables makes the flutter characteristics vary nonlinearly as shape variables change. The computation cost of finite difference method is high and it cannot solve precisely shape sensitivities. An analytic method is developed to compute sensitivities of flutter characteristics of low aspect ratio wings to shape parameters, which include aspect ratio, taper ratio, sweep angle, and area. On the basis of the equivalent plate model and piston theory, analytic sensitivities of mass, stiffness and damping matrices with respect to various shape parameters are computed. The equivalent plate model is a continuous aeroelasticity analysis model oriented toward wing design. The flutter equation is solved by tracking the root locus of the system state space model. Lancaster's adjoint method is used to solve the eigenvalue derivatives and shape sensitivities of flutter characteristics. Linear Taylor approximation based on the analytic sensitivities is used to predict the variation of flutter speed with respect to shape variables. Comparison of these results with those from reanalysis indicates that Taylor approximation based on analytic sensitivities can precisely predict trends of flutter characteristics near the baseline configuration, but the applied neighborhood is small for sweep and area. The method can help designers make a judicious choice of wing shape parameters for preventing flutter in the preliminary design phase of aircraft.

A Combined Shape and Topology Optimization Based on Isogeometric Boundary Element Method for 3D Acoustics

A combined shape and topology optimization algorithm based on isogeometric boundary element method for 3D acoustics is developed in this study.The key treatment involves using adjoint variable method in shape sensitivity analysis with respect to non-uniform rational basis splines control points,and in topology sensitivity analysis with respect to the artificial densities of sound absorption material.OpenMP tool in Fortran code is adopted to improve the efficiency of analysis.To consider the features and efficiencies of the two types of optimization methods,this study adopts a combined iteration scheme for the optimization process to investigate the simultaneous change of geometry shape and distribution of material to achieve better noise control.Numerical examples,such as sound barrier,simple tank,and BeTSSi submarine,are performed to validate the advantage of combined optimization in noise reduction,and to demonstrate the potential of the proposed method for engineering problems.

Shape Optimal System for Linear Elastic Structures

An integrated system FSOP2D,including modules for the shape optimal modeling,structural analysis,sensitivity analysis,optimal method library and post- processing,is developed.By selecting fictitious loads as the design variables that has a linear relationship with the grid point locations and using design sensitivity analysis of the domain method,it is easier to solve the velocity field.In the course of optimal iterations,mesh distortion is kept to a minimum,sensitivity derivatives of object function,stress constraints and displacement constraints are derived.Computation of sensitivity analysis is achieved in the system.Two engineering examples are used to prove the system's effectiveness,the optimal results can successfully be obtained by lesser number of iterations.

Shape optimization of axisymmetric solids with the finite cell method using a fixed grid

In this work, a design procedure extending the B-spline based finite cell method into shape optimization is developed for axisymmetric solids involving the centrifugal force effect. We first replace the traditional conforming mesh in the finite element method with structured cells that are fixed during the whole design process with a view to avoid the sophisticated re-meshing and eventual mesh distortion.Then, B-spline shape functions are further implemented to yield a high-order continuity field along the cell boundary in stress analysis. By means of the implicit description of the shape boundary, stress sensitivity is analytically derived with respect to shape design variables. Finally, we illustrate the efficiency and accuracy of the proposed protocol by several numerical test cases as well as a whole design procedure carried out on an aeronautic turbine disk.

Differential Evolution Based High-order Peak Filter Design with Application to Compensation of Contact-induced Vibration in HDD Servo Systems

Sensitivity loop shaping using add-on peak filters is a simple and effective method to reject narrow-band disturbances in hard disk drive （HDD） servo systems. The parallel peak filter is introduced to provide high-gain magnitude in the concerned frequency range of open-loop transfer function. Different from almost all the known peak filters that possess second-order structures, we explore in this paper bow high-order peak filters can be designed to improve the loop shaping performance. The main idea is to replace some of the constant coefficients of common second-order peak filter by frequency-related transfer functions, and then differential evolution （DE） algorithm is adopted to perform optimal design. We creatively introduce chromosome coding and fitness function design, which are original and the key steps that lead to the success of DE applications in control system design. In other words, DE is modified to achieve a novel design for hard disk drive control. Owing to the remarkable searching ability of DE, the expected shape of sensitivity function can be achieved by incorporating the resultant high-order peak filter in parallel with baseline feedback controller. As a result, a seventh-order peak filter is designed to compensate for contact-induced vibration in a high-density HDD servo system, where the benefits of high-order filter are clearly demonstrated.