FUNDAMENTAL FREQUENCY MAXIMIZATION DESIGN FOR CONTINUOUS FIBER-REINFORCED COMPOSITE STRUCTURES

The objective of this investigation is to carry out the topology design optimization of the pickup suspension of high-speed optical pickups in DVD’s or CD ROM’s. The specific design target here is to increase the torsional eigenfrequency of the pickup as high as possible while keeping the focusing eigenfrequency between 25 Hz and 35 Hz, and the tracking eigenfrequency between 43 Hz and 57 Hz. These frequency ranges are set to meet other design constraints such as servo-controllability. A typical pickup consists of a bobbin having an optical lens and suspension plates to support it. Since the eigenfrequencies of the bobbin itself are in the order of 10 kHz, it can be modeled as a point mass when dealing with the low-frequency dynamic characteristics in consideration. These modeling techniques are verified in the previous researchers. In modeling the bobbin, we also consider its moments of inertia. In designing the suspension system, damping bond is usually applied to control the quality factors at the focusing and tracking frequencies. The location of the damping treatment on the suspension system may be determined by an optimization method, but this is not pursued in this work since the result by the earlier work can be applied to the present suspension system. Unlike static problems such as compliance minimization problems with single and multiple loads or compliant mechanism problems with single and multiple input/outputs, optimization problems involving eigenvalues suffer from mode-switching, which often causes serious difficulties in solution convergence. Mode-switching represents the phenomenon that eigenmodes are changed during the update of design variables. If the design target were simply to maximize a few lowest eigenfrequencies, the mode-switching problem would be handled rather easily. However, the present optimization problem is not the case because we must follow the eigenfrequencies of the specific modes such as tracking, focusing and twisting modes during the optimization process. To handle this situation satisfactorily, we should employ a technique to track the desired modes. In the present investigation, the desired modes are traced by means of the modal assurance criterion (MAC), which has been widely used in experimental modal analysis. For the pickup consisting of a bobbin and suspension plates, the present design goal can be achieved by optimizing the configuration of the suspension plates. To find an optimal plate configuration, we employ the topology optimization method, but the specific method employed here is the multiscale topology optimization method. In the multiscale optimization method, the density design variables are transformed into multiscaled design variables by a series of nonlinear and linear transformations. With the multiscale topology optimization method, the optimization can be completed more efficiently than the optimization by 9th AIAA/ISSMO Symposium on Multidisciplinary Analysis and Optimization 4-6 September 2002, Atlanta, Georgia AIAA 2002-5483 Copyright © 2002 by the author(s). Published by the American Institute of Aeronautics and Astronautics, Inc., with permission. the standard single-scale direct density method. As an optimizer, the feasible direction method is employed to handle effectively multiple constraints on eigenfrequencies. By the present application of the topology optimization method, the twisting eigenfrequency has been maximized while the focusing and tracking eigenfrequencies are kept in the prescribed frequency range. The optimized suspension plate in the present work outperforms the designs improved from the existing rectangular bend-type plates.

An approach for reliability-based topology optimization of interval parameters structures under dynamic loads is proposed. We modify the equivalent static loads method for non linear static response structural optimization (ESLSO) to solve the dynamic reliability optimization problem. In our modified ESLSO, the equivalent static loads (ESLs) are redefined to consider the uncertainties. The new ESLs including all the uncertainties from geometric dimensions, material properties and loading conditions generate the same interval response field as dynamic loads. Based on the definition of the interval non-probabilistic reliability index, we construct the static reliability topology optimization model using ESLs. The method of moving asymptotes (MMA) is employed as the optimization problem solver. The applicability and validity of the proposed model and numerical techniques are demonstrated with three numerical examples.

A domain evolution method to suppress the eigenfrequency and eigenmode errors caused by low-density elements in dynamic topology optimization

Aiming at the problems such as low computational efficiency and long process in dynamic topology optimization, combined with bi-directional evolutional structure optimization, the dynamic optimization problem is transformed into the static optimization problem in multiple load cases. Newmark method is used to analyze the structure dynamics load. The topology optimization model based on equivalent static load is established. On the basis of the equivalent static load, multi-objective dynamics evolutionary structure optimization is studied. And the mathematical model of the dynamic stiffness and natural frequency about the multi-objective optimization is established. The mathematical formula of the sensitivity is deduced. Then a complete optimization iterative process is given. The numerical example illustrates that it is feasible to solve the multi-objective dynamic topology optimization with equivalent static loads. Modal tracking technique is introduced to the multi-objective dynamic topology optimization. The numerical example shows that modal tracking technology can track the required modal in the optimization process.

A hybrid algorithm for solving structural topology optimization problems is presented. This hybrid algorithm combines the method of moving asymptotes (MMA) algorithm and the modified globally convergent version of the method of moving asymptotes (MGCMMA) algorithm in the optimization process. This hybrid algorithm preserves the advantages of both MMA and MGCMMA. The optimizer is switched from MMA to MGCMMA automatically, depending on the numerical oscillation value during the optimization. This hybrid algorithm has improved calculation efficiency and accelerated convergence when compared with the MMA or MGCMMA algorithm, which is demonstrated with three examples.

Zero density lower bounds in topology optimization

Topology optimization for linear stationary stochastic dynamics: Applications to frame structures

The exhaust volute, an important component of a centrifugal compressor, plays a crucial role in improving overall compressor efficiency. Traditional design methods rely heavily on designer’s experience and often result in low design efficiency. In this study, a topology optimization design method for the exhaust volute flow channel is proposed to address this issue. The optimization objective focuses on minimizing flow energy dissipation within the design domain while considering flow compressibility. The sensitivity of the objective function to design variables is calculated using the discrete adjoint method. In the open-source platform OpenFOAM, the finite volume method is utilized to solve governing equations with darcy source term and adjoint equations, and the Method of Moving Asymptotes (MMA) algorithm is applied to solve the optimization problem. Numerical examples of different volute types in two and three dimensionals are used to demonstrate the effectiveness of the proposed method. The results show that the topology optimization method proposed in the present work can quickly obtain the optimal volute configuration.

An optimization method is proposed for the simultaneous design of structural and control systems using the equivalent static loads. The two structural and control systems are not completely independent and need to be considered in a unified fashion. Furthermore, an integrated system design is unavoidable to exhibit a good performance in the time domain. The analysis for the integrated system is conducted for the transient-state in a dynamic manner. The constraints for the structural and control systems are defined in the time domain as well. Therefore, a physically small scale problem in structural analysis easily becomes quite a large scale in an optimization problem. A new equivalent static loads (ESLs) method, which deals with the structural design variables as well as the control design variables, is proposed to solve physically large scale problems. A finite element dynamic equation is defined with control forces and a dynamic response optimization problem is formulated. Linear static response optimization is carried out with the ESLs. The control forces for the linear static response optimization are considered as design variables. Shape variables are utilized to handle the design variables for the control forces. Several examples are solved to validate the proposed method.

Shape optimization in laminated composite plates

The non-uniform distributed pressure of impact wave is usually simplified into concentrated or uniform load equivalently in the optimization design of constrained layer damping structure. However, for the thin-walled structure, it becomes necessary to regard the load as a non-uniform distribution. In this paper, a topology optimization approach is proposed considering the blast load with non-uniform distribution, aiming to unveil its impact on optimization layouts and dynamic responses. Initially, the smoothed particle hydrodynamics (SPH) algorithm is used to obtain the blast pressure what are extracted and integrated into the optimization model. Subsequently, the relative density is regarded as design variable. The construction of material penalty model and the topology optimization model are based on polynomial interpolation scheme (PIS). The sensitivity of objective function is deduced employing an improved adjoint variable method (AVM) to fit the load forms, and the Newmark-[Formula: see text] method is used to calculate the dynamic response. The optimization criterion (OC) is adopted to update the design variables. Finally, two numerical examples are used to exhibit the validity and accuracy of the presented methodology. The findings indicate that the distributed form, spread velocity, excited position and excited amplitude of the blast load all exert a notable influence on optimization results and dynamic response. These results underscore the valuable engineering application of this research and introduce a fresh perspective to the challenge of topology optimization under the blast case.

The crane performance depends largely on its box girder structure. The problem of structure topology optimization for a box girder is investigated in this study. Firstly, a comprehensive analysis to box girder is given and a topology optimization model for the bridge crane girder structure is established. Secondly, based on the optimization model, the box girder is optimized with finite element software Patran/Nastran and an improved Method of Moving Asymptotes (MMA). Finally, some satisfied results are obtained from the optimization procedure and useful conclusions are presented.

Recently, pipelines have been extensively applied in engineering transportation because of their excellent continuity and high efficiency. Nevertheless, harmful noise and vibration will be generated in complex engineering application environments. We conducted a comprehensive study on the construction of three-dimensional pipelines for transporting gas–liquid two-phase flow using fiber-reinforced composite materials (FRC). Building upon this foundation, we developed an innovative pipeline configuration incorporating bidirectional nonlinear energy sinks (NES) and implemented parameter optimization techniques to maximize the vibration suppression performance of the system. According to the Euler–Bernoulli beam theory, the three-dimensional governing equations of the pipelines acted by the external excitations were established by adopting Hamilton's variational principle. The ordinary differential equation of the system motion was obtained by discretizing variables utilizing the Galerkin technique. The frequency response characteristics were achieved using the harmonic balance method combined with a pseudo-arc length extension approach. The effects of parameters such as fiber orientation angle, damping coefficient, liquid volume coefficient, liquid velocity, and external excitation amplitude on the frequency responses of the FRC three-dimensional pipe were explored. To ensure the correctness of this analytical method, the present results were contrasted with the response curve obtained by the Runge–Kutta technique. Additionally, the nonlinear dynamic evolution of the pipelines, including the bifurcation and chaos, was further predicted using global bifurcation diagrams incorporated with phase diagrams and Poincaré diagrams, which provided a significant reference for the design of the pipes conveying the two-phase flow. Additionally, this study designed two additional NES attached on the pipeline structure to conduct the three-dimensional vibration control, analyzed their vibration reduction effect, and optimized the control parameters through genetic algorithm to improve their vibration control effect.

Concurrent topology optimization of sandwich structures with multi-configuration and variable-diameter lattice infill

The stacker crane is a long-and-thin structure with a large length-to-width ratio. It is difficult to obtain a topology configuration with good period properties using traditional optimization methods. While the mathematical model of periodic topology optimization—in which the elements’ relative densities are selected as design variables, and mean compliance as the objective function—is established. To find a topology configuration with a good period property, an additional constraint condition must be imported into the mathematical model. According to the optimization criteria method, the iterative formula of design variables is derived in the virtual sub domain. To verify the capability and availability of the proposed method, periodic topology optimization of a single-mast stacker crane is investigated in this paper. The results show that configurations with good periodicity can be obtained when the number of sub domains is varied. After considering mean compliance and complexity, the optimal configuration has eight periods. A preliminary lightweight design scheme is proposed based on this configuration of a stacker crane, which is a periodic feature structure.