scholarly journals Microstructural Topology Optimization of Constrained Layer Damping on Plates for Maximum Modal Loss Factor of Macrostructures

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Zhanpeng Fang ◽  
Lei Yao ◽  
Shuxia Tian ◽  
Junjian Hou
Keyword(s):  
Topology Optimization ◽  
Loss Factor ◽  
Strain Energy ◽  
Design Method ◽  
Optimization Method ◽  
Constrained Layer Damping ◽  
Viscoelastic Materials ◽  
Modal Strain Energy ◽  
Design Variables ◽  
Microstructural Topology Optimization

This paper presents microstructural topology optimization of viscoelastic materials for the plates with constrained layer damping (CLD) treatments. The design objective is to maximize modal loss factor of macrostructures, which is obtained by using the Modal Strain Energy (MSE) method. The microstructure of the viscoelastic damping layer is composed of 3D periodic unit cells. The effective elastic properties of the unit cell are obtained through the strain energy-based method. The density-based topology optimization is adopted to find optimal microstructures of viscoelastic materials. The design sensitivities of modal loss factor with respect to the design variables are analyzed and the design variables are updated by Method of Moving Asymptotes (MMA). Numerical examples are given to demonstrate the validity of the proposed optimization method. The effectiveness of the optimal design method is illustrated by comparing a solid and an optimized cellular viscoelastic material as applied to the plates with CLD treatments.

scholarly journals Dynamic Optimization of Constrained Layer Damping Structure for the Headstock of Machine Tools with Modal Strain Energy Method

2017 ◽  
Vol 2017 ◽  
pp. 1-13 ◽  
Author(s):  
Yakai Xu ◽  
Weiguo Gao ◽  
Yuhan Yu ◽  
Dawei Zhang ◽  
Xiangsong Zhao ◽  
...  
Keyword(s):  
Loss Factor ◽  
Strain Energy ◽  
Dynamic Stiffness ◽  
Optimization Method ◽  
Original Structure ◽  
Damping Capacity ◽  
Machining Accuracy ◽  
Constrained Layer Damping ◽  
Modal Strain Energy ◽  
Damping Material

Dynamic stiffness and damping of the headstock, which is a critical component of precision horizontal machining center, are two main factors that influence machining accuracy and surface finish quality. Constrained Layer Damping (CLD) structure is proved to be effective in raising damping capacity for the thin plate and shell structures. In this paper, one kind of high damping material is utilized on the headstock to improve damping capacity. The dynamic characteristic of the hybrid headstock is investigated analytically and experimentally. The results demonstrate that the resonant response amplitudes of the headstock with damping material can decrease significantly compared to original cast structure. To obtain the optimal configuration of damping material, a topology optimization method based on the Evolutionary Structural Optimization (ESO) is implemented. Modal Strain Energy (MSE) method is employed to analyze the damping and to derive the sensitivity of the modal loss factor. The optimization results indicate that the added weight of damping material decreases by 50%; meanwhile the first two orders of modal loss factor decrease by less than 23.5% compared to the original structure.

Topology Optimization for Constrained Layer Damping Plates Using Evolutionary Structural Optimization Method

2014 ◽  
Vol 894 ◽  
pp. 158-162 ◽  
Author(s):  
Bing Qin Wang ◽  
Bing Li Wang ◽  
Zhi Yuan Huang
Keyword(s):  
Topology Optimization ◽  
Energy Dissipation ◽  
Structural Optimization ◽  
Design Variable ◽  
Loss Factor ◽  
Optimization Approach ◽  
Constrained Layer Damping ◽  
Modal Strain Energy ◽  
Evolutionary Structural Optimization ◽  
Constrained Damping

The evolutionary structural optimization (ESO) is used to optimize constrained damping layer structure. Considering the vibration and energy dissipation mode of the plate with constrained layer damping treatment, the elements of constrained damping layers and modal loss factor are considered as design variable and objective function, while damping material consumption is considered as a constraint. The sensitivity of modal loss factor to design variable is further derived using modal strain energy analysis method. Numerical example is used to demonstrate the effectiveness of the proposed topology optimization approach. The results show that vibration energy dissipation of the plates can be enhanced by the optimal constrained layer damping layout.

A preliminary design method for axisymmetric turbomachinery disks based on topology optimization

2021 ◽  
pp. 095440622110395
Author(s):  
Bo Wang ◽  
Guangming Wang ◽  
Kuo Tian ◽  
Yunfeng Shi ◽  
Caihua Zhou ◽  
...  
Keyword(s):  
Topology Optimization ◽  
Optimization Problem ◽  
Design Method ◽  
Optimization Method ◽  
Preliminary Design ◽  
Optimal Result ◽  
Density Distribution Function ◽  
Design Variables ◽  
Turbine Disks ◽  
Controlling Element

The topology optimization can be used to obtain preliminary turbomachinery disk designs which meet strength requirement. In order to eliminate enclosed holes which challenge manufacturing processes and to ensure distinct solid-void interface in the optimal result obtained by the topology optimization, a density distribution function is introduced for each element column in the design domain. Then, a parameter in each function is used to determine the disk’s thickness at corresponding radial position by controlling element densities. Once thicknesses at all radial positions are optimized, the shape of disk is thus determined. In this way, the optimization problem can be simplified by using these parameters as design variables. Illustrative examples are carried out to demonstrate the effectiveness of the proposed method in designing both compressor disks and turbine disks in comparison to the software T-Axis Disk and shape optimization method.

scholarly journals Modifications to the Method of Modal Strain Energy for Improved Estimates of Loss Factors for Damped Structures

2007 ◽  
Vol 14 (5) ◽  
pp. 339-353 ◽  
Author(s):  
Peter J. Torvik ◽  
Brian Runyon
Keyword(s):  
Loss Factor ◽  
Strain Energy ◽  
Prototype System ◽  
Constrained Layer Damping ◽  
Modal Strain Energy ◽  
High Loss ◽  
Analysis And Design ◽  
Dissipative Material ◽  
Complex Valued ◽  
Loss Factors

The method of Modal Strain Energy (MSE) enables predictions of modal loss factors for vibrating systems from finite element analyses without evaluation of a complex-valued frequency response or a complex-valued frequency. While the method is simple, some error results; especially if the dissipative material has the high loss factor characteristic of materials added to increase system damping. Several methods for reducing this error through modifications to MSE have been suggested. In this work, the exact loss factor for a simple mechanical system is found. The method of Modal Strain Energy (MSE) is then used to find the loss factor for that prototype system and errors are evaluated in terms of system parameters. Comparisons are also made to predictions with several modifications to MSE. A modification due to Rongong is found to provide significant improvement. The use of this modification together with MSE is shown to lead to lower and upper bounds for the system loss factor. As the prototype system is shown to be mechanically equivalent to constrained layer damping configurations, the findings are applicable to the analysis and design of optimized sandwich beams, plates, and damping tapes. Results are given for beams and plates with constrained layer treatments.

Origami Design by Topology Optimization

2013 ◽  
Vol 135 (11) ◽  
Author(s):  
Kazuko Fuchi ◽  
Alejandro R. Diaz
Keyword(s):  
Topology Optimization ◽  
Design Method ◽  
Optimization Method ◽  
Optimal Combination ◽  
Ground Structure ◽  
Line Segments ◽  
Folding Pattern ◽  
Design Variables ◽  
3D Geometry ◽  
Dimensional Domain

An origami design method based on topology optimization is introduced. The design of a folding pattern is cast as a problem of assigning presence and type of fold to lines in a “ground structure,” using folding angles as design variables. A ground structure for origami design has lines drawn on a two dimensional domain, showing all line segments that may appear as crease lines in the folded geometry. For a given ground structure and folding angles, the 3D geometry of the folded sheet can be computed using the mathematics of origami. A topology optimization method is then used to find an optimal combination of folding angles, which results in a folding pattern with desired, target geometric properties.

scholarly journals Topology Optimization of Hard-Coating Thin Plate for Maximizing Modal Loss Factors

Coatings ◽  
2021 ◽  
Vol 11 (7) ◽  
pp. 774
Author(s):  
Haitao Luo ◽  
Rong Chen ◽  
Siwei Guo ◽  
Jia Fu
Keyword(s):  
Topology Optimization ◽  
Objective Function ◽  
Composite Plates ◽  
Optimization Method ◽  
Hard Coating ◽  
Design Variables ◽  
Coating Composite ◽  
Damping Materials ◽  
Topology Optimization Method ◽  
Loss Factors

At present, hard coating structures are widely studied as a new passive damping method. Generally, the hard coating material is completely covered on the surface of the thin-walled structure, but the local coverage cannot only achieve better vibration reduction effect, but also save the material and processing costs. In this paper, a topology optimization method for hard coated composite plates is proposed to maximize the modal loss factors. The finite element dynamic model of hard coating composite plate is established. The topology optimization model is established with the energy ratio of hard coating layer to base layer as the objective function and the amount of damping material as the constraint condition. The sensitivity expression of the objective function to the design variables is derived, and the iteration of the design variables is realized by the Method of Moving Asymptote (MMA). Several numerical examples are provided to demonstrate that this method can obtain the optimal layout of damping materials for hard coating composite plates. The results show that the damping materials are mainly distributed in the area where the stored modal strain energy is large, which is consistent with the traditional design method. Finally, based on the numerical results, the experimental study of local hard coating composites plate is carried out. The results show that the topology optimization method can significantly reduce the frequency response amplitude while reducing the amount of damping materials, which shows the feasibility and effectiveness of the method.

Structural Topology Optimization Using Frame Elements Based on the Complementary Strain Energy Concept for Eigen-Frequency Maximization

2005 ◽  
Author(s):  
Akihiro Takezawa ◽  
Shinji Nishiwaki ◽  
Kazuhiro Izui ◽  
Masataka Yoshimura
Keyword(s):  
Topology Optimization ◽  
Cross Sections ◽  
Strain Energy ◽  
Optimization Procedure ◽  
Optimization Method ◽  
Structural Topology ◽  
Energy Concept ◽  
Conceptual Design Phase ◽  
Complementary Strain ◽  
Topology Optimization Method

This paper discuses a new topology optimization method using frame elements for the design of mechanical structures at the conceptual design phase. The optimal configurations are determined by maximizing multiple eigen-frequencies in order to obtain the most stable structures for dynamic problems. The optimization problem is formulated using frame elements having ellipsoidal cross-sections, as the simplest case. Construction of the optimization procedure is based on CONLIN and the complementary strain energy concept. Finally, several examples are presented to confirm that the proposed method is useful for the topology optimization method discussed here.

Structural topology optimization of bridge girders in cable supported bridges

2018 ◽  
Author(s):  
Mads Baandrup ◽  
Ole Sigmund ◽  
Niels Aage
Keyword(s):  
Topology Optimization ◽  
Large Scale ◽  
Design Method ◽  
Optimization Method ◽  
Bridge Girders ◽  
Structural Topology ◽  
Box Girders ◽  
Box Girder ◽  
Fine Mesh ◽  
Further Development

<p>This work applies a ultra large scale topology optimization method to study the optimal structure of bridge girders in cable supported bridges.</p><p>The current classic orthotropic box girder designs are limited in further development and optimiza­ tion, and suffer from substantial fatigue issues. A great disadvantage of the orthotropic girder is the loads being carried one direction at a time, thus creating stress hot spots and fatigue problems. Hence, a new design concept has the potential to solve many of the limitations in the current state­ of-the-art.</p><p>We present a design method based on ultra large scale topology optimization. The highly detailed structures and fine mesh-discretization permitted by ultra large scale topology optimization reveal new design features and previously unseen eff ects. The results demonstrate the potential of gener­ ating completely different design solutions for bridge girders in cable supported bridges, which dif­ fer significantly from the classic orthotropic box girders.</p><p>The overall goal of the presented work is to identify new and innovative, but at the same time con­ structible and economically reasonable, solutions tobe implemented into the design of future cable supported bridges.</p>

Topology Optimization Algorithm for Plates and Shells Subjected to Plastic Deformations

1998 ◽  
Author(s):  
Kohei Yuge ◽  
Nobuhiro Iwai ◽  
Noboru Kikuchi
Keyword(s):  
Topology Optimization ◽  
Optimization Method ◽  
Homogenization Method ◽  
Finite Deformations ◽  
Thin Shells ◽  
Plastic Deformations ◽  
Material Tensor ◽  
Design Variables ◽  
Interpolation Technique ◽  
Plates And Shells

Abstract A topology optimization method for plates and shells subjected to plastic deformations is presented. The algorithms is based on the generalized layout optimization method invented by Bendsϕe and Kikuchi (1988), where an admissible design domain is assumed to be composed of microstructures with periodic cavities. The sizes of the cavities and the rotational angles of the microstructures are design variables which are optimized so as to minimize the applied work. The macroscopic material tensor for the porous material is numerically calculated by the homogenization method for the sensitivity analysis. In this paper, the method is applied to two-dimensional elasto-plastic problems. A database of the material tensor and its interpolation technique are presented. The algorithm is expanded into thin shells subjected to finite deformations. Several numerical examples are shown to demonstrate the effectiveness of these algorithms.

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