Free-Form Optimization of Thin-Walled Structure for Frequency Response Problem

We present a node-based free-form optimization method for designing forms of thin-walled structures in order to control vibration displacements or mode at a prescribed frequency. A squared displacement error norm is introduced at the prescribed surface as the objective functional to control the vibration displacements to target values in a frequency response problem. It is assumed that the thin-walled structure is varied in the normal direction to the surface and the thickness is constant. A nonparametric shape optimization problem is formulated, and the shape gradient function is theoretically derived using the material derivative method and the adjoint variable method. The shape gradient function obtained is applied to the surface of the thin-walled structure as a fictitious traction force to vary the form. With this free-form optimization method, an optimum thin-walled structure with a smooth free-form surface can be obtained without any shape parameterization. The calculated results show the effectiveness of the proposed method for the optimal free-form design of thin-walled structures with vibration mode control.

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Shape Identification for Controlling the Static Deformation of Frame Structures

Volume 1A: 34th Computers and Information in Engineering Conference ◽

10.1115/detc2014-34265 ◽

2014 ◽

Author(s):

Koki Kameyama ◽

Masatoshi Shimoda ◽

Takashi Morimoto

Keyword(s):

Optimization Method ◽

Frame Structure ◽

Static Deformation ◽

Free Form ◽

Frame Structures ◽

Shape Identification ◽

Shape Gradient ◽

Deformation Control ◽

Out Of Plane ◽

Gradient Function

The deformation control is an important design problem in the stiffness design of structures and it also enables to give a function to the structures. This paper proposes a non-parametric, or a node-based shape optimization method based on the variational method for controlling the static deformation of spatial frame structures. As the objective functional, we introduce the sum of squared error norms to the desired displacements on specified members. Under the assumption that each member varies in the out-of-plane direction to the centroidal axis, the shape gradient function and the optimality conditions are theoretically derived. The shape gradient function is applied to a gradient method in a function space with a Laplacian smoother. With this method, an optimal free-form frame structure with smoothness can be identified for a desired static deformation. The validity and effectiveness were verified through design examples.

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The optimal control of assembly deviation for large thin-walled structures based on basic deviation patterns

Proceedings of the Institution of Mechanical Engineers Part B Journal of Engineering Manufacture ◽

10.1177/09544054211024565 ◽

2021 ◽

pp. 095440542110245

Author(s):

Chang Gao ◽

Haidong Yu ◽

Ke Yuan ◽

Xinmin Lai

Keyword(s):

Great Influence ◽

Optimization Method ◽

Propagation Model ◽

Control Points ◽

Assembly Process ◽

Thin Walled Structures ◽

Deviation Propagation ◽

Thin Walled ◽

Deviation Pattern ◽

Assembly Deviation

The deviation vector at arbitrary location of large thin-walled structure caused by manufacturing process is different and has the characteristic of field distribution, which has great influence on the assemble quality. The deviation of each point on the part is not independent, and the final assembly deviation is difficult to be controlled. In this paper, the deviation field of large thin-walled structure is described by the linear combination of a series of basic deviation patterns. The deviation propagation model is established to quantify the contribution of basic deviation patterns between parts and assembly. A new two-step optimization method based on the adjustment of key control points of the part is proposed for the deviation control of large thin-walled structures. Firstly, the effective independent method is employed to obtain the optimal measurement points, which may characterize all basic deviation patterns of the part accurately. Then a new optimization model is developed to determine the key control points for special basic deviation pattern, which have little influence on the other basic deviation patterns. Based on the genetic optimization algorithm, the optimal key control points and the adjusted quantities for special basic deviation pattern are obtained, simultaneously. A case study on the assembly process of two cylindrical thin-walled parts with initial deviations measured by the Laser Scan Device is conducted. The basic deviation pattern with great influence on the deviation of assembly is determined firstly. The key control points and the corresponding adjusted quantities for this basic deviation pattern are calculated. The results indicate that the deviation of the assembled structure may be suppressed by the adjusted deformation of the key control points of parts. It is useful on the deviation control for the assembly process of large thin-walled structures.

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