Shape Identification for Controlling the Static Deformation of Frame Structures

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.

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

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Masatoshi Shimoda ◽  
Yang Liu
Keyword(s):  
Frequency Response ◽  
Optimization Method ◽  
Free Form ◽  
Error Norm ◽  
Material Derivative ◽  
Shape Gradient ◽  
Thin Walled Structures ◽  
Target Values ◽  
Gradient Function ◽  
Thin Walled

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.

Modal Characteristics of Planar Multi-Story Frame Structures

2016 ◽  
Vol 32 (5) ◽  
pp. 501-514 ◽  
Author(s):  
H.-P. Lin ◽  
S.-C. Chang ◽  
C. Chu
Keyword(s):  
Finite Element ◽  
Linear System ◽  
Finite Element Methods ◽  
Analytical Methods ◽  
Theoretical Method ◽  
Frame Structure ◽  
Frame Structures ◽  
Modal Characteristics ◽  
Out Of Plane ◽  
The Matrix

AbstractIn linear system, in-plane motions are decoupled from out-of-plane motions for planar frame structures. A theoretical method is proposed that permits the efficient calculations of modal characteristics of planar multi-story frame structures. There are 3 × m beam components for a planar m-story frame structure. By analyzing the transverse and longitudinal motions of each component simultaneously and considering the compatibility requirements across each frame joint, the undetermined variables of the entire m-story frame structure system can be reduced to six, regardless of the number of stories, and that can be determined by the application of the boundary conditions. The main feature of this method is to decrease the dimensions of the matrix involved in the finite element methods and certain other analytical methods.

Free-form optimization method of frame structures for elastic buckling

2016 ◽  
Vol 82 (841) ◽  
pp. 16-00229-16-00229 ◽  
Author(s):  
Masatoshi SHIMODA ◽  
Ryo YOSHIMOTO
Keyword(s):  
Optimization Method ◽  
Free Form ◽  
Frame Structures ◽  
Elastic Buckling

Bridging Topological Results and Thin-Walled Frame Structures Considering Manufacturability

2021 ◽  
Vol 143 (9) ◽  
Author(s):  
Jiantao Bai ◽  
Yanfang Zhao ◽  
Guangwei Meng ◽  
Wenjie Zuo
Keyword(s):  
Topology Optimization ◽  
Cross Section ◽  
Structural Complexity ◽  
Optimization Method ◽  
Frame Structure ◽  
Frame Structures ◽  
Manufacturing Constraints ◽  
Numerical Examples ◽  
Thin Walled ◽  
Topology Optimization Method

Abstract Topology optimization has been intensively studied and extensively applied in engineering design. However, the optimized results often take the form of a solid frame structure; hence, it is difficult to apply the topological results in the design of a thin-walled frame structure. Therefore, this paper proposes a novel bridging method to transform the topological results into a lightweight thin-walled frame structure while satisfying the stiffness and manufacturing requirements. First, the optimized topological results are obtained using the classical topology optimization method, which is smoothed to reduce structural complexity. Then, the initial thin-walled frame structure is created by referring to the smoothed topological results, in which the thin-walled cross section is designed according to the mechanical properties and manufacturing requirements. Furthermore, the size and shape of the thin-walled frame structure is optimized to minimize mass with the stiffness and manufacturing constraints. Finally, numerical examples demonstrate that the proposed method can reasonably design an optimized thin-walled frame structure from the topological results.

Non-parametric free-form optimization method for frame structures

2014 ◽  
Vol 50 (1) ◽  
pp. 129-146 ◽  
Author(s):  
Masatoshi Shimoda ◽  
Yang Liu ◽  
Takashi Morimoto
Keyword(s):  
Optimization Method ◽  
Free Form ◽  
Frame Structures ◽  
Non Parametric

scholarly journals Topological Optimization of Aircraft Frame Structures with the Variable Density Method

2018 ◽  
Vol 198 ◽  
pp. 05008
Author(s):  
ying-lei Li ◽  
zong-jie Cao ◽  
Zi-li Wang
Keyword(s):  
Topology Optimization ◽  
Lagrange Function ◽  
Optimization Method ◽  
Variable Density ◽  
Frame Structure ◽  
Topological Optimization ◽  
Frame Structures ◽  
Distribution Law ◽  
Structural Distribution ◽  
Density Method

In this paper, a variable density topological optimization method is derived on the basis of Lagrange function, and the RAMP interpolation model is selected to optimize the frame structure of aircrafts with variable density method. For an example, the ordinary frame structure of the domestic planes is taken to illustrate validity of the presented method. The numerical model of the aircraft frames is obtained. The optimal design analysis of the model structural distribution and the weight loss requirement of the aircraft frame structures are realized. In conclusion, the structural distribution law of the topology optimization is summarized according to the topology optimization structures.

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