Tailoring static deformation of frame structures based on a non-parametric shape–size optimization method

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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Non-parametric free-form optimization method for frame structures

Structural and Multidisciplinary Optimization ◽

10.1007/s00158-013-1037-z ◽

2014 ◽

Vol 50 (1) ◽

pp. 129-146 ◽

Cited By ~ 15

Author(s):

Masatoshi Shimoda ◽

Yang Liu ◽

Takashi Morimoto

Keyword(s):

Optimization Method ◽

Free Form ◽

Frame Structures ◽

Non Parametric

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Non-parametric shape optimization method for robust design of solid, shell, and frame structures considering loading uncertainty

Structural and Multidisciplinary Optimization ◽

10.1007/s00158-018-2144-7 ◽

2018 ◽

Vol 59 (5) ◽

pp. 1543-1565 ◽

Cited By ~ 4

Author(s):

Masatoshi Shimoda ◽

Tomohiro Nagano ◽

Jin-Xing Shi

Keyword(s):

Shape Optimization ◽

Robust Design ◽

Optimization Method ◽

Frame Structures ◽

Solid Shell ◽

Loading Uncertainty ◽

Non Parametric

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Determination of Reactivity Ratios from Binary Copolymerization Using the k-Nearest Neighbor Non-Parametric Regression

Polymers ◽

10.3390/polym13213811 ◽

2021 ◽

Vol 13 (21) ◽

pp. 3811

Author(s):

Iosif Sorin Fazakas-Anca ◽

Arina Modrea ◽

Sorin Vlase

Keyword(s):

Experimental Data ◽

Nearest Neighbor ◽

Optimization Method ◽

Reactivity Ratios ◽

Data Sets ◽

K Nearest Neighbor ◽

Integration Algorithm ◽

Data Set ◽

Parametric Regression ◽

Non Parametric

This paper proposes a new method for calculating the monomer reactivity ratios for binary copolymerization based on the terminal model. The original optimization method involves a numerical integration algorithm and an optimization algorithm based on k-nearest neighbour non-parametric regression. The calculation method has been tested on simulated and experimental data sets, at low (<10%), medium (10–35%) and high conversions (>40%), yielding reactivity ratios in a good agreement with the usual methods such as intersection, Fineman–Ross, reverse Fineman–Ross, Kelen–Tüdös, extended Kelen–Tüdös and the error in variable method. The experimental data sets used in this comparative analysis are copolymerization of 2-(N-phthalimido) ethyl acrylate with 1-vinyl-2-pyrolidone for low conversion, copolymerization of isoprene with glycidyl methacrylate for medium conversion and copolymerization of N-isopropylacrylamide with N,N-dimethylacrylamide for high conversion. Also, the possibility to estimate experimental errors from a single experimental data set formed by n experimental data is shown.

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