Xiaozhong Chen^1,*, Zhijian Mao¹

Molecular & Cellular Biomechanics, Vol.15, No.4, pp. 229-241, 2018, DOI:10.32604/mcb.2018.03818

Abstract Shape optimization of orthopedic fixation plate is of great importance in the treatment of complex fracture. Therefore, a method in this paper to automatically optimize the complex shape of anatomical plate according to static analysis. Based on the theory of finite element analysis (FEA), our approach is processed as follows. First, the three-dimensional finite element model of the fracture fixation is constructed. Next, according to the type and feature of fracture, the anatomical plate was parameterized in two levels (the bounding surface and plate model). Then, parameter constraints are set up to meet the needs of surgical fracture treatment. Finally,… More >

P.P. Prochazka¹, M.J. Valek¹

CMES-Computer Modeling in Engineering & Sciences, Vol.87, No.3, pp. 207-224, 2012, DOI:10.3970/cmes.2012.087.207

Abstract In classical theories of homogenization and localization of composites the effect of shape of inclusions is not taken into account. This is probably done because of very small fibers in classical composites based on epoxy matrix. Applying more precise theoretical and numerical tools appears that the classical theories desire corrections in this direction. Today many types of materials their fiber are much bigger and with various material properties are used and behave as typical composites. They enable producers to create the fiber cross-sections and model them in various shapes, so that it is meaningful to carry out the optimization. In… More >

Anant Diwakar¹, D. N.Srinath¹, Sanjay Mittal¹

CMES-Computer Modeling in Engineering & Sciences, Vol.69, No.1, pp. 61-90, 2010, DOI:10.3970/cmes.2010.069.061

Abstract Aerodynamic shape optimization of airfoils is carried out for two values of Reynolds numbers: 10³ and 10⁴, for an angle of attack of 5^o. The objective functions used are (a) maximization of lift (b) minimization of drag and (c) minimization of drag to lift ratio. The surface of the airfoil is parametrized by a 4^th order non-uniform rational B-Spline (NURBS) curve with 61 control points. Unlike the efforts in the past, the relatively large number of control points used in this study offer a rich design shape with the possibility of local bumps and valleys on the airfoil surface. The… More >

D.N. Srinath¹, Sanjay Mittal¹, Veera Manek²

CMES-Computer Modeling in Engineering & Sciences, Vol.51, No.2, pp. 169-190, 2009, DOI:10.3970/cmes.2009.051.169

Abstract A continuous adjoint method is formulated and implemented for the multi-point shape optimization of airfoils at low Re. The airfoil shape is parametrized with a non-uniform rational B-Spline (NURBS). Optimization studies are carried out for two different objective functions. The first involves an inverse function on the lift coefficient over a range of Re. The objective is to determine a shape that results in a lift coefficient of 0.4 at three values of Re: 10, 100 and 500. The second objective involves a direct function on the lift coefficient over a range of angles of attack,a. The lift coefficient is… More >

Hokyung Shim¹, Vinh Thuy Tran Ho^1,,Semyung Wang^1,2, Daniel A. Tortorelli³

CMES-Computer Modeling in Engineering & Sciences, Vol.37, No.2, pp. 175-202, 2008, DOI:10.3970/cmes.2008.037.175

Abstract This paper presents a topological shape optimization technique for electromagnetic problems using a level set method and radial basis functions. The proposed technique is a level set (LS) based optimization dealing with geometrical shape derivatives and topological design. The shape derivative is computed by an adjoint variable method to avoid numerous sensitivity evaluations. A level set model embedded into the scalar function of higher dimensions is propagated to represent the design boundary of a domain. The level set function interpolated into a fixed initial domain is evolved by using the Hamilton-Jacobi equation. The moving free boundaries (dynamic interfaces) represented in… More >

S.Y. Wang^1,2, M.Y. Wang³

CMES-Computer Modeling in Engineering & Sciences, Vol.13, No.2, pp. 119-148, 2006, DOI:10.3970/cmes.2006.013.119

Abstract In this paper, an implicit free boundary parametrization method is presented as an effective approach for simultaneous shape and topology optimization of structures. The moving free boundary of a structure is embedded as a zero level set of a higher dimensional implicit level set function. The radial basis functions (RBFs) are introduced to parametrize the implicit function with a high level of accuracy and smoothness. The motion of the free boundary is thus governed by a mathematically more convenient ordinary differential equation (ODE). Eigenvalue stability can be guaranteed due to the use of inverse multiquadric RBF splines. To perform both… More >

C.T.M. Anflor¹, R.J. Marczak²

CMES-Computer Modeling in Engineering & Sciences, Vol.78, No.3&4, pp. 151-168, 2011, DOI:10.3970/cmes.2011.078.151

Abstract This paper aims to demonstrate the final result of an optimization process when a smooth technique is introduced between intermediary iterations of a topological optimization. In a topological optimization process is usual irregular boundary results as the final shape. This boundary irregularity occurs when the way of the material is removed is not very suitable. Avoiding an optimization post-processing procedure some techniques of smooth are implemented in the original optimization code. In order to attain a regular boundary a smoothness technique is employed, which is, Bezier curves. An algorithm was also developed to detect during the optimization process which curve… More >

Zhiming Gao², Yichen Ma³

CMES-Computer Modeling in Engineering & Sciences, Vol.66, No.2, pp. 135-164, 2010, DOI:10.3970/cmes.2010.066.135

Abstract Shape optimization technique has an increasing role in fluid dynamics problems governed by distributed parameter systems. In this paper, we present the problem of shape optimization of two dimensional viscous flow governed by the time dependent Navier-Stokes equations. The minimization problem of the viscous dissipated energy was established in the fluid domain. We derive the structure of continuous shape gradient of the cost functional by using the differentiability of a saddle point formulation with a function space parametrization technique. Finally a gradient type algorithm with mesh adaptation and mesh movement strategies is successfully and efficiently applied. More >

S.Y. Wang^1,2, K.M. Lim^2,3, B.C. Khoo^2,3, M.Y. Wang⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.21, No.1, pp. 1-40, 2007, DOI:10.3970/cmes.2007.021.001

Abstract The level set method is a numerical technique for simulating moving interfaces. In this paper, an unconditionally BIBO (Bounded-Input-Bounded-Output) time-stable consistent meshfree level set method is proposed and applied as a more effective approach to simultaneous shape and topology optimization. In the present level set method, the meshfree infinitely smooth inverse multiquadric Radial Basis Functions (RBFs) are employed to discretize the implicit level set function. A high level of smoothness of the level set function and accuracy of the solution to the Hamilton-Jacobi partial differential equation (PDE) can be achieved. The resulting dynamic system of coupled Ordinary Differential Equations (ODEs)… More >

S.Y. Wang^1,2, K.M. Lim^2,3, B.C. Khoo^2,3, M.Y. Wang⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.18, No.3, pp. 155-182, 2007, DOI:10.3970/cmes.2007.018.155

Abstract In this paper, a geometric deformation constrained level set method is presented as an effective approach for structural shape and topology optimization. A level set method is used to capture the motion of the free boundary of a structure. Furthermore, the geometric deformation of the free boundary is constrained to preserve the structural connectivity and/or topology during the level set evolution. An image-processing-based structural connectivity and topology preserving approach is proposed. A connected components labeling technique based on the 4-neighborhood connectivity measure and a binary image is used for the present region identification. The corresponding binary image after an exploratory… More >