scholarly journals Topology Optimization Methods for 3D Structural Problems: A Comparative Study

2021 ◽  
Author(s):  
Daniel Yago ◽  
Juan Cante ◽  
Oriol Lloberas-Valls ◽  
Javier Oliver
Keyword(s):  
Topology Optimization ◽  
Structural Optimization ◽  
Objective Function ◽  
Computational Cost ◽  
Optimization Methods ◽  
Structural Problems ◽  
Evolutionary Structural Optimization ◽  
And Topology ◽  
The Common ◽  
Computational Platform

AbstractThe work provides an exhaustive comparison of some representative families of topology optimization methods for 3D structural optimization, such as the Solid Isotropic Material with Penalization (SIMP), the Level-set, the Bidirectional Evolutionary Structural Optimization (BESO), and the Variational Topology Optimization (VARTOP) methods. The main differences and similarities of these approaches are then highlighted from an algorithmic standpoint. The comparison is carried out via the study of a set of numerical benchmark cases using industrial-like fine-discretization meshes (around 1 million finite elements), and Matlab as the common computational platform, to ensure fair comparisons. Then, the results obtained for every benchmark case with the different methods are compared in terms of computational cost, topology quality, achieved minimum value of the objective function, and robustness of the computations (convergence in objective function and topology). Finally, some quantitative and qualitative results are presented, from which, an attempt of qualification of the methods, in terms of their relative performance, is done.

A More Effective Formulation of the Path Generation Mechanism Synthesis Problem

1994 ◽  
Author(s):  
Irfan Ullah ◽  
Sridhar Kota
Keyword(s):  
Objective Function ◽  
Error Function ◽  
Mathematical Optimization ◽  
Optimization Methods ◽  
Complex Nature ◽  
Mechanism Synthesis ◽  
Structural Error ◽  
Crank Angle ◽  
The Common ◽  
Selection Of

Abstract Use of mathematical optimization methods for synthesis of path-generating mechanisms has had only limited success due to the very complex nature of the commonly used Structural Error objective function. The complexity arises, in part, because the objective function represents not only the error in the shape of the coupler curve, but also the error in location, orientation and size of the curve. Furthermore, the common introduction of timing (or crank angle), done generally to facilitate selection of corresponding points on the curve for calculating structural error, has little practical value and unnecessarily limits possible solutions. This paper proposes a new objective function, based on Fourier Descriptors, which allows search for coupler curve of the desired shape without reference to location, orientation, or size. The proposed objective function compares overall shape properties of curves rather than making point-by-point comparison and therefore does not requires prescription of timing. Experimental evidence is provided to show that it is much easier to search the space of the proposed objective function compared to the structural error function.

scholarly journals Structural optimization in ESAC: annals 2011

2014 ◽  
Vol 5 ◽  
pp. A09
Author(s):  
Ji-Hong Zhu ◽  
Wei-Hong Zhang
Keyword(s):  
Topology Optimization ◽  
Structural Optimization ◽  
Material Properties ◽  
Numerical Results ◽  
Multiphase Materials ◽  
And Topology ◽  
Effective Material Properties

The purpose of this paper is to give an overall introduction of the structural optimization research works in ESAC group in 2011. Four main topics are involved, i.e. 1) topology optimization with multiphase materials, 2) integrated layout and topology optimization, 3) prediction of effective material properties and 4) composite design. More detailed techniques and some numerical results are also presented and discussed here.

FIXED GRID FINITE ELEMENT ANALYSIS FOR 3D STRUCTURAL PROBLEMS

2005 ◽  
Vol 02 (04) ◽  
pp. 569-586 ◽  
Author(s):  
MANUEL J. GARCÍA ◽  
MIGUEL A. HENAO ◽  
OSCAR E. RUIZ
Keyword(s):  
Structural Optimization ◽  
Material Properties ◽  
Stiffness Matrix ◽  
Computational Cost ◽  
Evolutionary Strategies ◽  
Two Dimensional ◽  
Additional Advantage ◽  
Fixed Grid ◽  
Structural Problems ◽  
Global Stiffness Matrix

Fixed Grid (FG) methodology was first introduced by García and Steven as an engine for numerical estimation of two-dimensional elasticity problems. The advantages of using FG are simplicity and speed at a permissible level of accuracy. Two-dimensional FG has been proved effective in approximating the strain and stress field with low requirements of time and computational resources. Moreover, FG has been used as the analytical kernel for different structural optimization methods as Evolutionary Structural Optimization, Genetic Algorithms (GA), and Evolutionary Strategies. FG consists of dividing the bounding box of the topology of an object into a set of equally sized cubic elements. Elements are assessed to be inside (I), outside (O) or neither inside nor outside (NIO) of the object. Different material properties assigned to the inside and outside medium transform the problem into a multi-material elasticity problem. As a result of the subdivision NIO elements have non-continuous properties. They can be approximated in different ways which range from simple setting of NIO elements as O to complex non-continuous domain integration. If homogeneously averaged material properties are used to approximate the NIO element, the element stiffness matrix can be computed as a factor of a standard stiffness matrix thus reducing the computational cost of creating the global stiffness matrix. An additional advantage of FG is found when accomplishing re-analysis, since there is no need to recompute the whole stiffness matrix when the geometry changes. This article presents CAD to FG conversion and the stiffness matrix computation based on non-continuous elements. In addition inclusion/exclusion of O elements in the global stiffness matrix is studied. Preliminary results shown that non-continuous NIO elements improve the accuracy of the results with considerable savings in time. Numerical examples are presented to illustrate the possibilities of the method.

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.

Study of Parametric and Non-Parametric Optimization of a Rotor-Bearing System

2014 ◽  
Author(s):  
Youngwon Hahn ◽  
John I. Cofer
Keyword(s):  
Topology Optimization ◽  
Critical Speed ◽  
Parametric Optimization ◽  
Optimization Methods ◽  
Optimization Process ◽  
Support Structure ◽  
And Topology ◽  
Design Variables ◽  
Rotor Bearing ◽  
Non Parametric

The optimization techniques most widely used in various industrial fields for structural optimization generally can be placed into two categories: parametric optimization and non-parametric optimization. In parametric optimization, the parametric variables defining a geometric model are used as design variables. For example, all dimensions defining a structural shape in a CAD (Computer-Aided Design) system can be used as parameters in an optimization process to achieve a desired objective. In non-parametric optimization, an initial outer boundary of the geometry is defined and the optimization process either removes mass without changing the node locations in the calculation mesh (topology optimization) or directly manipulates the node locations (shape optimization) to achieve a desired objective. Nowadays, the combination of both parametric and non-parametric optimization methods can provide an attractive approach to satisfy the requirements of advanced levels of structural performance. While optimization methods have been widely used in many turbomachinery applications, such as turbine and compressor blading, combustors, and casings, in the rotordynamics field, relatively little work has been done to investigate methods for the overall optimization of rotor-bearing-support structures to achieve desired system behavior. In this paper, a combined parametric and non-parametric optimization method is applied to a rotor-bearing-support structure in order to achieve the desired critical speed and unbalance response. The bearing design variables are selected as parametric design variables and topology optimization is applied to the support structure. The entire optimization workflow is constructed in the commercial software Isight, and Abaqus and ATOM (Abaqus Topology Optimization Module) are used for rotordynamics analysis and topology optimization. The desired critical speed and unbalance response can be obtained with the optimized topology of the support structure.

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