B-Spline Based Robust Topology Optimization

2015 ◽  
Author(s):  
Yu Gu ◽  
Xiaoping Qian
Keyword(s):  
Topology Optimization ◽  
Optimization Problems ◽  
Compliant Mechanism ◽  
Analytical Description ◽  
Minimal Length ◽  
Optimization Approach ◽  
Material Density ◽  
B Spline ◽  
B Splines ◽  
Robust Formulation

In this paper, we present an extension of the B-spline based density representation to a robust formulation of topology optimization. In our B-spline based topology optimization approach, we use separate representations for material density distribution and analysis. B-splines are used as a representation of density and the usual finite elements are used for analysis. The density undergoes a Heaviside projection to reduce the grayness in the optimized structures. To ensure minimal length control so the resulting designs are robust with respect to manufacturing imprecision, we adopt a three-structure formulation during the optimization. That is, dilated, intermediate and eroded designs are used in the optimization formulation. We give an analytical description of minimal length of features in optimized designs. Numerical examples have been implemented on three common topology optimization problems: minimal compliance, heat conduction and compliant mechanism. They demonstrate that the proposed approach is effective in generating designs with crisp black/white transition and is accurate in minimal length control.

Design of Compliant Structural Mechanisms Using B-Spline Elements

2011 ◽  
Author(s):  
Ashok V. Kumar ◽  
Anand Parthasarathy
Keyword(s):  
Inverse Problem ◽  
Topology Optimization ◽  
Compliant Mechanisms ◽  
Spline Approximation ◽  
Structural Response ◽  
Field Application ◽  
Optimization Approach ◽  
Objective Functions ◽  
B Spline ◽  
Spline Basis

Structural design is an inverse problem where the geometry that fits a specific design objective is found iteratively through repeated analysis or forward problem solving. In the case of compliant structures, the goal is to design the structure for a particular desired structural response that mimics traditional mechanisms and linkages. It is possible to state the inverse problem in many different ways depending on the choice of objective functions used and the method used to represent the shape. In this paper, some of the objective functions that have been used in the past, for the topology optimization approach to designing compliant mechanisms are compared and discussed. Topology optimization using traditional finite elements often do not yield well-defined smooth boundaries. The computed optimal material distributions have shape irregularities unless special techniques are used to suppress them. In this paper, shape is represented as the contours or level sets of a characteristic function that is defined using B-spline approximation to ensure that the contours, which represent the boundaries, are smooth. The analysis is also performed using B-spline elements which use B-spline basis functions to represent the displacement field. Application of this approach to design a few simple mechanisms is presented.

Topology Optimization of Compliant Mechanisms Using Evolutionary Algorithm With Design Geometry Encoded as a Graph

2002 ◽  
Author(s):  
Shamim Akhtar ◽  
Kang Tai ◽  
Jitendra Prasad
Keyword(s):  
Topology Optimization ◽  
Evolutionary Algorithm ◽  
Optimization Problems ◽  
Compliant Mechanism ◽  
Evolutionary Process ◽  
Optimization Procedure ◽  
Structural Topology ◽  
Mutation Operators ◽  
Design Variables ◽  
Straight Line

This paper describes an intuitive way of defining geometry design variables for solving structural topology optimization problems using an evolutionary algorithm (EA). The geometry representation scheme works by defining a skeleton which represents the underlying topology/connectivity of the continuum structure. As the effectiveness of any EA is highly dependent on the chromosome encoding of the design variables, the encoding used here is a graph which reflects this underlying topology so that the genetic crossover and mutation operators of the EA can recombine and preserve any desirable geometric characteristics through succeeding generations of the evolutionary process. The overall optimization procedure is applied to design a straight-line compliant mechanism : a large displacement flexural structure that generates a vertical straight line path at some point when given a horizontal straight line input displacement at another point.

A Topology Optimization Approach and its Application in the Design of a Key Connecting Component of a Harvester

2011 ◽  
Vol 308-310 ◽  
pp. 2471-2477
Author(s):  
Xiang Chen ◽  
Xin Jun Liu
Keyword(s):  
Topology Optimization ◽  
Optimization Problems ◽  
Engineering Application ◽  
Convergence Speed ◽  
Optimization Approach ◽  
Penalization Method ◽  
Weight Method ◽  
Derivation Process

This paper focuses on an approach to topology optimization and its engineering application. Based on SIMP (Solid Isotropic Microstructure with Penalization) method combined with Guide-Weight method, an approach to solve topology optimization problems is proposed. Then the topology optimization is applied in the design of a key connecting component in a sorghum harvester by the use of proposed method. The derivation process of the iteration formulations demonstrates that the proposed approach has the advantages of easiness to derive and good universality. The result is satisfactory and the convergence speed is fast enough for engineering application.

A Moving Morphable Voids Approach for Topology Optimization With Closed B-Splines

2019 ◽  
Vol 141 (8) ◽  
Author(s):  
Bingxiao Du ◽  
Wen Yao ◽  
Yong Zhao ◽  
Xiaoqian Chen
Keyword(s):  
Topology Optimization ◽  
B Spline ◽  
B Splines ◽  
Spline Curves ◽  
Beam Design ◽  
Merging Process ◽  
Order Degree ◽  
Structural Boundary ◽  
Ks Function ◽  
Selection Of

Topology optimization with moving morphable voids (MMVs) is studied in this paper. B-spline curves are used to represent the boundaries of MMVs in the structure. Kreisselmeier–Steinhauser (KS)-function is also implemented to preserve the smoothness of the structural boundary in case the intersection of the curves happen. In order to study the influence of continuity, we propose pseudo-periodic closed B-splines (PCBSs) to construct curves with an arbitrary degree. The selection of PCBS parameters, especially the degree of B-spline, is studied and discussed. The classic Messerschmitt–Bolkow–Blohm (MBB) case is taken as an example in the numerical experiment. Results show that with the proper choice of B-spline degrees and number of control points, PCBSs have enough flexibility and stability to represent the optimized material distribution. We further reveal the mechanism of the merging process of holes and find that high-order degree PCBS could preserve more separated voids. A support beam design problem of microsatellite is also studied as an example to demonstrate the capability of the proposed method.

Efficient Filtering in Topology Optimization via B-Splines1

2015 ◽  
Vol 137 (3) ◽  
Author(s):  
Mingming Wang ◽  
Xiaoping Qian
Keyword(s):  
Topology Optimization ◽  
Three Dimensional ◽  
Processing Unit ◽  
Optimization Scheme ◽  
B Spline ◽  
B Splines ◽  
Central Processing ◽  
Filter Size ◽  
Density Filter ◽  
3D Topology

This paper presents a B-spline based approach for topology optimization of three-dimensional (3D) problems where the density representation is based on B-splines. Compared with the usual density filter in topology optimization, the new B-spline based density representation approach is advantageous in both memory usage and central processing unit (CPU) time. This is achieved through the use of tensor-product form of B-splines. As such, the storage of the filtered density variables is linear with respect to the effective filter size instead of the cubic order as in the usual density filter. Numerical examples of 3D topology optimization of minimal compliance and heat conduction problems are demonstrated. We further reveal that our B-spline based density representation resolves the bottleneck challenge in multiple density per element optimization scheme where the storage of filtering weights had been prohibitively expensive.

Design of Compliant Mechanisms for Amplification of Induced Strain Actuators

1999 ◽  
Author(s):  
Shawn Canfield ◽  
Mary I. Frecker
Keyword(s):  
Topology Optimization ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Design Procedure ◽  
Computation Time ◽  
Mechanical Efficiency ◽  
Optimality Criteria ◽  
Optimization Approach ◽  
Detail Design ◽  
Problem Formulations

Abstract The focus of this paper is on designing compliant mechanism amplifiers for piezoelectric actuators using a topology optimization approach. Two optimization formulations are developed: one in which the overall stroke amplification or geometric advantage (GA) is maximized, and another where the mechanical efficiency (ME) of the amplifier is maximized. Two solution strategies are used, Sequential Linear Programming (SLP) and an Optimality Criteria method, and results are compared with respect to computation time and mechanism performance. Design examples illustrate the characteristics of both problem formulations, and physical prototypes have been fabricated as proof of concept. An automated detail design procedure has also been developed which allows the topology optimization results obtained in MATLAB to be directly translated into a neutral 3-D solid geometry format for import into other CAE programs.

A Robust Optimization Approach Using Taguchi’s Loss Function for Solving Nonlinear Optimization Problems

1991 ◽  
Author(s):  
Balaji Ramakrishnan ◽  
S. S. Rao
Keyword(s):  
Nonlinear Optimization ◽  
Loss Function ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Optimization Approach ◽  
Beam Design ◽  
Robust Formulation ◽  
Machining Parameter ◽  
Machining Characteristics ◽  
Taguchi’S Loss Function

Abstract The application of the concept of robust design, based on Taguchi’s loss function, in formulating and solving nonlinear optimization problems is investigated. The effectiveness of the approach is illustrated with two examples. The first example is a machining parameter optimization problem wherein the production cost, tool life and production rate are optimized with limitations on machining characteristics such as cutting power, cutting tool temperature and surface finish. The second example is a welded beam design problem where the dimensions of the weldment and the beam are found without exceeding the limitations stated on the shear stress in the weld, normal stress in the beam, buckling load on the beam and tip deflection of the beam. The results are highlighted by comparing the solutions of the robust formulation with those obtained from the conventional formulation. The methodology presented in this work is expected to be useful in the design of products and processes which are least sensitive to the noises and which reflect in higher quality.

Compliant Mechanism Design Through Topology Optimization Using Pseudo-Rigid-Body Models

2016 ◽  
Author(s):  
Venkatasubramanian Kalpathy Venkiteswaran ◽  
Omer Anil Turkkan ◽  
Hai-Jun Su
Keyword(s):  
Finite Element ◽  
Topology Optimization ◽  
Rigid Body ◽  
Finite Element Methods ◽  
Compliant Mechanism ◽  
Beam Theory ◽  
Deformation Analysis ◽  
Optimization Approach ◽  
Algebraic Equations ◽  
Kinematic Loops

The initial design of compliant mechanisms for a specific application can be a challenging task. This paper introduces a topology optimization approach for planar mechanisms based on graph theory. It utilizes pseudo-rigid-body models, which allow the kinetostatic equations to be represented as nonlinear algebraic equations. This reduces the complexity of the system compared to beam theory or finite element methods, and has the ability to incorporate large deformations. Integer variables are used for developing the adjacency matrix, which is optimized by a genetic algorithm. Dynamic penalty functions describe the general and case-specific constraints. A symmetric 3R model is used to represent the beams in the mechanism. The design space is divided into rectangular segments while kinematic and static equations are derived using kinematic loops. The effectiveness of the approach is demonstrated with the example of an inverter mechanism. The results are compared against finite element methods to prove the validity of the new model as well as the accuracy of the approach outlined here. Future implementations of this method will include stress and deformation analysis and also introduce multi-material designs using different pseudo-rigid-body models.

Efficient Filtering in Topology Optimization via B-Splines

2014 ◽  
Author(s):  
Mingming Wang ◽  
Xiaoping Qian
Keyword(s):  
Topology Optimization ◽  
Three Dimensional ◽  
Optimization Scheme ◽  
B Spline ◽  
Numerical Examples ◽  
B Splines ◽  
Cpu Time ◽  
Filter Size ◽  
Density Filter ◽  
3D Topology

This paper presents a B-spline based approach for topology optimization of three-dimensional (3D) problems where the density representation is based on B-splines. Compared with the usual density filter in topology optimization, the new B-spline based density representation approach is advantageous in both memory usage and CPU time. This is achieved through the use of tensor-product form of B-splines. As such, the storage of the filtered density variables is linear with respect to the effective filter size instead of the cubic order as in the usual density filter. Numerical examples of 3D topology optimization of minimal compliance and heat conduction problems are demonstrated. We further reveal that our B-spline based density representation resolves the bottleneck challenge in multiple density per element optimization scheme where the storage of filtering weights had been prohibitively expensive.

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