Numerical Experiments in Using Voronoi Cell Finite Elements for Topology Optimization

2009 ◽  
Author(s):  
James M. Gibert ◽  
Georges M. Fadel
Keyword(s):  
Topology Optimization ◽  
Isotropic Material ◽  
Numerical Experiments ◽  
Voronoi Cell ◽  
Material Model ◽  
Topological Optimization ◽  
Advantages And Disadvantages ◽  
Compliance Minimization ◽  
Design Variables ◽  
Standard Linear

This paper provides two separate methodologies for implementing the Voronoi Cell Finite Element Method (VCFEM) in topological optimization. Both exploit two characteristics of VCFEM. The first approach utilizes the property that a hole or inclusion can be placed in the element: the design variables for the topology optimization are sizes of the hole. In the second approach, we note that VCFEM may mesh the design domain as n sided polygons. We restrict our attention to hexagonal meshes of the domain while applying Solid Isotropic Material Penalization (SIMP) material model. Researchers have shown that hexagonal meshes are not subject to the checker boarding problem commonly associated with standard linear quad and triangle elements. We present several examples to illustrate the efficacy of the methods in compliance minimization as well as discuss the advantages and disadvantages of each method.

scholarly journals DESIGN OF THE MOUNTING BRACKET FOR THE OPTICAL SOLAR SENSOR OF THE SPACECRAFT USING TOPOLOGICAL OPTIMIZATION

2021 ◽  
pp. 98-105
Author(s):  
Sergey Shaposhnikov ◽  
◽  
Yevgeny Kishov ◽  
Lyubov Zimnyakova ◽  
◽  
...  
Keyword(s):  
Thermal Analysis ◽  
Topology Optimization ◽  
Thermal Resistance ◽  
Thermal Structure ◽  
Material Model ◽  
Topological Optimization ◽  
Lateral Acceleration ◽  
Distribution Data ◽  
Mass Reduction ◽  
Software Module

Object of the research is a bracket of solar sensor mounting of spacecraft. Goal of the research is to reduce mass of the spacecraft bracket subject to strength and thermal resistance considerations. Mass reduction is carried using topology optimization based on SIMP-material model (Solid Isotropic Material with Penalization). Optimization problem statement is compliance(or strain energy) minimization subject to volume constraint. For strength and thermal analysis finite element method is used implemented in Ansys Workbench 18.2 software. As result of topology optimization, a material distribution data inside a design domain is obtained for different volume fractions. Based on that result new CAD-model has been developed using Siemens NX software which taking into account manufacturing constraints and providing manufacturing of the designed part using machining. Structural analysis performed for two load cases corresponds to launch regime and maximum lateral acceleration has shown that optimized structure has sufficient strength. Thermal analysis performed in Steady State Thermal software module has shown that thermal resistance requirement also met. As result of proposed research bracket mass reduction of 2.5 times has been achieved. Directions of future work has been outlined. Improvement of proposed method may consist from incorporating of coupled thermal-structure analysis into topology optimization process.

Damage Identification Using Static and Dynamic Responses Based on Topology Optimization and Lasso Regularization

2020 ◽  
Author(s):  
Ryo Sugai ◽  
Akira Saito ◽  
Hidetaka Saomoto
Keyword(s):  
Topology Optimization ◽  
Numerical Experiments ◽  
Damage Identification ◽  
Dynamic Responses ◽  
High Fidelity ◽  
Dynamic Problems ◽  
Objective Functions ◽  
Identification Method ◽  
Design Variables ◽  
Active Design

Abstract This paper presents a damage identification method based on topology optimization and Lasso regularization. The method uses static displacements or dynamic responses to identify damages of structures. The method has the potential to identify damages with high fidelity, in comparison with ordinary damage identification method based on optimization with parameterized geometry of the damages. However, it is difficult to precisely detect damage using topology optimization due mostly to the large number of design variables. Therefore, supposing that the damage is sufficiently small, we propose a method adding Lasso regularization to the objective functions to suppress active design variables during topology optimization process. To verify the effectiveness of the proposed method, we conducted a set of numerical experiments for static and dynamic problems. We have succeeded in suppressing active design variables and delete artificially generated damages and the location and shape of damage have been precisely identified.

Topological Optimization Design of Top Beam of the Longmen Milling Machine Based on Hyperworks

2013 ◽  
Vol 378 ◽  
pp. 65-68
Author(s):  
Ning Jia ◽  
Fu Yun Liu ◽  
Yun Ze Yang ◽  
Lin Gan ◽  
Qing Qing Chang
Keyword(s):  
Topology Optimization ◽  
Optimization Design ◽  
Optimal Allocation ◽  
Volume Fraction ◽  
Lightweight Design ◽  
Topological Optimization ◽  
Design Domain ◽  
Milling Machine ◽  
Optimal Distribution ◽  
Design Variables

Topology optimization is a kind of optimized method, which can seek for an optimal allocation of structural material according to the load,constraints and optimization goals .To achieve the lightweight design of the top beam, establishing a minimum strain as the objective function, the volume fraction as the constraint conditions, and the density of design domain as the design variables,implementing the topology optimization for the top beam,the optimal distribution of top beam material is obtained, which provide a basis for the manufacture of top beam.

Topology Optimization of Continuum Structures Based on SIMP

2011 ◽  
Vol 255-260 ◽  
pp. 14-19 ◽  
Author(s):  
Hong Zhang ◽  
Xiao Hui Ren
Keyword(s):  
Mathematical Model ◽  
Topology Optimization ◽  
Isotropic Material ◽  
Optimization Design ◽  
Optimality Criteria ◽  
Continuum Structures ◽  
Good Convergence ◽  
Minimum Compliance ◽  
Design Variables ◽  
Optimality Criteria Method

An Optimality Criteria method for topology optimization of continuum structures based on Solid Isotropic Material with Penalization (SIMP) was proposed. The minimum compliance of structures was selected as the objective function of the problem. A mathematical model for topology optimization design of statically loaded structures and the update scheme for the design variables were set. The examples showed that the algorithm has good convergence and application values.

scholarly journals A NON-GRADIENT APPROACH FOR THREE DIMENSIONAL TOPOLOGY OPTIMIZATION

2021 ◽  
Vol 59 (3) ◽  
pp. 368
Author(s):  
Minh Ngoc Nguyen ◽  
Nha Thanh Nguyen ◽  
Minh Tuan Tran
Keyword(s):  
Topology Optimization ◽  
Comparative Study ◽  
Isotropic Material ◽  
Three Dimensional ◽  
Logistic Function ◽  
Interpolation Scheme ◽  
Compliance Minimization ◽  
Material Interpolation ◽  
Density Filter ◽  
Gradient Approach

The present work is devoted to the extension of the non-gradient approach, namely Proportional Topology Optimization (PTO), for compliance minimization of three-dimensional (3D) structures. Two schemes of material interpolation within the framework of the solid isotropic material with penalization (SIMP), i.e. the power function and the logistic function are analyzed. Through a comparative study, the efficiency of the logistic-type interpolation scheme is highlighted.  Since no sensitivity is involved in the approach, a density filter is applied instead of sensitivity filter to avoid checkerboard issue

scholarly journals Multiscale structural optimization with concurrent coupling between scales

2021 ◽  
Author(s):  
Ryan Murphy ◽  
Chikwesiri Imediegwu ◽  
Robert Hewson ◽  
Matthew Santer
Keyword(s):  
Structural Optimization ◽  
Isotropic Material ◽  
Three Dimensional ◽  
Functionally Graded ◽  
Extremal Point ◽  
Optimization Framework ◽  
Compliance Minimization ◽  
Minimization Problems ◽  
Computational Expense ◽  
Design Variables

AbstractA robust three-dimensional multiscale structural optimization framework with concurrent coupling between scales is presented. Concurrent coupling ensures that only the microscale data required to evaluate the macroscale model during each iteration of optimization is collected and results in considerable computational savings. This represents the principal novelty of this framework and permits a previously intractable number of design variables to be used in the parametrization of the microscale geometry, which in turn enables accessibility to a greater range of extremal point properties during optimization. Additionally, the microscale data collected during optimization is stored in a reusable database, further reducing the computational expense of optimization. Application of this methodology enables structures with precise functionally graded mechanical properties over two scales to be derived, which satisfy one or multiple functional objectives. Two classical compliance minimization problems are solved within this paper and benchmarked against a Solid Isotropic Material with Penalization (SIMP)–based topology optimization. Only a small fraction of the microstructure database is required to derive the optimized multiscale solutions, which demonstrates a significant reduction in the computational expense of optimization in comparison to contemporary sequential frameworks. In addition, both cases demonstrate a significant reduction in the compliance functional in comparison to the equivalent SIMP-based optimizations.

scholarly journals Topology Optimization of Hard-Coating Thin Plate for Maximizing Modal Loss Factors

Coatings ◽  
2021 ◽  
Vol 11 (7) ◽  
pp. 774
Author(s):  
Haitao Luo ◽  
Rong Chen ◽  
Siwei Guo ◽  
Jia Fu
Keyword(s):  
Topology Optimization ◽  
Objective Function ◽  
Composite Plates ◽  
Optimization Method ◽  
Hard Coating ◽  
Design Variables ◽  
Coating Composite ◽  
Damping Materials ◽  
Topology Optimization Method ◽  
Loss Factors

At present, hard coating structures are widely studied as a new passive damping method. Generally, the hard coating material is completely covered on the surface of the thin-walled structure, but the local coverage cannot only achieve better vibration reduction effect, but also save the material and processing costs. In this paper, a topology optimization method for hard coated composite plates is proposed to maximize the modal loss factors. The finite element dynamic model of hard coating composite plate is established. The topology optimization model is established with the energy ratio of hard coating layer to base layer as the objective function and the amount of damping material as the constraint condition. The sensitivity expression of the objective function to the design variables is derived, and the iteration of the design variables is realized by the Method of Moving Asymptote (MMA). Several numerical examples are provided to demonstrate that this method can obtain the optimal layout of damping materials for hard coating composite plates. The results show that the damping materials are mainly distributed in the area where the stored modal strain energy is large, which is consistent with the traditional design method. Finally, based on the numerical results, the experimental study of local hard coating composites plate is carried out. The results show that the topology optimization method can significantly reduce the frequency response amplitude while reducing the amount of damping materials, which shows the feasibility and effectiveness of the method.

scholarly journals Stable and Efficient Modeling of Anelastic Attenuation in Seismic Wave Propagation

2012 ◽  
Vol 12 (1) ◽  
pp. 193-225 ◽  
Author(s):  
N. Anders Petersson ◽  
Björn Sjögreen
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Half Space ◽  
Material Model ◽  
Second Order ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Space Problem ◽  
Standard Linear Solid ◽  
Standard Linear

AbstractWe develop a stable finite difference approximation of the three-dimensional viscoelastic wave equation. The material model is a super-imposition of N standard linear solid mechanisms, which commonly is used in seismology to model a material with constant quality factor Q. The proposed scheme discretizes the governing equations in second order displacement formulation using 3N memory variables, making it significantly more memory efficient than the commonly used first order velocity-stress formulation. The new scheme is a generalization of our energy conserving finite difference scheme for the elastic wave equation in second order formulation [SIAM J. Numer. Anal., 45 (2007), pp. 1902-1936]. Our main result is a proof that the proposed discretization is energy stable, even in the case of variable material properties. The proof relies on the summation-by-parts property of the discretization. The new scheme is implemented with grid refinement with hanging nodes on the interface. Numerical experiments verify the accuracy and stability of the new scheme. Semi-analytical solutions for a half-space problem and the LOH.3 layer over half-space problem are used to demonstrate how the number of viscoelastic mechanisms and the grid resolution influence the accuracy. We find that three standard linear solid mechanisms usually are sufficient to make the modeling error smaller than the discretization error.

scholarly journals A Sequential Approach for Aerodynamic Shape Optimization with Topology Optimization of Airfoils

2021 ◽  
Vol 26 (2) ◽  
pp. 34
Author(s):  
Isaac Gibert Martínez ◽  
Frederico Afonso ◽  
Simão Rodrigues ◽  
Fernando Lau
Keyword(s):  
Topology Optimization ◽  
Shape Optimization ◽  
Volume Fraction ◽  
Optimization Techniques ◽  
Free Form ◽  
Aerodynamic Shape Optimization ◽  
Sequential Approach ◽  
Airfoil Surface ◽  
Aerodynamic Shape ◽  
Design Variables

The objective of this work is to study the coupling of two efficient optimization techniques, Aerodynamic Shape Optimization (ASO) and Topology Optimization (TO), in 2D airfoils. To achieve such goal two open-source codes, SU2 and Calculix, are employed for ASO and TO, respectively, using the Sequential Least SQuares Programming (SLSQP) and the Bi-directional Evolutionary Structural Optimization (BESO) algorithms; the latter is well-known for allowing the addition of material in the TO which constitutes, as far as our knowledge, a novelty for this kind of application. These codes are linked by means of a script capable of reading the geometry and pressure distribution obtained from the ASO and defining the boundary conditions to be applied in the TO. The Free-Form Deformation technique is chosen for the definition of the design variables to be used in the ASO, while the densities of the inner elements are defined as design variables of the TO. As a test case, a widely used benchmark transonic airfoil, the RAE2822, is chosen here with an internal geometric constraint to simulate the wing-box of a transonic wing. First, the two optimization procedures are tested separately to gain insight and then are run in a sequential way for two test cases with available experimental data: (i) Mach 0.729 at α=2.31°; and (ii) Mach 0.730 at α=2.79°. In the ASO problem, the lift is fixed and the drag is minimized; while in the TO problem, compliance minimization is set as the objective for a prescribed volume fraction. Improvements in both aerodynamic and structural performance are found, as expected: the ASO reduced the total pressure on the airfoil surface in order to minimize drag, which resulted in lower stress values experienced by the structure.

Efficient Sensitivity Analysis for Multibody Dynamics Systems Using an Iterative Steps Method With Application in Topology Optimization

2011 ◽  
Author(s):  
Guang Dong ◽  
Zheng-Dong Ma ◽  
Gregory Hulbert ◽  
Noboru Kikuchi ◽  
Sudhakar Arepally ◽  
...  
Keyword(s):  
Sensitivity Analysis ◽  
Topology Optimization ◽  
Multibody Dynamics ◽  
Optimization Problem ◽  
Finite Difference Methods ◽  
Analysis Method ◽  
Topology Optimization Problem ◽  
Design Variables ◽  
Sensitivity Analysis Method ◽  
Rotational Motions

Efficient and reliable sensitivity analyses are critical for topology optimization, especially for multibody dynamics systems, because of the large number of design variables and the complexities and expense in solving the state equations. This research addresses a general and efficient sensitivity analysis method for topology optimization with design objectives associated with time dependent dynamics responses of multibody dynamics systems that include nonlinear geometric effects associated with large translational and rotational motions. An iterative sensitivity analysis relation is proposed, based on typical finite difference methods for the differential algebraic equations (DAEs). These iterative equations can be simplified for specific cases to obtain more efficient sensitivity analysis methods. Since finite difference methods are general and widely used, the iterative sensitivity analysis is also applicable to various numerical solution approaches. The proposed sensitivity analysis method is demonstrated using a truss structure topology optimization problem with consideration of the dynamic response including large translational and rotational motions. The topology optimization problem of the general truss structure is formulated using the SIMP (Simply Isotropic Material with Penalization) assumption for the design variables associated with each truss member. It is shown that the proposed iterative steps sensitivity analysis method is both reliable and efficient.

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