scholarly journals Topology Optimization Using Parabolic Aggregation Function with Independent-Continuous-Mapping Method

2013 ◽  
Vol 2013 ◽  
pp. 1-18
Author(s):  
Tie Jun ◽  
Sui Yun-kang
Keyword(s):  
Topology Optimization ◽  
Strain Energy ◽  
Stress Singularity ◽  
Continuous Mapping ◽  
Stress Constraints ◽  
Aggregation Function ◽  
Sensitivity Analyses ◽  
Stress Concentrations ◽  
Filter Function ◽  
Design Variables

This paper concentrates on finding the optimal distribution for continuum structure such that the structural weight with stress constraints is minimized where the physical design domain is discretized by finite elements. A novel Independent-Continuous-Mapping (ICM) method is proposed to convert equivalently the binary design variables which is used to indicate material or void in the various elements to independent continuous design variables. Moreover, three smooth mappings about weight, stiffness, and stress of the structural elements are introduced to formulate the objective function based on the so-called concepts of polish function and weighting filter function. A new general continuous approach for topology optimization is given which can eliminate the stress singularity phenomena more efficiently than the traditionalε-relaxation method, and an alternative strain energy method for the stress constraints is proposed to overcome the difficulty in stress sensitivity analyses. Mathematically, by means of a generalized aggregation KS-like function defined as the parabolic aggregation function, a topology optimization model is formulated with the weight objective and single parabolic global strain energy constraints. The numerical examples demonstrate that the proposed methods effectively remove the stress concentrations and generate black-and-white designs for practically sized problems.

scholarly journals Three-Dimensional Dynamic Topology Optimization with Frequency Constraints Using Composite Exponential Function and ICM Method

2015 ◽  
Vol 2015 ◽  
pp. 1-10
Author(s):  
Hongling Ye ◽  
Ning Chen ◽  
Yunkang Sui ◽  
Jun Tie
Keyword(s):  
Topology Optimization ◽  
Exponential Function ◽  
Three Dimensional ◽  
Continuous Mapping ◽  
Taylor Series Expansion ◽  
Optimal Model ◽  
Filter Function ◽  
Frequency Constraints ◽  
Design Variables ◽  
Dynamic Topology

The dynamic topology optimization of three-dimensional continuum structures subject to frequency constraints is investigated using Independent Continuous Mapping (ICM) design variable fields. The composite exponential function (CEF) is selected to be a filter function which recognizes the design variables and to implement the changing process of design variables from “discrete” to “continuous” and back to “discrete.” Explicit formulations of frequency constraints are given based on filter functions, first-order Taylor series expansion. And an improved optimal model is formulated using CEF and the explicit frequency constraints. Dual sequential quadratic programming (DSQP) algorithm is used to solve the optimal model. The program is developed on the platform of MSC Patran & Nastran. Finally, numerical examples are given to demonstrate the validity and applicability of the proposed method.

scholarly journals Microstructural Topology Optimization of Constrained Layer Damping on Plates for Maximum Modal Loss Factor of Macrostructures

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Zhanpeng Fang ◽  
Lei Yao ◽  
Shuxia Tian ◽  
Junjian Hou
Keyword(s):  
Topology Optimization ◽  
Loss Factor ◽  
Strain Energy ◽  
Design Method ◽  
Optimization Method ◽  
Constrained Layer Damping ◽  
Viscoelastic Materials ◽  
Modal Strain Energy ◽  
Design Variables ◽  
Microstructural Topology Optimization

This paper presents microstructural topology optimization of viscoelastic materials for the plates with constrained layer damping (CLD) treatments. The design objective is to maximize modal loss factor of macrostructures, which is obtained by using the Modal Strain Energy (MSE) method. The microstructure of the viscoelastic damping layer is composed of 3D periodic unit cells. The effective elastic properties of the unit cell are obtained through the strain energy-based method. The density-based topology optimization is adopted to find optimal microstructures of viscoelastic materials. The design sensitivities of modal loss factor with respect to the design variables are analyzed and the design variables are updated by Method of Moving Asymptotes (MMA). Numerical examples are given to demonstrate the validity of the proposed optimization method. The effectiveness of the optimal design method is illustrated by comparing a solid and an optimized cellular viscoelastic material as applied to the plates with CLD treatments.

TOPOLOGY OPTIMIZATION OF STRUCTURE WITH GLOBAL STRESS CONSTRAINTS BY INDEPENDENT CONTINUUM MAP METHOD

2006 ◽  
Vol 03 (03) ◽  
pp. 295-319 ◽  
Author(s):  
Y. K. SUI ◽  
X. R. PENG ◽  
J. L. FENG ◽  
H. L. YE
Keyword(s):  
Topology Optimization ◽  
Optimization Model ◽  
Strain Energy ◽  
Local Stress ◽  
Stress Constraints ◽  
Weighting Coefficient ◽  
Load Case ◽  
Weighting Method ◽  
Global Strain ◽  
Energy Constraints

We establish topology optimization model in terms of Independent Continuum Map method (ICM), so as to avoid the difficulties caused by multiple objective functions of compliance, owing to referring to weight as objective function. Using the distorted-strain-energy criterion, we transform stress constraints on all elements into structure strain-energy constraints in global sense. Then, the problem of topological optimum of continuum structure subjected to global strain-energy constraints is formulated and solved. The process of optimization is conducted through three basic steps which include the computation of the minimum strain energy of structure corresponding to the maximum strain-energy under the load case due to prescribing weight constraint, the determination of the allowable strain-energy of structure for every load case by using a formula from our numerical tests, as well as the establishment and solution of optimization model with the weight function due to all allowable strain energies. A strategy that is available to cope with complicated load ill-posedness in terms of different complementary approaches one by one is presented in the present work. Several numerical examples demonstrate that the topology path of transferring forces can be obtained more readily by global strain energy constraints rather than local stress constraints, and the problem of load ill-posedness can be tackled very well by the weighting method with regard to structural strain energy as weighting coefficient.

A SIMPLIFIED ANALYTICAL PROCEDURE FOR SEISMIC ANALYSIS OF TIMBER LIGHT-FRAME SHEAR WALLS

2019 ◽  
Vol 3 (Special Issue on First SACEE'19) ◽  
pp. 173-180
Author(s):  
Giorgia Di Gangi ◽  
Giorgio Monti ◽  
Giuseppe Quaranta ◽  
Marco Vailati ◽  
Cristoforo Demartino
Keyword(s):  
Analytical Procedure ◽  
Seismic Analysis ◽  
Shear Walls ◽  
Element Model ◽  
Sensitivity Analyses ◽  
Width Ratio ◽  
Damping Factor ◽  
Equivalent Viscous Damping ◽  
Design Variables ◽  
Depth Analysis

The seismic performance of timber light-frame shear walls is investigated in this paper with a focus on energy dissipation and ductility ensured by sheathing-to-framing connections. An original parametric finite element model has been developed in order to perform sensitivity analyses. The model considers the design variables affecting the racking load-carrying capacity of the wall. These variables include aspect ratio (height-to-width ratio), fastener spacing, number of vertical studs and framing elements cross-section size. A failure criterion has been defined based on the observation of both the global behaviour of the wall and local behaviour of fasteners in order to identify the ultimate displacement of the wall. The equivalent viscous damping has been numerically assessed by estimating the damping factor which is in use in the capacity spectrum method. Finally, an in-depth analysis of the results obtained from the sensitivity analyses led to the development of a simplified analytical procedure which is able to predict the capacity curve of a timber light-frame shear wall.

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 An efficient approach to reliability-based topology optimization for the structural lightweight design of planar continuum structures

2021 ◽  
Vol 37 ◽  
pp. 270-281
Author(s):  
Fangfang Yin ◽  
Kaifang Dang ◽  
Weimin Yang ◽  
Yumei Ding ◽  
Pengcheng Xie
Keyword(s):  
Topology Optimization ◽  
Lightweight Design ◽  
Integrated Design ◽  
Optimization Methods ◽  
Filter Function ◽  
Continuum Structures ◽  
Performance Indexes ◽  
Reliability Method ◽  
Economic Indexes ◽  
The Impact

Abstract In order to solve the application restrictions of deterministic-based topology optimization methods arising from the omission of uncertainty factors in practice, and to realize the calculation cost control of reliability-based topology optimization. In consideration of the current reliability-based topology optimization methods of continuum structures mainly based on performance indexes model with a power filter function. An efficient probabilistic reliability-based topology optimization model that regards mass and displacement as an objective function and constraint is established based on the first-order reliability method and a modified economic indexes model with a composite exponential filter function in this study. The topology optimization results obtained by different models are discussed in relation to optimal structure and convergence efficiency. Through numerical examples, it can be seen that the optimal layouts obtained by reliability-based models have an increased amount of material and more support structures, which reveals the necessity of considering uncertainty in lightweight design. In addition, the reliability-based modified model not only can obtain lighter optimal structures compared with traditional economic indexes models in most circumstances, but also has a significant advantage in convergence efficiency, with an average increase of 44.59% and 64.76% compared with the other two reliability-based models. Furthermore, the impact of the reliability index on the results is explored, which verifies the validity of the established model. This study provides a theoretical reference for lightweight or innovative feature-integrated design in engineering applications.

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.

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