Topology Optimization With Multiple Constraints

1995 ◽  
Author(s):  
R. J. Yang
Keyword(s):  
Finite Element ◽  
Topology Optimization ◽  
Optimization Problem ◽  
Optimality Criteria ◽  
Topology Design ◽  
Structural Components ◽  
Material Density ◽  
Structural Responses ◽  
Mathematical Programming Method ◽  
General Optimization Problem

Abstract Topology optimization is used for determining the best layout of structural components to achieve predetermined performance goals. The density method which uses material density of each finite element as the design variable is employed. Unlike the most common approach which uses the optimality criteria methods, the topology design problem is formulated as a general optimization problem and is solved by the mathematical programming method. One of the major advantages of this approach is its generality; thus it can solve various problems, e.g. multi-objective and multi-constraint problems. In this study, the structural weight is chosen as the objective function and structural responses such as the compliances, displacements, and the natural frequencies are treated as the constraints. The MSC/NASTRAN finite element code is employed for response analyses. One example with four different optimization formulations was used to demonstrate this approach.

Topology Optimization Using Node-Based Smoothed Finite Element Method

2015 ◽  
Vol 07 (06) ◽  
pp. 1550085 ◽  
Author(s):  
Z. C. He ◽  
G. Y. Zhang ◽  
L. Deng ◽  
Eric Li ◽  
G. R. Liu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Topology Optimization ◽  
Optimization Design ◽  
Solid Mechanics ◽  
Optimality Criteria ◽  
Topology Optimization Problem ◽  
Design Variables ◽  
Smoothed Finite Element Method ◽  
Element Method

The node-based smoothed finite element method (NS-FEM) proposed recently has shown very good properties in solid mechanics, such as providing much better gradient solutions. In this paper, the topology optimization design of the continuum structures under static load is formulated on the basis of NS-FEM. As the node-based smoothing domain is the sub-unit of assembling stiffness matrix in the NS-FEM, the relative density of node-based smoothing domains serves as design variables. In this formulation, the compliance minimization is considered as an objective function, and the topology optimization model is developed using the solid isotropic material with penalization (SIMP) interpolation scheme. The topology optimization problem is then solved by the optimality criteria (OC) method. Finally, the feasibility and efficiency of the proposed method are illustrated with both 2D and 3D examples that are widely used in the topology optimization design.

Review of Methods of Mechanical Digital Design Based on Topology Optimization

2013 ◽  
Vol 288 ◽  
pp. 193-201
Author(s):  
Xiu Ye Wang ◽  
Han Zhao ◽  
Zu Fang Zhang ◽  
Yong Wang
Keyword(s):  
Topology Optimization ◽  
Optimization Algorithms ◽  
Optimality Criteria ◽  
Digital Design ◽  
Structural Topology ◽  
Optimality Criteria Method ◽  
Mathematical Programming Method ◽  
Pde Methods ◽  
Volume Method ◽  
Element Method

The basic mathematical model of topology optimization of continuum structures is introduced at first. Then the authors focus on reviewing the development of PDE methods and optimization algorithms. This paper details the development and applications of Finite Element Method, Boundary Element Method and Finite Volume Method. This paper also illustrates several typical applications and achievements of optimization algorithms, such as Optimality Criteria method, mathematical programming method and intelligent algorithm. Based on our research, this paper finally summarizes the process of the structural topology optimization and describes the directions of the topology optimization in the field of mechanical digital design.

Structural Topology Design Considering Reliability

2005 ◽  
Vol 297-300 ◽  
pp. 1901-1906 ◽  
Author(s):  
Seung Jae Min ◽  
Seung Hyun Bang
Keyword(s):  
Topology Optimization ◽  
Design Optimization ◽  
Optimization Problem ◽  
Performance Measure ◽  
Topology Design ◽  
Optimization Process ◽  
Programming Algorithm ◽  
Probabilistic Design ◽  
Most Probable Point ◽  
Design Variables

In the design optimization process design variables are selected in the deterministic way though those have uncertainties in nature. To consider variances in design variables reliability-based design optimization problem is formulated by introducing the probability distribution function. The concept of reliability has been applied to the topology optimization based on a reliability index approach or a performance measure approach. Since these approaches, called double-loop singlevariable approach, requires the nested optimization problem to obtain the most probable point in the probabilistic design domain, the time for the entire process makes the practical use infeasible. In this work, new reliability-based topology optimization method is proposed by utilizing single-loop singlevariable approach, which approximates searching the most probable point analytically, to reduce the time cost and dealing with several constraints to handle practical design requirements. The density method in topology optimization including SLP (Sequential Linear Programming) algorithm is implemented with object-oriented programming. To examine uncertainties in the topology design of a structure, the modulus of elasticity of the material and applied loadings are considered as probabilistic design variables. The results of a design example show that the proposed method provides efficiency curtailing the time for the optimization process and accuracy satisfying the specified reliability.

scholarly journals Comparative Study of Peridynamics and Finite Element Method for Practical Modeling of Defects Cracks in Topology Optimization

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1407
Author(s):  
Peyman Lahe Motlagh ◽  
Adnan Kefal
Keyword(s):  
Finite Element ◽  
Topology Optimization ◽  
Comparative Study ◽  
Strain Energy ◽  
Optimality Criteria ◽  
Design Stage ◽  
Design Domain ◽  
Optimum Topology ◽  
Strain Stress

Recently, topology optimization of structures with cracks becomes an important topic for avoiding manufacturing defects at the design stage. This paper presents a comprehensive comparative study of peridynamics-based topology optimization method (PD-TO) and classical finite element topology optimization approach (FEM-TO) for designing lightweight structures with/without cracks. Peridynamics (PD) is a robust and accurate non-local theory that can overcome various difficulties of classical continuum mechanics for dealing with crack modeling and its propagation analysis. To implement the PD-TO in this study, bond-based approach is coupled with optimality criteria method. This methodology is applicable to topology optimization of structures with any symmetric/asymmetric distribution of cracks under general boundary conditions. For comparison, optimality criteria approach is also employed in the FEM-TO process, and then topology optimization of four different structures with/without cracks are investigated. After that, strain energy and displacement results are compared between PD-TO and FEM-TO methods. For design domain without cracks, it is observed that PD and FEM algorithms provide very close optimum topologies with a negligibly small percent difference in the results. After this validation step, each case study is solved by integrating the cracks in the design domain as well. According to the simulation results, PD-TO always provides a lower strain energy than FEM-TO for optimum topology of cracked structures. In addition, the PD-TO methodology ensures a better design of stiffer supports in the areas of cracks as compared to FEM-TO. Furthermore, in the final case study, an intended crack with a symmetrically designed size and location is embedded in the design domain to minimize the strain energy of optimum topology through PD-TO analysis. It is demonstrated that hot-spot strain/stress regions of the pristine structure are the most effective areas to locate the designed cracks for effective redistribution of strain/stress during topology optimization.

3D-Printable Unit Cell Design for Cubic and Orthotropic Porous Microstructures Using Topology Optimization Based on Optimality Criteria Algorithm

2018 ◽  
Vol 10 (06) ◽  
pp. 1850060 ◽  
Author(s):  
Alireza Moshki ◽  
Akbar Ghazavizadeh ◽  
Ali Asghar Atai ◽  
Mostafa Baghani ◽  
Majid Baniassadi
Keyword(s):  
Topology Optimization ◽  
Optimization Technique ◽  
Optimality Criteria ◽  
Unit Cell ◽  
Topology Design ◽  
Two Phase ◽  
Topology Identification ◽  
Young’S Moduli ◽  
Periodic Microstructures ◽  
Porous Microstructures

Optimal design of porous and periodic microstructures through topology identification of the associated periodic unit cell (PUC) constitutes the topic of this work. Here, the attention is confined to two-phase heterogeneous materials in which the topology identification of manufacturable 3D-PUC is conducted by means of a topology optimization technique. The associated objective function is coupled with 3D numerical homogenization approach that connects the elastic properties of the 3D-PUC to the target product. The topology optimization methodology that is adopted in this study is the combination of solid isotropic material with penalization (SIMP) method and optimality criteria algorithm (OCA), referred to as SIMP-OCA methodology. The fairly simple SIMP-OCA is then generalized to handle the topology design of 3D manufacturable microstructures of cubic and orthotropic symmetry. The performance of the presented methodology is experimentally validated by fabricating real prototypes of extremal elastic constants using additive manufacturing. Experimental evaluation is performed on two designed microstructures: an orthotropic sample with Young’s moduli ratios [Formula: see text], [Formula: see text] and a cubic sample with negative Poisson’s ratio of [Formula: see text]. In all practical examples studied, laboratory measurements are in reasonable agreement with the prescribed values; thus, corroborating the applicability of the proposed methodology.

A Hybrid Contact Implementation Framework for Finite Element Analysis and Topology Optimization of Machine Tools

2020 ◽  
Vol 142 (8) ◽  
Author(s):  
Esra Yuksel ◽  
Ahmet Semih Erturk ◽  
Erhan Budak
Keyword(s):  
Finite Element ◽  
Topology Optimization ◽  
Structural Optimization ◽  
Machine Tool ◽  
Machine Tools ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Contact Stiffness ◽  
Contact Forces ◽  
Implementation Framework

Abstract Machine tool contacts must be represented accurately for reliable prediction of machine behavior. In structural optimization problems, contact constraints are represented as an additional minimization problem based on computational contact mechanics theory. An accurate contact constraint representation is challenging for structural optimization problems: (i) “No penetration” rule dictated by Hertz-Signorini-Moreau (HSM) conditions at contacts is satisfied by varying the contact stiffness during a finite element (FE) solution without control of a user which causes increased contact stiffness “erroneously” to avoid penetration of contacting node pairs in an FE solution; and (ii) the reliability of solutions varies according to the chosen computational contact method. This paper is devoted to the topology optimization of machine tools with contact constraints. A hybrid approach is followed that combines the computational contact problem framework and an obtained stable contact stiffness function (analytically or experimentally). According to the proposed method, the existing optimization problem in FE literature is restated in a reliable form for machine tool applications. To avoid the existing computational challenges and reliability problems, contact forces are directly mapped onto an FE model used in the restated topology optimization problem with the help of proposed method. In this study, the existing and the proposed methods for contact are investigated by means of the solid isotropic material with penalization model (SIMP) algorithm for topology optimization. The effectiveness of the proposed method is demonstrated by comparing the experimental measurements on a prototype machine tool manufactured according to the optimization solutions of the proposed method and those of a conventional machine tool.

Design 3D Thermo-Mechanical Structures with Multidisciplinary Topology Optimization

2012 ◽  
Vol 466-467 ◽  
pp. 1212-1216
Author(s):  
San Bao Hu ◽  
Li Ping Chen ◽  
Yu Zhang ◽  
Ming Jiang
Keyword(s):  
Heat Transfer ◽  
Topology Optimization ◽  
Design Variable ◽  
Optimization Problem ◽  
Three Dimensional ◽  
Topology Design ◽  
Design Domain ◽  
3D Design ◽  
Topology Optimization Problem ◽  
The Common

This paper presents an approach for solving the multidisciplinary topology optimization (MTO). To simplifying the description, a three-dimensional (3D) “heat transfer-thermal stress” coupling topology design problem is used as an instance to interpret the solving scheme. Unlike the common multiphysics topology optimization problem which usually modeled in a 3D domain or a 2D domain alternatively, the topology optimization problem mentioned in this paper has a 3D design domain (the design variable is referred as ρ1) and two 2D design domains (the design variable is referred as ρ2and ρ3) together in one mathematical model. Although all the model and solving method are based on a certain design instance, the solving scheme presented in this paper can be used as an efficient method for solving the boundary coupling MTO.

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