Developing Benchmark Problems for Civil Structural Applications of Continuum Topology Optimization

2012 ◽  
Author(s):  
Colby C. Swan
Keyword(s):  
Topology Optimization ◽  
Benchmark Problems ◽  
Structural Applications

A Comparative Study of the Formulations for Topology Optimization of Compliant Mechanisms

2008 ◽  
Author(s):  
Sangamesh R. Deepak ◽  
M. Dinesh ◽  
Deepak Sahu ◽  
Salil Jalan ◽  
G. K. Ananthasuresh
Keyword(s):  
Topology Optimization ◽  
Comparative Study ◽  
Compliant Mechanisms ◽  
Computation Time ◽  
Initial Guess ◽  
Benchmark Problems ◽  
Topology Optimization Problem ◽  
Linear Elastic ◽  
Frame Element ◽  
Force Direction

The topology optimization problem for the synthesis of compliant mechanisms has been formulated in many different ways in the last 15 years, but there is not yet a definitive formulation that is universally accepted. Furthermore, there are two unresolved issues in this problem. In this paper, we present a comparative study of five distinctly different formulations that are reported in the literature. Three benchmark examples are solved with these formulations using the same input and output specifications and the same numerical optimization algorithm. A total of 35 different synthesis examples are implemented. The examples are limited to desired instantaneous output direction for prescribed input force direction. Hence, this study is limited to linear elastic modeling with small deformations. Two design parameterizations, namely, the frame element based ground structure and the density approach using continuum elements, are used. The obtained designs are evaluated with all other objective functions and are compared with each other. The checkerboard patterns, point flexures, the ability to converge from an unbiased uniform initial guess, and the computation time are analyzed. Some observations are noted based on the extensive implementation done in this study. Complete details of the benchmark problems and the results are included. The computer codes related to this study are made available on the internet for ready access.

scholarly journals Robust Topology Optimization Under Load and Geometry Uncertainties by Using New Sparse Grid Collocation Method

2019 ◽  
Author(s):  
Seyyed Ali Latifi Rostami ◽  
Ali Ghoddosian
Keyword(s):  
Topology Optimization ◽  
Applied Load ◽  
Grid Method ◽  
Optimization Methods ◽  
Optimization Method ◽  
Monte Carlo Sampling ◽  
Sparse Grid ◽  
Benchmark Problems ◽  
Robust Topology Optimization ◽  
Cheap Alternative

In this paper, a robust topology optimization method presents that insensitive to the uncertainty in geometry and applied load. Geometric uncertainty can be introduced in the manufacturing variability. Applied load uncertainty is occurring in magnitude and angle of force. These uncertainties can be modeled as a random field. A memory-less transformation of random fields used to random variation modeling. The Adaptive Sparse Grid Collocation (ASGC) method combined with the uncertainty models provides robust designs by utilizing already developed deterministic solvers. The proposed algorithm provides a computationally cheap alternative to previously introduced stochastic optimization methods based on Monte Carlo sampling by using the adaptive sparse grid method. Numerical examples, such as a 2D simply supported beam and cantilever beam as benchmark problems, are used to show the effectiveness and superiority of the ASGC method.

A Comparative Study of the Formulations and Benchmark Problems for the Topology Optimization of Compliant Mechanisms

2008 ◽  
Vol 1 (1) ◽  
Author(s):  
Sangamesh R. Deepak ◽  
M. Dinesh ◽  
Deepak K. Sahu ◽  
G. K. Ananthasuresh
Keyword(s):  
Topology Optimization ◽  
Comparative Study ◽  
Compliant Mechanisms ◽  
Initial Guess ◽  
Benchmark Problems ◽  
Topology Optimization Problem ◽  
Linear Elastic ◽  
Frame Element ◽  
Force Direction ◽  
Computer Codes

The topology optimization problem for the synthesis of compliant mechanisms has been formulated in many different ways in the past 15years, but there is not yet a definitive formulation that is universally accepted. Furthermore, there are two unresolved issues in this problem. In this paper, we present a comparative study of five distinctly different formulations that are reported in the literature. Three benchmark examples are solved with these formulations using the same input and output specifications and the same numerical optimization algorithm. A total of 35 different synthesis examples are implemented. The examples are limited to desired instantaneous output direction for prescribed input force direction. Hence, this study is limited to linear elastic modeling with small deformations. Two design parametrizations, namely, the frame element-based ground structure and the density approach using continuum elements, are used. The obtained designs are evaluated with all other objective functions and are compared with each other. The checkerboard patterns, point flexures, and the ability to converge from an unbiased uniform initial guess are analyzed. Some observations and recommendations are noted based on the extensive implementation done in this study. Complete details of the benchmark problems and the results are included. The computer codes related to this study are made available on the internet for ready access.

Topology Optimization Under Stress Relaxation Effect Using Internal Element Connectivity Parameterization

2019 ◽  
Vol 14 (2) ◽  
Author(s):  
Meisam Takalloozadeh ◽  
Gil ho Yoon
Keyword(s):  
Topology Optimization ◽  
High Temperature ◽  
Stress Relaxation ◽  
Nonlinear Problems ◽  
Relaxation Effect ◽  
Benchmark Problems ◽  
Adjoint Sensitivity ◽  
Creep Effect ◽  
Numerical Instabilities ◽  
Internal Element

The creep phenomenon has enormous effect on the stress and displacement distribution in the structures. Redistribution of the stress field is one of these effects which is called stress relaxation. The importance of stress relaxation in the design of structures is increasing due to engineering applications especially in high temperature. However, this phenomenon has remained absent from the structural optimization studies. In the present study, the effect of stress relaxation due to high temperature creep is considered in topology optimization (TO). Internal element connectivity parameterization (I-ECP) method is utilized for performing TO. This method is shown to be effective to overcome numerical instabilities in nonlinear problems. Time-dependent adjoint sensitivity formulation is implemented for I-ECP including creep effect. Several benchmark problems are solved, and the optimum layouts obtained by linear and nonlinear methods are compared to show the efficiency of the proposed method and to show the effect of stress relaxation on the optimum layout.

A Multi-Scale Topology Optimization Approach for Optimal Macro-Layout and Local Grading of TPMS-Based Lattices

2021 ◽  
Author(s):  
Niclas Strömberg
Keyword(s):  
Topology Optimization ◽  
Additive Manufacturing ◽  
Local Density ◽  
Bulk Material ◽  
Transversely Isotropic ◽  
Benchmark Problems ◽  
Optimization Approach ◽  
Lattice Structures ◽  
Efficient Design ◽  
Multi Scale

Abstract The use of lattice structures in design for additive manufacturing has quickly emerged as a popular and efficient design alternative for creating innovative multifunctional lightweight solutions. In particular, the family of triply periodic minimal surfaces (TPMS) studied in detail by Schoen for generating frame-or shell-based lattice structures seems extra promising. In this paper a multi-scale topology optimization approach for optimal macro-layout and local grading of TPMS-based lattice structures is presented. The approach is formulated using two different density fields, one for identifying the macro-layout and another one for setting the local grading of the TPMS-based lattice. The macro density variable is governed by the standard SIMP formulation, but the local one defines the orthotropic elasticity of the element following material interpolation laws derived by numerical homogenization. Such laws are derived for frame- and shell-based Gyroid, G-prime and Schwarz-D lattices using transversely isotropic elasticity for the bulk material. A nice feature of the approach is that the lower and upper additive manufacturing limits on the local density of the TMPS-based lattices are included properly. The performance of the approach is excellent, and this is demonstrated by solving several three-dimensional benchmark problems, e.g., the optimal macro-layout and local grading of Schwarz-D lattice for the established GE-bracket is identified using the presented approach.

Topology optimization of structures with coupled finite element – Element-free Galerkin method

2017 ◽  
Vol 232 (5) ◽  
pp. 731-745 ◽  
Author(s):  
Yaqing Zhang ◽  
Wenjie Ge ◽  
Xinxing Tong ◽  
Min Ye
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Topology Optimization ◽  
Level Density ◽  
Coupling Method ◽  
Benchmark Problems ◽  
Convergence Criterion ◽  
Displacement Boundary ◽  
Energy Convergence ◽  
Element Method

A topology optimization, based on a coupling method of finite element and meshless method, is proposed for continuum structure. A reasonable arrangement of the meshless domain can guarantee the accuracy of the meshless methods and meanwhile keep the computational efficiency of the finite element method. Besides, as the coupling method is adopted, the displacement boundary conditions are applied to finite elements nodes by standard finite element method. A dual-level density approximant is carried out to approximate and interpolate a unified and continuous density field. An unstable nodes phenomenon is observed in the interface domain, leading to nonconvergence of the equilibrium iterations. A smooth blending function and an energy convergence criterion are used to circumvent the convergent difficulty. Three benchmark problems of topology optimization are given to demonstrate the effectiveness of the proposed approach. Neither “islanding” phenomenon nor other common numerical instabilities of the SIMP method occur in this approach.

scholarly journals Size, shape, and topology optimization of planar and space trusses using mutation-based improved metaheuristics

2017 ◽  
Vol 5 (2) ◽  
pp. 198-214 ◽  
Author(s):  
Ghanshyam G. Tejani ◽  
Vimal J. Savsani ◽  
Vivek K. Patel ◽  
Poonam V. Savsani
Keyword(s):  
Topology Optimization ◽  
Optimization Problems ◽  
Search Space ◽  
Truss Structures ◽  
Benchmark Problems ◽  
Truss Topology Optimization ◽  
Random Mutation ◽  
Shape And Topology Optimization ◽  
And Topology ◽  
Space Trusses

Abstract In this study, simultaneous size, shape, and topology optimization of planar and space trusses are investigated. Moreover, the trusses are subjected to constraints for element stresses, nodal displacements, and kinematic stability conditions. Truss Topology Optimization (TTO) removes the superfluous elements and nodes from the ground structure. In this method, the difficulties arise due to unacceptable and singular topologies; therefore, the Grubler's criterion and the positive definiteness are used to handle such issue. Moreover, the TTO is challenging due to its search space, which is implicit, non-convex, non-linear, and often leading to divergence. Therefore, mutation-based metaheuristics are proposed to investigate them. This study compares the performance of four improved metaheuristics (viz. Improved Teaching–Learning-Based Optimization (ITLBO), Improved Heat Transfer Search (IHTS), Improved Water Wave Optimization (IWWO), and Improved Passing Vehicle Search (IPVS)) and four basic metaheuristics (viz. TLBO, HTS, WWO, and PVS) in order to solve structural optimization problems. Highlights Improvements in four recently designed metaheuristics. Use of random mutation-based search technique. Applications on challenging/benchmark problems of simultaneous size, shape, and topology optimization of truss structures. Improvements effective over basic metaheuristics.

scholarly journals A Firefly Algorithm Based Hybrid Method for Structural Topology Optimization

2020 ◽  
Author(s):  
Hailu Shimels Gebremedhen ◽  
Dereje Engida Woldemichael ◽  
Fakhruldin Mohd Hashim
Keyword(s):  
Topology Optimization ◽  
Hybrid Algorithm ◽  
Firefly Algorithm ◽  
Optimization Problems ◽  
Optimality Criteria ◽  
Benchmark Problems ◽  
Material Distribution ◽  
Structural Topology ◽  
Weight Percentage ◽  
Design Variables

Abstract In this paper a firefly algorithm based hybrid algorithm through retaining global convergence of firefly algorithm and ability of generating connected topologies of optimality criteria (OC) method is proposed as an alternative method to solve stress-based topology optimization problems. Lower and upper limit of design variables (0 and 1) were used to find initial material distribution to initialize firefly algorithm based section of the hybrid algorithm. Input parameters, number of fireflies and number function evaluations were determined before implementation of firefly algorithm to solve formulated problems. Since direct application of firefly algorithm cannot generate connected topologies, outputs from firefly algorithm were used as an initial input material distribution for OC method. The proposed method was validated using two-dimensional benchmark problems and the results were compared with results using OC method. Weight percentage reduction, maximum stress induced, optimal material distribution and compliance were used to compare results. Results from the proposed method showed that the proposed method can generate connected topologies and generated topologies are free from interference of end users, which only dependence on boundary conditions or the design variables. From the results, the objective function (weight of the design domain) can be further reduced in the range of 5% to 15% compared to OC method.

scholarly journals A Firefly Algorithm Based Hybrid Method for Structural Topology Optimization

2020 ◽  
Author(s):  
Hailu Shimels Gebremedhen ◽  
Dereje Engida Woldemichael ◽  
Fakhruldin Mohd Hashim
Keyword(s):  
Topology Optimization ◽  
Hybrid Algorithm ◽  
Firefly Algorithm ◽  
Optimization Problems ◽  
Optimality Criteria ◽  
Benchmark Problems ◽  
Material Distribution ◽  
Structural Topology ◽  
Weight Percentage ◽  
Design Variables

Abstract In this paper, a firefly algorithm based hybrid algorithm through retaining global convergence of firefly algorithm and ability to generate connected topologies of optimality criteria (OC) method is proposed as an alternative method to solve stress-based topology optimization problems. The lower and upper limit of design variables (0 and 1) were used to find initial material distribution to initialize the firefly algorithm based section of the hybrid algorithm. Input parameters, the number of fireflies, and number function evaluations were determined before the implementation of the firefly algorithm to solve formulated problems. Since the direct application of the firefly algorithm cannot generate connected topologies, outputs from the firefly algorithm were used as an initial input material distribution for the OC method. The proposed method was validated using two-dimensional benchmark problems and the results were compared with results using the OC method. Weight percentage reduction, maximum stress-induced, optimal material distribution, and compliance were used to compare results. Results from the proposed method showed that the proposed method can generate connected topologies and generated topologies are free from the interference of end-users, which only dependence on boundary conditions or the design variables. From the results, the objective function (weight of the design domain) can be further reduced in the range of 5% to 15% compared to the OC method.

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