A NEW ELEMENT-BASED METHOD FOR SOLVING STRUCTURAL TOPOLOGY OPTIMIZATION PROBLEMS WITH NON-UNIFORM MESHES

Extends the evolutionary structural optimization method to the solution for the natural frequency optimization of a two‐dimensional structure with additional non‐structural lumped masses. Owing to the significant difference between a static optimization problem and a structural natural frequency optimization problem, five basic criteria for the evolutionary natural frequency optimization have been established. The inclusion of these criteria into the evolutionary structural optimization method makes it possible to solve structural natural frequency optimization problems for two‐dimensional structures with additional non‐structural lumped masses. Gives two examples to demonstrate the feasibility of the extended evolutionary structural optimization method when it is used to solve structural natural frequency optimization problems.

Structural topology optimization is a crucial approach for achieving lightweight design. An effective topology optimization algorithm must strike a balance between the objective functions, constraints, and design variables, which essentially reflects the symmetry and tradeoff between the objective and constraints. In this study, a topology optimization method grounded in load path theory is proposed. Element bearing capacity is quantified using the element birth and death method, with an explicit formulation derived via finite element theory. The effectiveness in evaluating structural performance is assessed through comparisons with stress distributions and topology optimization density maps. In addition, a novel evaluation index for element bearing capacity is proposed as the objective function in the topology optimization model, which is validated through thin plate optimization. Subsequently, sensitivity redistribution mitigates checkerboard patterns, while mesh filtering suppresses multi-branch structures and prevents local optima. The method is applied for the lightweight design of a triangular arm, with results benchmarked against the variable density method, demonstrating the feasibility and effectiveness of the proposed method. The element bearing capacity seeks to homogenize the load distribution of each element; the technique in this study can be extended to the optimization of symmetric structures.

A new fuzzy strategy for size and topology optimization of truss structures

Bi-directional evolutionary topology optimization of continuum structures subjected to inertial loads

Stress-based topology optimization and nonlinear structural topology optimization is gaining increasing attention in order to make topology optimization more realistic. Thus, this paper extends current concepts of topology optimization to the design of structures made of nonlinear materials. An extended bi-directional evolutionary structural optimization (BESO) method for stress minimization topology optimization of material nonlinear structures is proposed in this work. BESO method based on discrete variables can effectively avoid the well-known singularity problem in density-based methods with low-density elements. The maximum von Mises stress is approximated by the p-norm global stress. The sensitivity information for designing variable updates is derived in detail by adjoint method. As for the highly nonlinear stress behavior, the updated scheme takes advantages from two filters respectively of the sensitivity and topological variables to improve convergence. Moreover, the filtered sensitivity numbers are combined with their historical sensitivity information to further stabilize the optimization process. The effectiveness of the proposed method is demonstrated by several 2D benchmark design problems.

Запропоновано метод оптимізації неперервних функції багатьох змінних, який втілює підходи методів рою часток та моделювання штучної імунної системи. Проведено дослідження з метою визначення оптимальних налаштувань алгоритму, що реалізує запропонований метод. Показано, що запропонований метод може бути застосований як складова інформаційної технології супроводу підтримки управлінських рішень та розв’язання задач оптимізації технологічних процесів у металургійному виробництві. Метою роботи є розробка оригінального гібридного методу глобальної оптимізації на основі методу штучної імунної системи та методу рою частинок, а також формулювання рекомендацій щодо налаштування його параметрів. Запропонований метод має прискорити прийняття рішень при керуванні технологічними процесами у металургійному виробництві та підвищити їх точність. Методологія забезпечення рішення полягає у поєднанні основних пошукових операторів еволюційних методів оптимізації на основі рою часток і моделювання штучної імунної системи людини. Використовуються традиційні для ройового пошуку кроки з пошуку рішення та обміну інформацією про знайдені локальні оптимуми. Такий пошук доповнюється принципом змагальності, запозиченим у методі штучної імунної системи, для чого популяція поділяється на менші рої або пошукові команди. Також запропоновані кроки контролю різноманіття в рої та радіусу розсіювання часток. Останнє дозволяє вирішувати задачі як безумовної, так і умовної оптимізації у неперервному просторі високої розмірності. Наукова новизна отриманих у роботі результатів полягає в формулюванні нового еволюційного методу оптимізації в неперервному просторі на основі ройового інтелекту, який на відміну від відомих раніше ройових методів використовує принцип змагання підгруп рою та оператор стиснення популяції, властивих методу моделювання штучних імунних систем. Емпірично встановленні параметри методу, що визначають його ефективність. Висновки. Застосування запропонованого еволюційного методу пошукової оптимізації до мінімізації тестових функцій у неперервному просторі розмірністю до 20 показало його ефективність у порівнянні з відомими раніше. В подальшому актуальним бачиться застосування викладеного алгоритму для розв’язання задач оптимізації технологічних процесів у металургійному виробництві. Зокрема, даний алгоритм вбачається ефективним для задач шихтування, оптимізації використання феросплавів у ливарному виробництві, а також при прогнозуванні механічних властивостей готової продукції.

To date the design of structures via topology optimisation methods has mainly focused on single-objective problems. However, real-world design problems usually involve several different objectives, most of which counteract each other. Therefore, designers typically seek a set of Pareto optimal solutions, a solution for which no other solution is better in all objectives, which capture the trade-off between these objectives. This set is known as a smart Pareto set. Currently, only the weighted sums method has been used for generating Pareto fronts with topology optimisation methods. However, the weighted sums method is unable to produce evenly distributed smart Pareto sets. Furthermore, evenly distributed weights have been shown to not produce evenly spaced solutions. Therefore, the weighted sums method is not suitable for generating smart Pareto sets. Recently, the smart normal constraints method has been shown to be capable of directly generating smart Pareto sets. This work presents an updated smart normal constraint method, which is combined with a bi-directional evolutionary structural optimisation algorithm for multi-objective topology optimisation. The smart normal constraints method has been modified by further restricting the feasible design space for each optimisation run such that dominant and redundant points are not found. The algorithm is tested on several different structural optimisation problems. A number of different structural objectives are analysed, namely compliance, dynamic and buckling objectives. Therefore, the method is shown to be capable of solving various types of multi-objective structural optimisation problems. The goal of this work is to show that smart Pareto sets can be produced for complex topology optimisation problems. Furthermore, this research hopes to highlight the gap in the literature of topology optimisation for multi-objective problems.

The Evolutionary Structural Optimization (ESO) has been applied to find the optimal structural topology for design and construction purposes. However, its efficiency is low due to the imperfect deletion criteria. This paper presents an improved elimination criterion and the Windowed Evolutionary Structural Optimization (WESO) method. The former considers the structural average strain energy as the elimination criteria in the optimization, with the elimination rate set as a self-adaption state by an adjustable window. Thus, the problems of low optimization efficiency and distorted optimization results in the traditional ESO can be solved to a certain extent. The WESO method can then be extended and applied with a complex finite element model. It is found that the method has better optimal ability in handling discrete elements in vast structures. Compared with the other method, the WESO method has high computational efficiency and offers more stable and reliable topology than the Michell theoretical solution. Lastly, upon developing the optimal topology for a double-deck structure, it is shown that the WESO method has a great potential in civil engineering applications.

Isogeometric analysis (IGA) connects CAE with standard CAD design tools and has been utilized for a decade in structural optimization. FEA has a number of drawbacks, including a lack of linkage between analytic and geometric models, a shortage of continuity between components, and a lack of accuracy for high-order elements. Isogeometric analysis effectively overcomes these obstacles. This paper proposes the isogeometric topological optimization mathematical model depending on the asymmetric constitutive relationship of tension and compression microscopic materials. We provide a new density-based topology optimization formulation in which the design domain is limited to the B-spline space. A rectangular domain with a tensor-product is embedded in a design domain that is arbitrarily shaped. The density field is represented using B-splines. The intrinsic filter provided by the B-spline representation for topology optimization is governed by the degrees of B-spline and the knot spans. This B-spline effectively removes numerical artifacts and controls the minimum feature-length in; when the B-spline basis functions span many analysis elements. Benchmark problems in structural topology optimization are computed through Evolutionary Structural Optimization (ESO) algorithm. Comparisons of the optimal structure topologies using finite element analysis and isogeometric collocation methods are analyzed. The influence of different tension-compression stiffness ratios on the final structure topologies is listed and analyzed. The numerical results show the reliability and performance of the proposed mathematical formulation and asymmetry of natural structure.

The topology optimization design for continuum structures based on the element free Galerkin method

This article proposes a bacterial-chemotaxis-based bio-inspired algorithm (BCBTOA) to solve structural topology optimization problems in two and three-dimensional continuous, which describe the chemotactic strategy as a simulated process for removing material from a structure. A chemotaxis-based regularization numerical scheme was employed for common checkerboards and mesh dependence issues. The algorithm minimizes compliance and maximizes stiffness, so it is applied to various configurations of beams to show its efficiency, performance, and versatility. Then, the algorithm is evaluated to determine its effectiveness and computational performance. Results are compared with the Sequential Element Rejection and Admission (SERA) method and the Soft Bidirectional Evolutionary Structural Optimization (Soft BESO) method using several performance metrics. The results showed that BCBTOA possessed a better computational performance on some benchmark problems and showed layouts with entirely clear gray areas.

This work presents a novel approach for the solution of multi-material topology optimization problems of elastic structures coupling the Direct Meshless Local Petrov–Galerkin (DMLPG) method with the Gradual Bi-direction Evolutionary Structural Optimization (gBESO) method. In recent years, meshless methods have been used in several engineering fields, showing some advantages compared to mesh-based methods. DMLPG is a truly meshless method, which achieves results with good accuracy and computational efficiency, avoiding the numerical integration of complicated shape functions by adopting low-degree polynomials. In the proposed algorithm, DMLPG is used to obtain smooth nodal displacements, strains and stresses, and gBESO updates the structural geometry based on design sensitivity values of the compliance while it gradually increases the Young's modulus of the material. The optimization problem minimizes the compliance objective function subject to volume constraints. Numerical examples demonstrate the applicability and validity of the technique.

A simple and compact Python code for complex 3D topology optimization

This paper presents an efficient and comprehensive MATLAB code to solve two-dimensional structural topology optimization problems, including minimum mean compliance, compliant mechanism synthesis and multi-load compliance problems. The Unsmooth Variational Topology Optimization (UNVARTOP) method, developed by the authors in a previous work, is used in the topology optimization code, based on the finite element method (FEM), to compute the sensitivity and update the topology. The paper also includes instructions to improve the bisection algorithm, modify the computation of the Lagrangian multiplier by using an Augmented Lagrangian to impose the constraint, implement heat conduction problems and extend the code to three-dimensional topology optimization problems. The code, intended for students and newcomers in topology optimization, is included as an appendix (Appendix A) and it can be downloaded from https://github.com/DanielYago together with supplementary material.

This paper proposes a bio-inspired evolutionary computational algorithm for structure topology optimization. It integrates the merits of evolutionary structure optimization and level set method for structure topology optimization. Traditional Level Set Method algorithm depends on the initial topology to some extent. New holes cannot be evolved within the updated topology during the optimization iteration. The algorithm proposed in this paper combines the merits of ESO techniques with that of LSM scheme, allowing new holes to be automatically inserted in regions with low deformation energy at prescribed iterations of the optimization. The nodal neighboring region is adopted in the proposed algorithm. Numerical example shows that good result can be gotten through less optimization iteration. The approach can solve complex structures easily, in which holes cannot be properly layed out in advance. The proposed method considerably improves the ability of LSM to find the optimal topology. The validity and efficiency of the proposed algorithm are supported by some benchmark examples in this paper.