Special Issue "Novel Methods of Topology Optimization and Engineering Applications"

Submission Deadline: 31 May 2021 (closed)
Guest Editors
Prof. Kai Long, North China Electric Power University, China
Prof. Xiaodong Huang, Swinburne University of Technology, Australia
Dr. Quhao Li, Shandong University, China
Dr. Xuan Wang, Hefei University of Technology, China
Prof. Zunyi Duan, Northwestern Polytechnical University, China


As a promising design tool, topology optimization has experienced tremendous progress. Aiming to allocate the available material to maximize system performance while satisfying multiple constraints, a number of branches have come into emergence, e.g. homogenization method, Solid Isotropic Material with Penalization (SIMP), Evolutionary Structural Optimization (ESO) and Bi-directional Evolutionary Structural Optimization (BESO), level set method (LSM), phase field method, moving morphable components or voids (MMC, MMV) method. In recent years, several novel methods on topology optimization have emerged, such as parametric level set method, moving morphable components method, new bubble method and the combination with traditional technique.


We initiate this special issue to highlight the new developments of topology optimization methods and their applications, with particular focus on theory developments, numerical implementations and potential applications.


Potential topics include but are not limited to:

(1) New topology optimization method, theory, numerical technique and its engineering application

(2) Metamaterial material design, bionics design, multi-scale design by topology optimization method

(3) Topology optimization method related to nonlinearity, buckling, stress, fatigue and multiple physical problems

(4) Topology optimization combined with large-scale computation or reliability

Topology optimization, multi-scale design, bionics design, nonlinear topology optimization

Published Papers

  • Topology Optimization with Aperiodic Load Fatigue Constraints Based on Bidirectional Evolutionary Structural Optimization
  • Abstract Because of descriptive nonlinearity and computational inefficiency, topology optimization with fatigue life under aperiodic loads has developed slowly. A fatigue constraint topology optimization method based on bidirectional evolutionary structural optimization (BESO) under an aperiodic load is proposed in this paper. In view of the severe nonlinearity of fatigue damage with respect to design variables, effective stress cycles are extracted through transient dynamic analysis. Based on the Miner cumulative damage theory and life requirements, a fatigue constraint is first quantified and then transformed into a stress problem. Then, a normalized termination criterion is proposed by approximate maximum stress measured by global… More
  •   Views:563       Downloads:442        Download PDF

  • An XBi-CFAO Method for the Optimization of Multi-Layered Variable Stiffness Composites Using Isogeometric Analysis
  • Abstract This paper presents an effective fiber angle optimization method for two and multi-layered variable stiffness composites. A gradient-based fiber angle optimization method is developed based on isogeometric analysis (IGA). Firstly, the element densities and fiber angles for two and multi-layered composites are synchronously optimized using an extended Bi-layered continuous fiber angle optimization method (XBi-CFAO). The densities and fiber angles in the base layer are attached to the control points. The structure response and sensitivity analysis are accomplished using the non-uniform rational B-spline (NURBS) based IGA. By the benefit of the B-spline space, this method is free from checkerboards, and no… More
  •   Views:691       Downloads:783        Download PDF

  • Fail-Safe Topology Optimization of Continuum Structures with Multiple Constraints Based on ICM Method
  • Abstract Traditional topology optimization methods may lead to a great reduction in the redundancy of the optimized structure due to unexpected material removal at the critical components. The local failure in critical components can instantly cause the overall failure in the structure. More and more scholars have taken the fail-safe design into consideration when conducting topology optimization. A lot of good designs have been obtained in their research, though limited regarding minimizing structural compliance (maximizing stiffness) with given amount of material. In terms of practical engineering applications considering fail-safe design, it is more meaningful to seek for the lightweight structure with… More
  •   Views:665       Downloads:524        Download PDF

  • An Improved Data-Driven Topology Optimization Method Using Feature Pyramid Networks with Physical Constraints
  • Abstract Deep learning for topology optimization has been extensively studied to reduce the cost of calculation in recent years. However, the loss function of the above method is mainly based on pixel-wise errors from the image perspective, which cannot embed the physical knowledge of topology optimization. Therefore, this paper presents an improved deep learning model to alleviate the above difficulty effectively. The feature pyramid network (FPN), a kind of deep learning model, is trained to learn the inherent physical law of topology optimization itself, of which the loss function is composed of pixel-wise errors and physical constraints. Since the calculation of… More
  •   Views:1060       Downloads:897        Download PDF

  • Thermoelastic Structural Topology Optimization Based on Moving Morphable Components Framework
  • Abstract This study investigates structural topology optimization of thermoelastic structures considering two kinds of objectives of minimum structural compliance and elastic strain energy with a specified available volume constraint. To explicitly express the configuration evolution in the structural topology optimization under combination of mechanical and thermal load conditions, the moving morphable components (MMC) framework is adopted. Based on the characteristics of the MMC framework, the number of design variables can be reduced substantially. Corresponding optimization formulation in the MMC topology optimization framework and numerical solution procedures are developed for several numerical examples. Different optimization results are obtained with structural compliance and… More
  •   Views:812       Downloads:557        Download PDF

  • Functionally Graded Cellular Structure Design Using the Subdomain Level Set Method with Local Volume Constraints
  • Abstract Functional graded cellular structure (FGCS) usually shows superior mechanical behavior with low density and high stiffness. With the development of additive manufacturing, functional graded cellular structure gains its popularity in industries. In this paper, a novel approach for designing functionally graded cellular structure is proposed based on a subdomain parameterized level set method (PLSM) under local volume constraints (LVC). In this method, a subdomain level set function is defined, parameterized and updated on each subdomain independently making the proposed approach much faster and more cost-effective. Additionally, the microstructures on arbitrary two adjacent subdomains can be connected perfectly without any additional… More
  •   Views:825       Downloads:602       Cited by:1        Download PDF

  • Multi-Material Topology Optimization of Structures Using an Ordered Ersatz Material Model
  • Abstract This paper proposes a new element-based multi-material topology optimization algorithm using a single variable for minimizing compliance subject to a mass constraint. A single variable based on the normalized elemental density is used to overcome the occurrence of meaningless design variables and save computational cost. Different from the traditional material penalization scheme, the algorithm is established on the ordered ersatz material model, which linearly interpolates Young's modulus for relaxed design variables. To achieve a multi-material design, the multiple floating projection constraints are adopted to gradually push elemental design variables to multiple discrete values. For the convergent element-based solution, the multiple… More
  •   Views:1039       Downloads:774        Download PDF

  • Fatigue Topology Optimization Design Based on Distortion Energy Theory and Independent Continuous Mapping Method
  • Abstract Fatigue failure is a common failure mode under the action of cyclic loads in engineering applications, which often occurs with no obvious signal. The maximum structural stress is far below the allowable stress when the structures are damaged. Aiming at the lightweight structure, fatigue topology optimization design is investigated to avoid the occurrence of fatigue failure in the structural conceptual design beforehand. Firstly, the fatigue life is expressed by topology variables and the fatigue life filter function. The continuum fatigue optimization model is established with the independent continuous mapping (ICM) method. Secondly, fatigue life constraints are transformed to distortion energy… More
  •   Views:1088       Downloads:745        Download PDF

  • A Combined Shape and Topology Optimization Based on Isogeometric Boundary Element Method for 3D Acoustics
  • Abstract A combined shape and topology optimization algorithm based on isogeometric boundary element method for 3D acoustics is developed in this study. The key treatment involves using adjoint variable method in shape sensitivity analysis with respect to non-uniform rational basis splines control points, and in topology sensitivity analysis with respect to the artificial densities of sound absorption material. OpenMP tool in Fortran code is adopted to improve the efficiency of analysis. To consider the features and efficiencies of the two types of optimization methods, this study adopts a combined iteration scheme for the optimization process to investigate the simultaneous change of… More
  •   Views:1207       Downloads:1108        Download PDF

  • Robust Topology Optimization of Periodic Multi-Material Functionally Graded Structures under Loading Uncertainties
  • Abstract This paper presents a robust topology optimization design approach for multi-material functional graded structures under periodic constraint with load uncertainties. To characterize the random-field uncertainties with a reduced set of random variables, the Karhunen-Loève (K-L) expansion is adopted. The sparse grid numerical integration method is employed to transform the robust topology optimization into a weighted summation of series of deterministic topology optimization. Under dividing the design domain, the volume fraction of each preset gradient layer is extracted. Based on the ordered solid isotropic microstructure with penalization (Ordered-SIMP), a functionally graded multi-material interpolation model is formulated by individually optimizing each preset… More
  •   Views:1087       Downloads:939       Cited by:1        Download PDF