arXiv subjects

Zongliang Du

Publications and source records attributed to Zongliang Du.

14 recordsLinked to original sources

arXiv2026

PIML-OFEM: A New Large-Scale Structural Analysis Method Based on Problem-Independent Machine Learning and Overlapping Finite Element Technique

High-resolution analysis and design of large-scale heterogeneous structures require accurate reduced-order models and efficient online computation. Existing multiscale methods must repeatedly construct local basis functions for different material distributions, whereas substructure-based problem-independent machine learning (PIML) methods can be limited by prescribed boundary displacement interpolation. We propose PIML-OFEM, an overlapping finite element method accelerated by problem-independent machine learning. Each substructure retains only its corner-node degrees of freedom. Oversampled numerical basis functions are constructed by solving local elasticity problems on extended domains and restricting the solutions to the target substructure, eliminating prescribed displacement interpolation on its boundary. Independently constructed local bases are blended through a partition-of-unity overlapping formulation to obtain a globally continuous displacement field. A U-Net learns the mapping from local Young's modulus distributions to numerical basis functions, replacing repeated online local solves and allowing the model to be reused across load cases and global boundary conditions. Numerical examples show close agreement with fine-scale finite element results in displacement and elemental strain energy. PIML-OFEM reduces online computational cost relative to direct finite element analysis and improves accuracy over PIML substructure models based on linear boundary interpolation. In topology optimization, the method supports stable high-resolution iterations with small filter radii and preserves fine-scale features, including local patterns resembling rank-2 microstructures. The framework provides an efficient physics-data approach for large-scale heterogeneous structural analysis and high-resolution topology optimization.

math.NA↗

arXiv2024

Optimal design of fast topological pumping

Utilizing synthetic dimensions generated by spatial or temporal modulation, topological pumping enables the exploration of higher-dimensional topological phenomena through lower-dimensional physical systems. In this letter, we propose a rational design paradigm of fast topological pumping based on 1D and 2D time-modulated discrete elastic lattices for the first time. Firstly, the realization of topological pumping is ensured by introducing quantitative indicators to drive a transition of the edge or corner state in the lattice spectrum. Meanwhile, with the help of limiting speed for adiabaticity to calculate the modulation time, a mathematical formulation of designing topological pumping with the fastest modulation speed is presented. By applying the proposed design paradigm, topological edge-bulk-edge and corner-bulk-corner energy transport are successfully achieved, with 11.2 and 4.0 times of improvement in modulation speed compared to classical pumping systems in the literature. In addition, applying to 1D and 2D space-modulated systems, the optimized modulation schemes can reduce the number of stacks to 5.3% and 26.8% of the classical systems while ensuring highly concentrated energy transport. This design paradigm is expected to be extended to the rational design of fast topological pumping in other physical fields.

cond-mat.other↗

arXiv2024

Real-time generative design of diverse, "truly" optimized structures with controllable structural complexities

Compared with traditional design methods, generative design significantly attracts engineers in various disciplines. In thiswork, howto achieve the real-time generative design of optimized structures with various diversities and controllable structural complexities is investigated. To this end, a modified Moving Morphable Component (MMC) method together with novel strategies are adopted to generate high-quality dataset. The complexity level of optimized structures is categorized by the topological invariant. By improving the cost function, the WGAN is trained to produce optimized designs with the input of loading position and complexity level in real time. It is found that, diverse designs with a clear load transmission path and crisp boundary, even not requiring further optimization and different from any reference in the dataset, can be generated by the proposed model. This method holds great potential for future applications of machine learning enhanced intelligent design.

cs.CE↗

arXiv2024

Explicit design optimization of air rudders for maximizing stiffness and fundamental frequency

In aerospace engineering, there is a growing demand for lightweight design through topology optimization. This paper presents a novel design optimization method for stiffened air rudders, commonly used for aircraft attitude control, based on the Moving Morphable Components (MMC) method. The stiffeners within the irregular enclosed design domain are modeled as MMCs and discretized by shell elements, accurately capturing their geometry and evolution during optimization process using explicit parameters. In order to maximize the stiffness and fundamental frequency of the rudder structures, numerical analysis algorithms were developed with shape sensitivity analysis conducted. To comply with the manufacturing requirement, a minimum thickness is prescribed for the stiffeners. Penalty strategies were developed for the thickness and density of stiffeners with thickness smaller than the threshold to meet the thickness requirement and suppress spurious modes. The method's effectiveness was demonstrated through optimization examples of two typical air rudders, illustrating the significance of stiffener's distribution on design objectives. The explicit modeling characteristics allow for directly importing the optimization results into CAD systems, significantly enhancing the engineering applicability.

math.OC↗

arXiv2023

A novel explicit design method for complex thin-walled structures based on embedded solid moving morphable components

In this article, a novel explicit approach for designing complex thin-walled structures based on the Moving Morphable Component (MMC) method is proposed, which provides a unified framework to systematically address various design issues, including topology optimization, reinforced-rib layout optimization, and sandwich structure design problems. The complexity of thin-walled structures mainly comes from flexible geometries and the variation of thickness. On the one hand, the geometric complexity of thin-walled structures leads to the difficulty in automatically describing material distribution (e.g., reinforced ribs). On the other hand, thin-walled structures with different thicknesses require various hypotheses (e.g., Kirchhoff-Love shell theory and Reissner-Mindlin shell theory) to ensure the precision of structural responses. Whereas for cases that do not fit the shell hypothesis, the precision loss of response solutions is nonnegligible in the optimization process since the accumulation of errors will cause entirely different designs. Hence, the current article proposes a novel embedded solid component to tackle these challenges. The geometric constraints that make the components fit to the curved thin-walled structure are whereby satisfied. Compared with traditional strategies, the proposed method is free from the limit of shell assumptions of structural analysis and can achieve optimized designs with clear load transmission paths at the cost of few design variables and degrees of freedom for finite element analysis (FEA). Finally, we apply the proposed method to several representative examples to demonstrate its effectiveness, efficiency, versatility, and potential to handle complex industrial structures.

cs.GR↗

arXiv2023

Efficient Design of Helical Higher-Order Topological Insulators in 3D Elastic Medium

Topological materials (TMs) are well-known for their topological protected properties. Phononic system has the advantage of direct observation and engineering of topological phenomena on the macroscopic scale. For the inverse design of 3D TMs in continuum medium, however, it would be extremely difficult to classify the topological properties, tackle the computational complexity, and search solutions in an infinite parameter space. This work proposed a systematic design framework for the 3D mechanical higher-order topological insulators (HOTIs) by combining the symmetry indicators (SI) method and the moving morphable components (MMC) method. The 3D unit cells are described by the MMC method with only tens of design variables. By evaluating the inherent singularity properties in the 3D mechanical system, the classic formulas of topological invariants are modified accordingly for elastic waves. Then a mathematical formulation is proposed for designing the helical multipole topological insulators (MTIs) featured corner states and helical energy fluxes, by constraining the corresponding topological invariants and maximizing the width of band gap. Mechanical helical HOTIs with different symmetries are obtained by this method and verified by full wave simulations. This design paradigm can be further extended to design 3D TMs among different symmetry classes and space groups, and different physical systems.

physics.app-ph↗

arXiv2022

Data-driven Topology Optimization (DDTO) for Three-dimensional Continuum Structures

Developing appropriate analytic-function-based constitutive models for new materials with nonlinear mechanical behavior is demanding. For such kinds of materials, it is more challenging to realize the integrated design from the collection of the material experiment under the classical topology optimization framework based on constitutive models. The present work proposes a mechanistic-based data-driven topology optimization (DDTO) framework for three-dimensional continuum structures under finite deformation. In the DDTO framework, with the help of neural networks and explicit topology optimization method, the optimal design of the three-dimensional continuum structures under finite deformation is implemented only using the uniaxial and equi-biaxial experimental data. Numerical examples illustrate the effectiveness of the data-driven topology optimization approach, which paves the way for the optimal design of continuum structures composed of novel materials without available constitutive relations.

math.OC↗

arXiv2022

A sequential linear programming (SLP) approach for uncertainty analysis-based data-driven computational mechanics

In this article, an efficient sequential linear programming algorithm (SLP) for uncertainty analysis-based data-driven computational mechanics (UA-DDCM) is presented. By assuming that the uncertain constitutive relationship embedded behind the prescribed data set can be characterized through a convex combination of the local data points, the upper and lower bounds of structural responses pertaining to the given data set, which are more valuable for making decisions in engineering design, can be found by solving a sequential of linear programming problems very efficiently. Numerical examples demonstrate the effectiveness of the proposed approach on sparse data set and its robustness with respect to the existence of noise and outliers in the data set.

math.OC↗

arXiv2022

An efficient and easy-to-extend Matlab code of the Moving Morphable Component (MMC) method for three-dimensional topology optimization

Explicit topology optimization methods have received ever-increasing interest in recent years. In particular, a 188-line Matlab code of the two-dimensional (2D) Moving Morphable Component (MMC)-based topology optimization method was released by Zhang et al. (Struct Multidiscip Optim 53(6):1243-1260, 2016). The present work aims to propose an efficient and easy-to-extend 256-line Matlab code of the MMC method for three-dimensional (3D) topology optimization implementing some new numerical techniques. To be specific, by virtue of the function aggregation technique, accurate sensitivity analysis, which is also easy-to-extend to other problems, is achieved. Besides, based on an efficient identification algorithm for load transmission path, the degrees of freedoms (DOFs) not belonging to the load transmission path are removed in finite element analysis (FEA), which significantly accelerates the optimization process. As a result, compared to the corresponding 188-line 2D code, the performance of the optimization results, the computational efficiency of FEA, and the convergence rate and the robustness of optimization process are greatly improved. For the sake of completeness, a refined 218-line Matlab code implementing the 2D-MMC method is also provided.

math.OC↗

arXiv2022

Topology optimization on complex surfaces based on the moving morphable component (MMC) method and computational conformal mapping (CCM)

In the present paper, an integrated paradigm for topology optimization on complex surfaces with arbitrary genus is proposed. The approach is constructed based on the two-dimensional (2D) Moving Morphable Component (MMC) framework, where a set of structural components are used as the basic units of optimization, and computational conformal mapping (CCM) technique, with which a complex surface represented by an unstructured triangular mesh can be mapped into a set of regular 2D parameter domains numerically. A multi-patch stitching scheme is also developed to achieve an MMC-friendly global parameterization through a number of local parameterizations. Numerical examples including a saddle-shaped shell, a torus-shape shell and a tee-branch pipe are solved to demonstrate the validity and efficiency of the proposed approach. It is found that compared with traditional approaches for topology optimization on 2D surfaces, optimized designs with clear load transmission paths can be obtained with much fewer numbers of design variables and degrees of freedom for finite element analysis (FEA) via the proposed approach.

math.OC↗

arXiv2021

A mechanistic-based data-driven approach to accelerate structural topology optimization through finite element convolutional neural network (FE-CNN)

In this paper, a mechanistic data-driven approach is proposed to accelerate structural topology optimization, employing an in-house developed finite element convolutional neural network (FE-CNN). Our approach can be divided into two stages: offline training, and online optimization. During offline training, a mapping function is built between high and low resolution representations of a given design domain. The mapping is expressed by a FE-CNN, which targets a common objective function value (e.g., structural compliance) across design domains of differing resolutions. During online optimization, an arbitrary design domain of high resolution is reduced to low resolution through the trained mapping function. The original high-resolution domain is thus designed by computations performed on only the low-resolution version, followed by an inverse mapping back to the high-resolution domain. Numerical examples demonstrate that this approach can accelerate optimization by up to an order of magnitude in computational time. Our proposed approach therefore shows great potential to overcome the curse-of-dimensionality incurred by density-based structural topology optimization. The limitation of our present approach is also discussed.

cs.LG↗

arXiv2019

Optimal design of shell-graded-infill structures by a hybrid MMC-MMV approach

In the present work, a hybrid MMC-MMV approach is developed for designing additive manufacturing-oriented shell-graded-infill structures. The key idea is to describe the geometry of a shell-graded-infill structure explicitly using some geometry parameters. To this end, a set of morphable voids is adopted to describe the boundary of the coating shell, while a set of morphable components combing with a coordinate perturbation technique are introduced to represent the graded infill distribution. Under such treatment, both the crisp boundary of the coating shell and the graded infill can be optimized simultaneously, with a small number of design variables. Numerical examples demonstrate the effectiveness of the proposed approach.

cs.CE↗

arXiv2018

An efficient Moving Morphable Component (MMC)-based approach for multi-resolution topology optimization

In the present work, a highly efficient Moving Morphable Component (MMC) based approach for multi-resolution topology optimization is proposed. In this approach, high-resolution optimization results can be obtained with much less number of degrees of freedoms (DOFs) and design variables since the finite element analysis model and the design optimization model are totally decoupled in the MMC-based problem formulation. This is achieved by introducing super-elements for structural response analysis and adopting a domain decomposition strategy to preserve the topology complexity of optimized structures. Both two-and three-dimensional numerical results demonstrate that substantial computational efforts can be saved with use of the proposed approach.

cs.CE↗

arXiv2017

Self-supporting structure design in additive manufacturing through explicit topology optimization

One of the challenging issues in additive manufacturing (AM) oriented topology optimization is how to design structures that are self-supportive in a manufacture process without introducing additional supporting materials. In the present contribution, it is intended to resolve this problem under an explicit topology optimization framework where optimal structural topology can be found by optimizing a set of explicit geometry parameters. Two solution approaches established based on the Moving Morphable Components (MMC) and Moving Morphable Voids (MMV) frameworks, respectively, are proposed and some theoretical issues associated with AM oriented topology optimization are also analyzed. Numerical examples provided demonstrate the effectiveness of the proposed methods.

physics.app-ph↗