Parametric Level Set Method Research Articles

A body-fitted adaptive mesh and Helmholtz-type filter based parameterized level-set method for structural topology optimization

A body-fitted adaptive mesh and Helmholtz-type filter based parameterized level-set method for structural topology optimization

A CAD-oriented parallel-computing design framework for shape and topology optimization of arbitrary structures using parametric level set

Recently, the high-resolution topology optimization to promote engineering applicability has gained much more attentions. However, an accurate and highly-efficient design framework for implementing shape and topology optimization of engineering structures with integration of CAD model is still in demand. In the current work, the critical intention is to develop a CAD-oriented parallel-computing design framework for arbitrary structures, where the Parametric Level Set Method (PLSM) is employed for shape and topology optimization. Firstly, an implicit identification model is constructed for generating a signed distance field using the vertex and normal information from the ‘STL’ file of engineering structures. The signed distance field is combined with the compactly supported radial basis functions (CSRBFs) to solve the initial level set function with a parametrization. This method is applied to present all domains, including design domains, Neumann boundary domains, Dirichlet boundary domains, and non-design domains. Secondly, the CPU parallel strategy is considered for allocating partitions of structural stiffness matrix in finite element analysis to different CPU cores for the parallel-computing to save computation costs. Thirdly, a parallel-computing design formulation is developed for performing shape and topology optimization of arbitrary structures, in which the partitioned terms of all design variables and stiffness matrix are concurrently computed on each CPU core. Finally, several classic benchmarks and the critical engineering structure of Virtual Reality (VR) glass part with extremely complex geometries, are discussed to demonstrate the effectiveness and efficiency of the proposed design framework.

Topology optimization with a parametric level set method for double porosity poroelastic sound-absorbing structures

Topology optimization with a parametric level set method for double porosity poroelastic sound-absorbing structures

Mesh adaptive-based parametric level set method for the design of heat sink based on two-layer thermal-fluid system

Mesh adaptive-based parametric level set method for the design of heat sink based on two-layer thermal-fluid system

A new efficient parametric level set method based on radial basis function-finite difference for structural topology optimization

To overcome a significant challenge in traditional parameterized level set methods based on globally supported radial basis functions, we propose employing a local differentiation construction of radial basis functions using finite difference, a technique previously applied to solving partial differential equations but novel in the context of topology optimization. We present a novel parameterized level set method for structural topology optimization of compliance minimization and compliant mechanism, with the main aim of reducing computational costs associated with fully dense matrices when approximating systems with a large number of collocation points. The new scheme implemented with rectangular mesh elements and polygonal mesh generation accommodates both rectangular and complex design domains. Numerical results are provided to demonstrate the algorithm's effectiveness.

A novel quasi-smooth tetrahedral numerical manifold method and its application in topology optimization based on parameterized level-set method

In this paper, a novel quasi-smooth tetrahedral numerical manifold method (NMM) and its two-dimensional (2D) counterpart are proposed. A new topology optimization method is established by combining the quasi-smooth manifold element (QSME) with the parameterized level set method (PLSM). The QSME introduces an innovative displacement function characterized by high accuracy and high-order continuity, effectively addressing the “linear dependence” (LD) issue inherent in traditional high-order NMM. To integrate QSME and PLSM, the corresponding optimization formulations and sensitivity analyses are provided. In order to fully utilize advantages of this novel quasi-smooth NMM and the PLSM, an element subdivision technique based on model recognition is proposed to accurately capture the physical boundaries. Additionally, a volume fraction update method based on element refinement is proposed. Taking advantage of the characteristics of the PLSM, a structure visualization method based on the sign distance function is developed to accurately describe curve boundary. This method allows for precise visualization of optimized structures. This study verifies high efficiency of the QSME-based PLSM for minimum compliance topology optimization problems in both 2D and 3D structures. Some representative structural optimization examples are tested to demonstrate effectiveness of the proposed method in both 2D and 3D problems, especially in complex design domain.

Buckling optimization of curvilinear fiber-reinforced composite structures using a parametric level set method

Buckling optimization of curvilinear fiber-reinforced composite structures using a parametric level set method

Continuous fiber reinforced meta-composites with tailorable Poisson’s ratio and effective elastic modulus: Design and experiment

Auxetic metamaterials, i.e., with negative Poisson’s ratio are attracting increasing attention. This study develops a novel method to design and investigate continuous fiber-reinforced meta-composites with tailorable negative Poisson’s ratio and effective elastic modulus. First, the design scheme based on parametric level set method, is proposed by combining fast marching method, filtering technology and matrix rotation for attaining the two-dimensional isotropic composites. A novel objective function considering both negative Poisson’s ratio and effective elastic modulus is introduced and the result demonstrate that it is effective to not only accelerate the numerical convergence but also achieve a larger negative Poisson’s ratio when compared with that using the currently-used objective function. By tailoring a weight ratio for balancing the negative Poisson’s ratio and effective elastic modulus, a general contradictive trend was captured. Experimentally, the specimens are accordingly fabricated via 3D printing. Then, the axial compression tests are performed with the aid of digital image correlation technology to characterize the deformation behaviors and evaluate the mechanical properties of the designed meta-composites. Experimental results show that, as the weight ratio increases from 0.02 to 1.57, the effective elastic modulus increases from 180.5 MPa to 310.3 MPa (enhanced by 71.9 %) while the negative Poisson’s ratio decreases from − 0.41 to − 0.036 (reduced by 91.4 %), proving the effectiveness of the design method. The design methods and experimental results can provide effective approaches and important information for designing novel continuous fiber reinforced meta-composites with tailorable mechanical performance.

A novel numerical manifold method and its application in parameterized LSM-based structural topology optimization

In this paper, a high-efficiency structural topology optimization framework based on combination of numerical manifold method (NMM) and parameterized level set method (PLSM) is established. The NMM uses two cover systems to discretize the model, which can accurately represent the complex boundary of the design domain. A new numerical manifold element has been derived for the application of NMM in PLSM-based optimization. To obtain enhanced accuracy for structural analysis, a multilevel subdivision technique for numerical manifold element generation is presented, and the related numerical integration scheme coupled with the interpolation point selection strategy is provided. For the proposed topology optimization, the new update method of element stiffness matrix is exclusively formulated as well as the calculation method of volume fraction. Some representative structural optimization problems demonstrate that the proposed structural topology optimization method is very effective for two-dimensional (2D) and three-dimensional (3D) structural topology optimization problems.

Dynamic response-oriented multiscale topology optimization for geometrically asymmetric sandwich structures with graded cellular cores

Compared with conventional symmetric sandwich structures with two identical face-sheets and uniform core, geometrically asymmetric sandwich structures (GASSs) enable better dynamic performance due to the expanded design space provided by two unidentical face-sheets and graded cellular cores (GCCs). This paper proposes a dynamic response-oriented multiscale topology optimization method for the GASSs, which is capable of designing the thicknesses of two solid face-sheets, graded distribution of GCCs and their topological configurations to minimize dynamic compliance. Specifically, at macroscale, a variable thickness sheet method is employed to optimize the thicknesses of two solid face-sheets and then generate an overall free distribution of cellular cores within sandwich layers. At microscale, a parametric level set method combining with a numerical homogenization approach is adopted to progressively optimize multiple representative cellular cores (RCCs), achieving their similar topological configurations. Benefitting from the level set-based topology description of RCCs, a shape interpolation technology is conveniently applied to interpolate the shapes of these RCCs to generate the configurations of GCCs. Moreover, a Kriging metamodel constructed by some cellular cores as sample points is adopted to predict the effective properties of each cellular core within sandwich layers, significantly reducing the computational burden. Several 2D and 3D numerical examples are illustrated to show the validity of the proposed method. The results indicate that the optimized GASSs show superior dynamic performances over the conventional sandwich structures designed by microscale and macroscale topology optimization, as well as filled with the commonly applied lattice and honeycomb cores.

Multi-constrained topology optimization of prefabricated joints in large-span latticed structures

In recent years, topology optimization (TO) has shown great potential in the optimal design of engineering structures. In this study, a parameterized level set (PLS) method capable of solving the compliance minimization problem with both stress and volume constraints is proposed to improve the design efficiency of nodal connections in large-span latticed structures. 3D topology optimization of assembled hub (AH) joints is conducted based on the proposed method. The performances of the optimal designs are compared with those of the traditional joints in terms of volume, stress distribution and compliance value. Different connection types and complex loading conditions are considered to satisfy the requirements of engineering practice. It is indicated that the proposed PLS method exhibits good stability and high computing efficiency during the optimization of AH joints. Compared with the study cases with a single volume constraint, the maximum von Mises stress is effectively controlled by simultaneously introducing the stress and volume constraints. In addition, the variation in the volume constraint has much greater influence on the compliance results than the stress constraint. The compliance continuously increases when the volume constraint decreases from 100% to 40%, while the difference in compliance is less than 1.5% with or without stress constraints. It is demonstrated that the performances of AH joints are significantly improved after the TO design. The reduction rates of mass are in the range of 25.2 % to 35.2 %, and the compliance value is reduced by 0.5 % to 7.6 % for all the study cases.

Optimization with manufacturing constraints for composite laminates reinforced by curvilinear fibers through a parametric level set method

This paper presents the design optimization with manufacturing constraints for composite laminates reinforced by curvilinear fibers by using a parametric level set method. In each layer of the composite laminate, a level set function is defined by using the compactly supported radial basis functions (CS-RBFs), and the iso-contours of each level set function represent the fiber paths in one layer of the laminate. By this means, the fiber orientation at an arbitrary point in a layer can be computed by the orientation of the tangent vector of the iso-contour passing through this point. To avoid structure defects (such as gap/overlap, wrinkling and delamination) that would arise if the fiber paths are not parallel or their curvature is too large, the gradient norm and contour curvature radius of the level set functions are considered as constraints in the design optimization. The p-norm method is used to aggregate the constraints to improve the optimization efficiency. The coefficients of CS-RBFs are considered as design variables. Several numerical examples of compliance minimization and eigen-frequency maximization are investigated to verify the proposed method.

Non-probabilistic reliability-based topology optimization (NRBTO) scheme for continuum structures based on the strength constraint parameterized level set method and interval mathematics

In this paper, a study on non-probabilistic reliability-based topology optimization (NRBTO) scheme for continuum structures based on the parameterized level set method (PLSM) is conducted. The P-norm is used to replace the local stress constraint with a single comprehensive stress constraint that approximates the maximum stress to optimize the structure model with minimum volume. In the interval-set model, the stress constraint is transformed into the non-probabilistic reliability-based scheme and the reliability is evaluated by the optimization feature distance (OFD). In the NRBTO scheme, the unknown-but-bounded (UBB) uncertainties of the material and external load of the optimized structure are considered. By interpolating the level set function (LSF) with the multiquadric (MQ) splines, the partial differential equation (PDE) is transformed into an ordinary differential equation (ODE). In addition, the interval parameter vertex method is employed to obtain the stress constraint interval, and the shape derivative and adjoint vector methods are used to obtain the evolution velocity field of LSF. The optimality criterion (OC) method is used to solve the optimization problem. Finally, three examples are given, and the optimization model of stiffness constraint is introduced, which not only verifies the applicability of the topology optimization scheme based on non-probabilistic reliability but also compares the difference between the topology optimization with strength constraint and the topology optimization with stiffness constraint.

Concurrent topology optimization of multiple components sharing partial design domain based on distance regularized parameterized level set method

AbstractIn this article, the distance regularized parameterized level set method (DRPLSM) is proposed, which introduces a specified energy functional into the level set equation as the distance regularization term. Geometric verification shows that the distance regularization scheme keeps the level set function near the structural boundary as an approximate signed distance function. Based on benchmark example of the cantilever beam, it is verified that the DRPLSM can avoid the re‐initialization of level set function in the optimization process and obtain smooth structural boundary. The DRPLSM is applied to multicomponent concurrent topology optimization with partially shared design domain for the first time. It makes the optimization results have smooth structural boundaries. The optimization objective of this algorithm is to minimize the structural compliance of all components. The sharing domain is divided into different design domains according to the strain energy of elements. The optimality of the proposed algorithm for partitioning the sharing domain is verified using the literature example with known optimal solutions. A symmetric structure example, a main and auxiliary optimization structure example and an example with design‐dependent boundary loads show that the proposed concurrent optimization algorithm has wide applicability.

Topology Optimization for Steady-State Navier-Stokes Flow Based on Parameterized Level Set Based Method

In this paper, we consider solving the topology optimization for steady-state incompressible Navier-Stokes problems via a new topology optimization method called parameterized level set method, which can maintain a relatively smooth level set function with a local optimality condition. The objective of topology optimization is to find an optimal configuration of the fluid and solid materials that minimizes power dissipation under a prescribed fluid volume fraction constraint. An artificial friction force is added to the Navier-Stokes equations to apply the no-slip boundary condition. Although a great deal of work has been carried out for topology optimization of fluid flow in recent years, there are few researches on the topology optimization of fluid flow with physical body forces. To simulate the fluid flow in reality, the constant body force (e.g., gravity) is considered in this paper. Several 2D numerical examples are presented to discuss the relationships between the proposed method with Reynolds number and initial design, and demonstrate the feasibility and superiority of the proposed method in dealing with unstructured mesh problems. Three 3D numerical examples demonstrate the proposed method is feasible in three-dimensional.

Stress-based topology optimization with the parameterized level-set method based on radial basis functions

Stress-based topology optimization with the parameterized level-set method based on radial basis functions

Two Interpolation Matrix Triangularization Methods for Parametric Level Set-Based Structural Topology Optimization

As an implementation form of basis function, interpolation matrices (IMs) have a crucial impact on parametric level set method (PLSM)-based structural topology optimization (STO). However, there are few studies on compressing IM into triangular matrix (TM) with less storage and computation. Algorithm using LU decomposition and Algorithm using innovative asymmetric basis functions that transform the IMs of compactly supported radial basis functions (CSRBFs) into highly sparse TMs are proposed. Theoretical derivation and numerical experiments show that they effectively improve computational efficiency.

An adaptive parametric level-set method for lung health monitoring with smartphone-based electrical impedance tomography

In this paper, an adaptive parametric level-set method is presented for lung health monitoring with smartphone-based electrical impedance tomography (EIT). Firstly, assuming that the conductivity distribution to be reconstructed is piecewise constant, the shape of lung-like targets is represented by a PLS function using a Gaussian radial basis function. Secondly, the unknown parameters (e.g. centers, widths, and weights) are computed adaptively without a prior information about targets. Thirdly, rectified Adam is proposed to adaptively adjust the learning rate during the iterative process. The proposed method is evaluated quantitatively by simulated lung imaging, water tank tests, and human breathing data. In addition, the robustness of the proposed method is performed by considering different gradient descent methods and different number of RBF centers. The reconstruction results show that the proposed method not only overcomes some problems associated with the traditional level-set method (e.g. reinitialization and use of signed distance function), but also avoids empirical parameter selections in the PLS method, resulting in faster imaging speed and better imaging quality with an average image correlation coefficient greater than 0.90. It is found that the one-second rate of the proposed method is closer to the true value with an average error of no more than 2% when the forced vital capacity tests are repeatedly performed on five volunteers with healthy lungs. The proposed method is promising in providing the reliable assessment of lung health monitoring with smartphone-based EIT.

Optimal Design of Electrode Topology of Dielectric Elastomer Actuators Based on the Parameterized Level Set Method.

Dielectric elastomer actuators (DEAs) are widely used to drive soft machines, and optimal design is required in more advanced designs of soft robots. In this research article, a computational approach is originally proposed and validated for the topology optimization of electrodes of DEAs. The nonlinear finite elements of absolute nodal coordinate formulation are applied to model the dynamic electromechanical behaviors of DEAs. The parameterized level set method is employed to optimize the electrode topology of DEAs. Then, the method of system-wise equivalent static load is employed to convert the optimization problem of dynamic responses into the static one. Based on the sensitivity analysis, the normal velocity field for optimizing the electrode topology is derived. Finally, two case studies are presented to validate the proposed optimization approach. The experimental test is also performed, and the measured results are compared with the numerical ones to further validate the proposed methodology.

Optimization of Train Diesel Engine for Maximizing Efficiency and Driving Quality Using Modified Parameterized Level-Set Method

Optimization of Train Diesel Engine for Maximizing Efficiency and Driving Quality Using Modified Parameterized Level-Set Method