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

Frontiers of Mechanical Engineering 2024年第1期19卷 149-160页

作者： Ye TIAN Tielin SHI Qi XIA State Key Laboratory of Intelligent Manufacturing Equipment and Technology Huazhong University of Science and TechnologyWuhan 430074China

Owing to their excellent performance and large design space,curvilinear fiber-reinforced composite structures have gained considerable attention in engineering fields such as aerospace and automobile.In addition to the stiffness and strength of such structures,their stability also needs to be taken into account in the design.This study proposes a level-set-based optimization framework for maximizing the buckling load of curvilinear fiber-reinforced composite structures.In the proposed method,the contours of the level set function are used to represent fiber paths.For a composite laminate with a certain number of layers,one level set function is defined by radial basis functions and expansion coefficients for each layer.Furthermore,the fiber angle at an arbitrary point is the tangent orientation of the contour through this point.In the finite element of buckling,the stiffness and geometry matrices of an element are related to the fiber angle at the element centroid.This study considers the parallelism constraint for fiber paths.With the sensitivity calculation of the objective and constraint functions,the method of moving asymptotes is utilized to iteratively update all the expansion coefficients regarded as design variables.Two numerical examples under different boundary conditions are given to validate the proposed approach.Results show that the optimized curved fiber paths tend to be parallel and equidistant regardless of whether the composite laminates contain holes or not.Meanwhile,the buckling resistance of the final design is significantly improved.

关键词： buckling optimization curvilinear fiber composite structure level set method manufacturing constraint

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A Low Mach Number IMEX Flux Splitting for the level set Ghost Fluid method

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Communications on Applied Mathematics and Computation 2023年第2期5卷 722-750页

作者： Jonas Zeifang Andrea Beck Faculty of Sciences Hasselt UniversityAgoralaan Gebouw DBE-3590 DiepenbeekBelgium Institute of Aerodynamics and Gas Dynamics University of StuttgartPfaffenwaldring 2170569 StuttgartGermany Laboratory of Fluid Dynamics and Technical Flows Otto von Guericke University MagdeburgUniversitatsplatz 239106 MagdeburgGermany

Considering droplet phenomena at low Mach numbers,large differences in the magnitude of the occurring characteristic waves are presented.As acoustic phenomena often play a minor role in such applications,classical explicit schemes which resolve these waves suffer from a very restrictive timestep restriction.In this work,a novel scheme based on a specific level set ghost fluid method and an implicit-explicit(IMEX)flux splitting is proposed to overcome this timestep restriction.A fully implicit narrow band around the sharp phase interface is combined with a splitting of the convective and acoustic phenomena away from the interface.In this part of the domain,the IMEX Runge-Kutta time discretization and the high order discontinuous Galerkin spectral element method are applied to achieve high accuracies in the bulk phases.It is shown that for low Mach numbers a significant gain in computational time can be achieved compared to a fully explicit method.Applica-tions to typical droplet dynamic phenomena validate the proposed method and illustrate its capabilities.

关键词： IMEX flux splitting level set method Ghost fluid method Low Mach number flows

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A level set method for the Simulation of Moving Contact Lines in Three Dimensions

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Communications in Computational Physics 2022年第10期32卷 1310-1331页

作者： Quan Zhao Shixin Xu Weiqing Ren Department of Mathematics National University of SingaporeSingapore119076 Zu Chongzhi Center for Mathematics and Computational Sciences Duke Kunshan University8 Duke AveKunshanJiangsuChina

We propose an efficient numerical method for the simulation of the twophase flows with moving contact lines in three dimensions.The mathematical model consists of the incompressible Navier-Stokes equations for the two immiscible fluids with the standard interface conditions,the Navier slip condition along the solid wall,and a contact angle condition(Ren et al.(2010)[28]).In the numerical method,the governing equations for the fluid dynamics are coupledwith an advection equation for a level-set function.The latter models the dynamics of the fluid interface.Following the standard practice,the interface conditions are taken into account by introducing a singular force on the interface in themomentum equation.This results in a single set of governing equations in the whole fluid domain.Similarly,the contact angle condition is imposed by introducing a singular force,which acts in the normal direction of the contact line,into theNavier slip condition.The newboundary condition,which unifies the Navier slip condition and the contact angle condition,is imposed along the solid wall.The model is solved using the finite difference method.Numerical results are presented for the spreading of a droplet on both homogeneous and inhomogeneous solid walls,as well as the dynamics of a droplet on an inclined plate under gravity.

关键词： level set method two-phase flow moving contact line dynamic contact angle Navier boundary condition

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level set method for numerical simulation of a cavitation bubble,its growth, collapse and rebound near a rigid wall

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Acta Mechanica Sinica 2007年第6期23卷 645-653页

作者： Juntao Huang Huisheng Zhang Department of Mechanics and Engineering Sciences Fudan University Shanghai 200433 China

A level set method of non-uniform grids is used to simulate the whole evolution of a cavitation bubble, including its growth, collapse and rebound near a rigid wall. Single-phase Navier-Stokes equation in the liquid region is solved by MAC projection algorithm combined with second-order ENO scheme for the advection terms. The moving inter-face is captured by the level set function, and the interface velocity is resolved by ＂one-side＂ velocity extension from the liquid region to the bubble region, complementing the second-order weighted least squares method across the interface and projection inside bubble. The use of non-uniform grid overcomes the difficulty caused by the large computational domain and very small bubble size. The computation is very stable without suffering from large flow-field gradients, and the results are in good agreements with other studies. The bubble interface kinematics, dynamics and its effect on the wall are highlighted, which shows that the code can effectively capture the ＂shock wave＂-like pressure and velocity at jet impact, toroidal bubble, and complicated pressure structure with peak, plateau and valley in the later stage of bubble oscillating.

关键词： level set method Cavitation bubble Collapsing and rebounding Jet impact Toroidal bubble

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A level set method FOR SIMULATION OF RISING BUBBLE

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Journal of Hydrodynamics 2004年第4期16卷 379-385页

作者： HUANGJun-tao ZHANGHui-sheng DepartmentofMechanicsandEngineeringSciences FudanUniversityShanghai200433China

A level set method, the TVD scheme of second-order upwind procedure coupledwith flux-limiter, and SIMPLE algorithm were incorporated to simulate the flow and interfacialmotion of immiscible two-fluids with large density ratio and viscosity ratios, large topologydistortion and surface tension. As a numerical example axi-symmetric rising bubbles wereinvestigated. It is found that the method is numerically stable and has good convergence propertyand the results are in good agreement with other works.

关键词： level set method high-resolution scheme SIMPLE algorithm rising bubble

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A level set method FOR STRUCTURAL TOPOLOGY OPTIMIZATION WITH MULTI-CONSTRAINTS AND MULTI-MATERIALS

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Acta Mechanica Sinica 2004年第5期20卷 507-518页

作者：梅玉林王晓明 Mechanical Engineering Department Dalian University of TechnologyDalian 116024China

Combining the vector level set model,the shape sensitivity analysis theory with the gradient projection technique,a level set method for topology optimization with multi-constraints and multi-materials is presented in this paper.The method implicitly describes structural material in- terfaces by the vector level set and achieves the optimal shape and topology through the continuous evolution of the material interfaces in the structure.In order to increase computational efficiency for a fast convergence,an appropriate nonlinear speed mapping is established in the tangential space of the active constraints.Meanwhile,in order to overcome the numerical instability of general topology opti- mization problems,the regularization with the mean curvature flow is utilized to maintain the interface smoothness during the optimization process.The numerical examples demonstrate that the approach possesses a good flexibility in handling topological changes and gives an interface representation in a high fidelity,compared with other methods based on explicit boundary variations in the literature.

关键词： level set method topology optimization multi-constraints multi-materials mean curvature flow

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level set method FOR NUMERICAL SIMULATION OF A CAVITATION BUBBLE COLLAPSING NEAR A RIGID WALL

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Journal of Hydrodynamics 2005年第6期17卷 647-653页

作者： HUANG Jun-tao ZHANG Hui-sheng Department of Mechanics and Engineering Science Fudan University Shanghai 200433 China

The level set method, TVD scheme of second order upwind procedure coupled with flux limiter, ENO velocity extension procedure inside the huhble, and MAC projection algorithm were incorporated to simulate the whole collapse e volution of a cavitation bubble near a rigid wall with many complicated phenomena, such as topology distortion and shrinking, jet impact, bubble breaking into a toroidal form, and diminishing volume to zero, etc. The huhhle shape, evolution and distribution of velocity and pressure fields of the fluid during the bubble collapsing were investigated. It is found that the method is numerically stable and has good convergence property, and the results are in good agreements with those in previous work.

关键词： level set method high resolution scheme,MAC projection cavitation hubble collapse toroidal huhhle

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level set method FOR TOPOLOGICAL OPTIMIZATION APPLYING TO STRUCTURE, MECHANISM AND MATERIAL DESIGNS

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Chinese Journal of Mechanical Engineering 2004年第2期17卷 200-209页

作者： Mei Yulin Wang Xiaoming Department of Mechanical Engineering,Dalian University of Technology,Dalian 116024,China Department of Mechanical Engineering Dalian University of Technology Dalian 116024

Based on a level set model, a topology optimization method has been suggestedrecently. It uses a level set to express the moving structural boundary, which can flexibly handlecomplex topological changes. By combining vector level set models with gradient projectiontechnology, the level set method for topological optimization is extended to a topologicaloptimization problem with multi-constraints, multi-materials and multi-load cases. Meanwhile, anappropriate nonlinear speed, mapping is established in the tangential space of the activeconstraints for a fast convergence. Then the method is applied to structure designs, mechanism andmaterial designs by a number of benchmark examples. Finally, in order to further improvecomputational efficiency and overcome the difficulty that the level set method cannot generate newmaterial interfaces during the optimization process, the topological derivative analysis isincorporated into the level set method for topological optimization, and a topological derivativeand level set algorithm for topological optimization is proposed.

关键词： level set method Topology optimization Mean curvature flow Materialdesign Mechanism design Topological derivative

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Adaptive Multi-Resolution method for 3D Reactive Flows with level set Front Capturing

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Communications in Computational Physics 2023年第3期33卷 849-883页

作者： Wenhua Ma Dongmi Luo Wenjun Ying Guoxi Ni Min Xiao Yibing Chen Institute of Applied Physics and Computational Mathematics Beijing 100094P.R.China College of Science China University of PetroleumBeijing 102249P.R.China School of Mathematical Sciences Shanghai Jiao Tong UniversityShanghai 200240P.R.China.

For compressible reactive flows with stiff source terms,a new block-based adaptive multi-resolution method coupled with the adaptive multi-resolution representation model for ZND detonation and a conservative front capturing method based on a level-set technique is presented.When simulating stiff reactive flows,underresolution in space and time can lead to incorrect propagation speeds of discontinuities,and numerical dissipation makes it impossible for traditional shock-capturing methods to locate the detonation front.To solve these challenges,the proposed method leverages an adaptive multi-resolution representation model to separate the scales of the reaction from those of fluid dynamics,achieving both high-resolution solutions and high efficiency.A level set technique is used to capture the detonation front sharply and reduce errors due to the inaccurate prediction of detonation speed.In order to ensure conservation,a conservative modified finite volume scheme is implemented,and the front transition fluxes are calculated by considering a Riemann problem.A series of numerical examples of stiff detonation simulations are performed to illustrate that the present method can acquire the correct propagation speed and accurately capture the sharp detonation front.Comparative numerical results also validate the approach’s benefits and excellent performance.

关键词： Compressible reactive flows reactive Euler equations three-dimensional simulation adaptive multi-resolution level set method sharp front capturing.

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Numerical simulation of 3-D water collapse with an obstacle by FEM-level set method

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Journal of Hydrodynamics 2015年第1期27卷 112-119页

作者：王吉飞万德成 State Key Laboratory of Ocean Engineering School of Naval Architecture Ocean and Civil EngineeringShanghai Jiao Tong University Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration

An interface capturing approach based on a level set function for simulating transient two-phase viscous incompressible flows is applied in this paper. A narrow-band signed distance function is adopted to indicate the phase fields and the interface. The multiphase flow is numerically solved by three stages with finite element method （FEM）：（1） solving a two-fluid Navier-Stokes （N-S） equations over the whole domain, （2） transporting the level set function with the obtained velocity field, （3） the level set function correction through a renormalization with continuous penalization which preserves the thickness of the interface. In this paper, the 3-D water colunm collapse with an obstacle is simulated, which yielded good agreement with the experimental data.

关键词： 3-D water collapse with an obstacle free surface interface capturing level set method finite element method

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