Brittle fracture on plates governed by topological derivatives

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Marcel Xavier ◽  
Nicolas Van Goethem
Keyword(s):  
Brittle Fracture ◽  
Crack Nucleation ◽  
Simple Algorithm ◽  
Topological Derivative ◽  
Mindlin Plate ◽  
Multiple Cracks ◽  
Plate Structures ◽  
Content Type ◽  
Fracture Modeling ◽  
Derivative Method

PurposeIn the paper an approach for crack nucleation and propagation phenomena in brittle plate structures is presented.Design/methodology/approachThe Francfort–Marigo damage theory is adapted to the Kirchhoff and Reissner–Mindlin plate bending models. Then, the topological derivative method is used to minimize the associated Francfort–Marigo shape functional. In particular, the whole damaging process is governed by a threshold approach based on the topological derivative field, leading to a notable simple algorithm.FindingsNumerical simulations are driven in order to verify the applicability of the proposed method in the context of brittle fracture modeling on plates. The obtained results reveal the capability of the method to determine nucleation and propagation including bifurcation of multiple cracks with a minimal number of user-defined algorithmic parameters.Originality/valueThis is the first work concerning brittle fracture modeling of plate structures based on the topological derivative method.

Topology optimization of structures subject to self-weight loading under stress constraints

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Renatha Batista dos Santos ◽  
Cinthia Gomes Lopes
Keyword(s):  
Topology Optimization ◽  
Stress Constraints ◽  
Topological Derivative ◽  
The Self ◽  
Von Mises Stress ◽  
Stress Constraint ◽  
Content Type ◽  
Derivative Method ◽  
Von Mises ◽  
Weight Loading

PurposeThe purpose of this paper is to present an approach for structural weight minimization under von Mises stress constraints and self-weight loading based on the topological derivative method. Although self-weight loading topology has been the subject of intense research, mainly compliance minimization has been addressed.Design/methodology/approachThe resulting minimization problem is solved with the help of the topological derivative method, which allows the development of efficient and robust topology optimization algorithms. Then, the derived result is used together with a level-set domain representation method to devise a topology design algorithm.FindingsNumerical examples are presented, showing the effectiveness of the proposed approach in solving a structural topology optimization problem under self-weight loading and stress constraint. When the self-weight loading is dominant, the presence of the regularizing term in the formulation is crucial for the design process.Originality/valueThe novelty of this research work lies in the use of a regularized formulation to deal with the presence of the self-weight loading combined with a penalization function to treat the von Mises stress constraint.

Three-dimensional computational study in a corrugated pipe inserted system filled with phase change material

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Ömer Akbal ◽  
Hakan F. Öztop ◽  
Nidal H. Abu-Hamdeh
Keyword(s):  
Phase Change ◽  
Phase Change Material ◽  
Computational Analysis ◽  
Computational Study ◽  
Three Dimensional ◽  
Simple Algorithm ◽  
Melting Time ◽  
Geometrical Parameters ◽  
Content Type ◽  
Change Material

Purpose The purpose of this paper is to make a three-dimensional computational analysis of melting in corrugated pipe inserted system filled with phase change material (PCM). The system was heated from the inner pipe, and temperature of the outer pipe was lower than that of inner pipe. Different geometrical ratio cases and two different temperature differences were tested for their effect on melting time. Design/methodology/approach A computational analysis through a pipe with corrugated pipe filled with PCM is analyzed. Finite volume method was applied with the SIMPLE algorithm method to solve the governing equations. Findings The results indicate that the geometrical parameters can be used to control the melting time inside the heat exchanger which, in turn, affect the energy efficiency. The fastest melting time is seen in Case 4 at the same temperature difference which is the major observation of the current work. Originality/value Originality of this work is to perform a three-dimensional analysis of melting of PCM in a corrugated pipe inserted pipe.

Effect of wall-mounted V-baffle position in a turbulent flow through a channel

2019 ◽  
Vol 29 (10) ◽  
pp. 3908-3937 ◽  
Author(s):  
Younes Menni ◽  
Ahmed Azzi ◽  
Ali J. Chamkha ◽  
Souad Harmand
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Stokes Equations ◽  
Numerical Study ◽  
Rectangular Channel ◽  
Simple Algorithm ◽  
Two Dimensions ◽  
Large Reynolds Number ◽  
Constant Property ◽  
Content Type

Purpose The purpose of this paper is to carry out a numerical study on the dynamic and thermal behavior of a fluid with a constant property and flowing turbulently through a two-dimensional horizontal rectangular channel. The upper surface was put in a constant temperature condition, while the lower one was thermally insulated. Two transverse, solid-type obstacles, having different shapes, i.e. flat rectangular and V-shaped, were inserted into the channel and fixed to the top and bottom walls of the channel, in a periodically staggered manner to force vortices to improve the mixing, and consequently the heat transfer. The flat rectangular obstacle was put in the first position and was placed on the hot top wall of the channel. However, the second V-shaped obstacle was placed on the insulated bottom wall, at an attack angle of 45°; its position was varied to find the optimum configuration for optimal heat transfer. Design/methodology/approach The fluid is considered Newtonian, incompressible with constant properties. The Reynolds averaged Navier–Stokes equations, along with the standard k-epsilon turbulence model and the energy equation, are used to control the channel flow model. The finite volume method is used to integrate all the equations in two-dimensions; the commercial CFD software FLUENT along with the SIMPLE-algorithm is used for pressure-velocity coupling. Various values of the Reynolds number and obstacle spacing were selected to perform the numerical runs, using air as the working medium. Findings The channel containing the flat fin and the 45° V-shaped baffle with a large Reynolds number gave higher heat transfer and friction loss than the one with a smaller Reynolds number. Also, short separation distances between obstacles provided higher values of the ratios Nu/Nu0 and f/f0 and a larger thermal enhancement factor (TEF) than do larger distances. Originality/value This is an original work, as it uses a novel method for the improvement of heat transfer in completely new flow geometry.

A topology optimization algorithm based on topological derivative and level-set function for designing phononic crystals

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Rolando Yera ◽  
Luisina Forzani ◽  
Carlos Gustavo Méndez ◽  
Alfredo E. Huespe
Keyword(s):  
Topology Optimization ◽  
Level Set ◽  
Optimization Algorithm ◽  
Phononic Crystal ◽  
Phononic Crystals ◽  
Lagrangian Function ◽  
Topological Derivative ◽  
Content Type ◽  
Level Set Function ◽  
Set Function

PurposeThis work presents a topology optimization methodology for designing microarchitectures of phononic crystals. The objective is to get microstructures having, as a consequence of wave propagation phenomena in these media, bandgaps between two specified bands. An additional target is to enlarge the range of frequencies of these bandgaps.Design/methodology/approachThe resulting optimization problem is solved employing an augmented Lagrangian technique based on the proximal point methods. The main primal variable of the Lagrangian function is the characteristic function determining the spatial geometrical arrangement of different phases within the unit cell of the phononic crystal. This characteristic function is defined in terms of a level-set function. Descent directions of the Lagrangian function are evaluated by using the topological derivatives of the eigenvalues obtained through the dispersion relation of the phononic crystal.FindingsThe description of the optimization algorithm is emphasized, and its intrinsic properties to attain adequate phononic crystal topologies are discussed. Particular attention is addressed to validate the analytical expressions of the topological derivative. Application examples for several cases are presented, and the numerical performance of the optimization algorithm for attaining the corresponding solutions is discussed.Originality/valueThe original contribution results in the description and numerical assessment of a topology optimization algorithm using the joint concepts of the level-set function and topological derivative to design phononic crystals.

Improvement of a topological level-set approach to find optimal topology by considering body forces

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Meisam Takalloozadeh ◽  
Gil Ho Yoon
Keyword(s):  
Topology Optimization ◽  
Level Set ◽  
Thermal Loading ◽  
Topological Derivative ◽  
Optimization Process ◽  
Optimal Topology ◽  
Content Type ◽  
Body Forces ◽  
Applied Forces ◽  
Level Set Approach

Purpose Body forces are always applied to structures in the form of the weight of materials. In some cases, they can be neglected in comparison with other applied forces. Nevertheless, there is a wide range of structures in civil and mechanical engineering in which weight or other types of body forces are the main portions of the applied loads. The optimal topology of these structures is investigated in this study. Design/methodology/approach Topology optimization plays an increasingly important role in structural design. In this study, the topological derivative under body forces is used in a level-set-based topology optimization method. Instability during the optimization process is addressed, and a heuristic solution is proposed to overcome the challenge. Moreover, body forces in combination with thermal loading are investigated in this study. Findings Body forces are design-dependent loads that usually add complexity to the optimization process. Some problems have already been addressed in density-based topology optimization methods. In the present study, the body forces in a topological level-set approach are investigated. This paper finds that the used topological derivative is a flat field that causes some instabilities in the optimization process. The main novelty of this study is a technique used to overcome this challenge by using a weighted combination. Originality/value There is a lack of studies on level-set approaches that account for design-dependent body forces and the proposed method helps to understand the challenges posed in such methods. A powerful level-set-based approach is used for this purpose. Several examples are provided to illustrate the efficiency of this method. Moreover, the results show the effect of body forces and thermal loading on the optimal layout of the structures.

An efficient coupled pressure–velocity solver for three-dimensional injection molding simulation using Schur complement preconditioned FGMRES

2019 ◽  
Vol 36 (4) ◽  
pp. 1101-1120
Author(s):  
Xiang Liu ◽  
Fei Guo ◽  
Yun Zhang ◽  
Junjie Liang ◽  
Dequn Li ◽  
...  
Keyword(s):  
Injection Molding ◽  
Three Dimensional ◽  
Simple Algorithm ◽  
Schur Complement ◽  
Gradient Term ◽  
Content Type ◽  
Coupled Problem ◽  
Parallel Performance ◽  
Injection Molding Simulation ◽  
Fully Coupled

Purpose The purpose of this paper is to develop a coupled approach to solve the pressure–velocity-coupled problem efficiently in the three-dimensional injection molding simulation. Design/methodology/approach A fully coupled pressure–velocity algorithm is developed to solve the coupled problem, by treating the pressure gradient term implicitly. And, the Schur complement preconditioned FGMRES is applied to decompose the resulting coupled pressure–velocity equation into pressure and velocity subsystems. Then, BoomerAMG is adopted to solve the pressure subsystem, and block Jacobi preconditioned FGMRES is applied to the velocity subsystem. Findings According to the several experiments, the fully coupled pressure–velocity algorithm was demonstrated to have faster convergence than the traditional SIMPLE algorithm, and the calculating time was reduced by up to 70 per cent. And, the Schur complement preconditioned FGMRES worked more efficiently than block Gauss–Seidel preconditioned FGMRES, block-selective AMG and AMG with block ILU(0) smoother and could take at least 47.4 per cent less time. The proposed solver had good scalability for different-size problems, including various cases with different numbers of elements. It also kept good speedup and efficiency in parallel performance. Originality/value A coupled solver has been proposed to effectively solve the coupled problem in the three-dimensional injection molding simulation, which is more robust and efficient than existing methods.

Conservative estimations of irradiation embrittlement of reactor pressure vessel steels for WWER-1000 lifetime prediction

2019 ◽  
Vol 15 (1) ◽  
pp. 246-257
Author(s):  
Nikolai Petrovich Anosov ◽  
Vladimir Nikolaevich Skorobogatykh ◽  
Lyubov’ Yur’yevna Gordyuk ◽  
Vasilii Anatol’evich Mikheev ◽  
Egor Vasil’yevich Pogorelov ◽  
...  
Keyword(s):  
Transition Temperature ◽  
Brittle Fracture ◽  
Pressure Vessel ◽  
Reactor Pressure Vessel ◽  
Lifetime Prediction ◽  
Critical Brittleness Temperature ◽  
Irradiation Embrittlement ◽  
Content Type ◽  
Brittleness Temperature ◽  
Reactor Pressure

Purpose The purpose of this paper is to consider a procedure of water-water energetic reactor (WWER) reactor pressure vessel (RPV) lifetime prediction at the stages of design and lifetime extension using the standard irradiation embrittlement parameters as defined in regulatory documents. A comparison is made of the brittle fracture resistance (BFR) values evaluated using two criteria: shift in the critical brittleness temperature ΔTc or shift in the brittle-to-ductile transition temperature ΔTp and without shifts (Tc and Tp). Design/methodology/approach The radiation resistance was determined using the following three approaches: calculation based on standard values ΔTc and Tc0 or ΔTp and Tp0 (a level of excessive conservatism); calculation based on standard value ΔTc and actual value Tc0 or actual values ΔTp and Tp0 (the level of realistic conservatism); or calculation based on actual values of Tc and Tc0 or Tp and Tp0 (the level of actual conservatism). The BFR was evaluated based on the results of testing the specimens subjected to irradiation in research reactors as well as surveillance specimens subjected to irradiation immediately under operating conditions. Findings The excessive conservatism in determining the actual lifetime of nuclear reactor vessel materials can be eliminated by using the immediate values of critical brittleness temperature and ductile-to-brittle transition temperature. Originality/value Obtained results can be applied to extend WWER vessel operating time at the stages of designing and operation due to substantiated decrease in conservatism. And it will allow carrying out a statistical substantiated assessment of the resistance to brittle fracture of the RPV steels.

Compliant assembly analysis including initial deviations and geometric nonlinearity, part II: Plate structure

2018 ◽  
Vol 233 (11) ◽  
pp. 3717-3732 ◽  
Author(s):  
Tao Liu ◽  
Zhi-min Li ◽  
Sun Jin ◽  
Wei Chen
Keyword(s):  
Geometric Nonlinearity ◽  
Mindlin Plate ◽  
Variation Analysis ◽  
Governing Equations ◽  
Plate Structures ◽  
Orthotropic Composite ◽  
Compliant Assembly ◽  
Variation Propagation ◽  
Springback Prediction ◽  
Assembly Analysis

Part I of this paper (Liu et al., “Compliant assembly analysis including initial deviations and geometric nonlinearity, part I: Beam structure”) has studied the variation propagation of beam structures with consideration of initial deviations and geometric nonlinearity. In practices, plate structures are more commonly used in manufacturing fields, and the attempt of this paper is to expand previous methodology for the assembly process of orthotropic composite plate structures. Similarly, initial deviations and von Kármán-type geometric nonlinearity are introduced into variation analysis model, with Mindlin plate theory accounting for shear effect. The analyzed plates are set as orthotropic composite materials, which also preserve the compatibility with isotropic metal materials. Governing equations and corresponding finite element expressions can be obtained by applying the principle of virtual work. Also, a linearized model or noninitial model can be regarded as a degradation of origin governing equations. A variation analysis approach for plate structures is proposed to make more refined assembly variation predictions with consideration of initial deviations, fixture errors, and matching deviations. The verification of the developed method is implemented with case studies on springback prediction of two composite plates assembly.

Numerical study on the effects of variable properties and nanoparticle diameter on nanofluid flow and heat transfer through micro-annulus

2017 ◽  
Vol 27 (8) ◽  
pp. 1851-1869 ◽  
Author(s):  
Morteza Heydari ◽  
Hossein Shokouhmand
Keyword(s):  
Heat Transfer ◽  
Shear Stress ◽  
Numerical Study ◽  
Simple Algorithm ◽  
Variable Properties ◽  
Temperature Dependent ◽  
Constant Property ◽  
Content Type ◽  
Nanoparticle Diameter ◽  
Flow And Heat Transfer

Purpose The purpose of this paper is to evaluate differences between the results of constant property and variable property approaches in solving the problem of Al2O3-water nanofluid heat transfer in an annular microchannel. Also, the effect of nanoparticle diameter on flow and heat transfer characteristics is investigated. Design/methodology/approach Thermo-physical properties of the nanofluid including density, specific heat, viscosity and thermal conductivity are assumed to be temperature dependent. Governing equations are descritized using the finite volume method and solved by SIMPLE algorithm. Findings The results reveal that the constant property assumption is unable to predict the correct trend of variations along the microchannel for some of the characteristics, especially when the range of temperature change near the wall is considerable. In the fully developed region, constant property solution overestimates the values of shear stress near the walls of the microchannel. In addition, the values of Nusselt numbers are different for the two solutions. Furthermore, a decrease in wall’s shear stress has been observed as a result of increasing nanoparticle size. Originality/value This paper reflects that how the friction factor and heat transfer vary along the microchannel in temperature dependent modeling, which is not reflected in the results of constant property approach. To the best of the authors’ knowledge, there is no similar investigation of the effect of nanofluid variable properties with Pr=5 or in annular geometry.

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