力学学报

STUDY ON HYPERSONIC BOUNDARY LAYER LIQUID FILM EVOLUTION AND COOLING MECHANISM

Luo Yintao, Han Guilai, Qian Lijuan, Jiang Zonglin, Liu Meikuan

Hypersonic liquid film cooling technology is to press out the cooling medium through a series of slits or holes, creat a low-temperature cooling film in the boundary layer of the surface of the aircraft to prevent the aerodynamic heating of the aircraft by hypersonic airflow. As an active cooling method, it has great application potential in surface thermal protection of hypersonic vehicle. In this paper, numerical methods and VOF model are used to study the spreading of liquid film at 25 km flight altitude and Ma=5 airflow. The evolution process and cooling mechanism of liquid film on a flat plate are discussed through the incident velocity, Angle, surface tension and viscosity coefficient of different cooling medium. The results show that under the action of air flow, the liquid film develops downstream to the wall surface, the existence of the liquid film leads to the boundary layer separation, and the continuous liquid film will be broken into liquid blocks at a certain position, and then further broken into droplets. The change of incident conditions and liquid properties will affect the development of the liquid film along the flow direction, which is manifested in the position of the fracture point and the thickness of the continuous liquid film. Within the computational domain set in this paper, the wall heat flow is reduced by 80% ~ 95%, and the cooling efficiency of the liquid film on the wall varies with the the change of the liquid film morphology.

2023, 55(5): 1039-1052. doi: 10.6052/0459-1879-22-512

HTML PDF

EXPERIMENTAL STUDY ON THE CHARACTERIZATION OF TRANSVERSE JET INTERACTION IN HYPERSONIC RAREFIED FLOW

Zhuo Yue, Luo Kai, Shang Jiahao, Yu Qinghao, Wang Qiu, Wang Yejun, Liang Jinhu, Zhao Wei

Jet interaction is an effective approach for hypersonic flight controls with higher agility and improved maneuverability. Previous researches are mainly focused on the mechanisms of jet interaction effects in continuous region, classical flowfield structures of jet interaction based on different models have been proposed theoretically, on the other hand, scarce experimental data on characterizations of jet interaction in rarefied region exist. Therefore, the objective of this work aims to experimentally investigate the effects of jet pressure and hypersonic rarefied flow condition on the characterizations of transverse jet interaction based on a flat plate model, whereas hypersonic rarefied flows are generated in a JFX detonation shock tunnel. Evolution and typical structure of transverse jet interaction in hypersonic rarefied flow are recorded using high-speed schlieren imaging approach, and variations of spatial positions of different shock waves are analyzed using imaging process technique. Compared to the flowfield without the presence of jet flow, the interaction between jet flow and hypersonic rarefied flow makes the flowfield much more complex. Oblique shock could instantaneously penetrate through the flowfield of jet interaction due to the pressure fluctuation of jet flow caused by the incoming flow. With increasing the jet pressure, the affecting region of the barrel shock gradually becomes broader. The spatial position of the oblique shock wave in the upstream of the triple point barely changes with an increase in the jet pressure, while in the downstream of the triple point, the bow shock moves upstream with increasing pressure. The spatial position of the barrel shock would not overlap with the other two when the jet pressure is low. The pressure reduction of the incoming hypersonic rarefied flow can broaden the affecting region of the barrel shock and thus move the bow shock upstream as well, but it has little influence on the spatial position of the oblique shock wave.

2023, 55(5): 1053-1062. doi: 10.6052/0459-1879-22-599

HTML PDF

PIV EXPERIMENT STUDY ON INTERACTION BETWEEN PULSED LASER PLASMA AND NORMAL SHOCK

Wang Diankai, Shi Jilin, Huang Longcheng, Wen Ming, Zhang Tengfei

The interaction between pulsed laser plasma and supersonic flow field has important application value on aircraft drag reduction and heat insulation, ignition and combustion assistance. In order to quantitatively study the velocity field and vortex structure, particle image velocimetry (PIV) experiments were carried out on laser plasma and its interaction with normal shock wave. The nanosecond pulse laser energy deposition system and PIV measurement system were established on the shock tube experimental platform. By quantitatively measuring, the flow characteristics of laser air bubbles and hot core induced by laser plasma are explored. The flow characteristics and evolution of laser plasma under the impact of normal shock waves are revealed, and the influence of laser energy magnitude and deposition position on the interaction process is given. The results show that the velocity distribution in the laser air bubble is not symmetrical about the breakdown point in the laser incidence direction, but the flow velocity near the laser incidence direction is slightly larger than that far from the laser incidence direction. The baroclinic pressure leads to the generation of vortex rings in the early stage of hot core evolution, and the later stage is dominated by shearing force. When the normal shock interacts with the laser air bubble interface and the hot core interface, the baroclinic vorticity is generated. When the laser energy is 87.8 mJ and the normal shock Mach number is 1.41, the vorticity generated at the hot core interface is one order of magnitude larger than that in the static air. The key process of the interaction between the laser and the normal shock wave is that the hot core evolves into a vortex ring under the impact of the normal shock wave. The deposition of laser energy in front of the shock wave can obtain a more significant vortex ring.

2023, 55(5): 1063-1074. doi: 10.6052/0459-1879-22-580

HTML PDF

LINEAR GLOBAL INSTABILITY OF THE PLANE FLOW WITH MEANDERING WALL

Ji Ziqing, Bai Yuchuan, Xu Haijue

In the hydrodynamic and processing research of meandering river, it is implicitly assumed that the relationship between secondary flow and secondary turbulence is the same as that between mean flow and turbulence in open channel flows. However, there is no relevant turbulence research to support this implicit assumption, due to the limitation of DNS model and PIV measurement at high Reynolds number. The differences and similarities research of turbulent structures development between meandering channel and straight channel flow are benefit to the secondary turbulent flow in meandering rivers. A planar two-dimensional NS equation in orthogonal coordinate system and the two-parameter perturbation method were established to solve the weak nonlinear laminar flow and flow instability problem in the meandering channel. And a governing equation, named with extended Orr-Sommerfeld (EOS) equation was derived to solve the eigenvalue problem of planer flow with meandering boundary. The weak nonlinear laminar flow is combination of a series of meandering harmonic components, in which the linear component causes the velocity difference between the two walls, and the nonlinear component increases exponentially with the increase of Reynolds number. The first modal of the disturbance growth rate spectrum is similar to that of the straight channel flow, which is composed of three type curves and divided four disturbance wave bands. However, the disturbance flow field at the longwave band and the shortwave band is different from that of the straight flow. Specially, the velocity disturbance at shortwave band is similar to that of the Kelvin-Helmholtz vortex, may due to the velocity difference caused by linear component of laminar. The two meandering parameters have a certain selectivity to the internal disturbance in channel. The larger the angular amplitude is, the faster the disturbance grows. With the increase of the meandering wavenumber, the disturbance growth rate increases at first and then decreases. The disturbed flow field is formed by superposition of a typical TS wave and a pair of wave packets. The wave packet pair has only longitudinal velocity components, with two envelopes controlled by the boundary wavenumber and interior TS wave with the same parameters as TS wave in the wave packet.

2023, 55(5): 1075-1086. doi: 10.6052/0459-1879-22-570

HTML PDF

DRAG REDUCTION OF PARTICLE-LADEN CHANNEL FLOW BY SPANWISE WALL OSCILLATION: A DIRECT NUMERICAL SIMULATION

Kang Xiaoxuan, Hu Jianxin, Lin Zhaowu, Pan Dingyi

Study on drag reduction of turbulent channel flow has its significance in both scientific researches and industry applications. The passive drag reduction technique that has been reported to be effective is to add dispersed materials into the single-phase turbulence. On the other hand, the active drag reduction technique, i.e., spanwise wall oscillation, which can be controlled in advance, has attracted wide attention in recent years. Drag reduction induced by spanwise wall oscillation has been successfully applied to single-phase turbulence, however, there is few attentions is paid to the drag reduction of particle-laden channel flow by the aforementioned active technique. Therefore, the drag reduction of particle-laden channel flow by spanwise wall oscillation is studied in this paper by direct numerical simulations. The major concern is two-folded: the first is the turbulent modulation and mechanism of particle-laden channel flow induced by spanwise wall oscillation, and the second is the coupling effect of laden particles and wall oscillation on drag reduction. Comparing with non-oscillation particle-laden channel flow, the wall drag of particle-laden channel flow is reduced by spanwise wall oscillation. The optimal oscillation period is found to achieve the maximum drag reduction rate, which is similar with the trend of single-phase channel flow. With the same volume fraction, channel flow with small size particle exhibits large drag reduction. Comparing with non-oscillation single-phase turbulence, for small oscillation period scenario the coupling contribution of laden particles and wall oscillation has weak and even negative effect on drag reduction, as the oscillation period increases the coupling contribution becomes significant and the maximum magnitude is around 10% of the overall drag reduction.

2023, 55(5): 1087-1098. doi: 10.6052/0459-1879-22-590

HTML PDF

SIMULATIONS OF NON-ISOTHERMAL VISCOELASTIC COMPLEX FLOWS BY IMPROVED SPH METHOD

Xu Xiaoyang, Zhao Yuting, Li Jiayu, Yu Peng

Non-isothermal viscoelastic fluid flow phenomena widely exist in nature and industrial productions, such as oil reservoir engineering, injection molding, etc. These flows generally exhibit a non-isothermal state. Accurate prediction of non-isothermal flow mechanism and complex rheological properties of viscoelastic fluid has important engineering application value. In this paper, an improved smoothed particle hydrodynamics (SPH) method is proposed for the numerical simulation of non-isothermal viscoelastic complex flow, in which the viscoelastic properties of the fluid are characterized by the eXtended Pom-Pom constitutive model. To improve the accuracy of simulation results, a kernel function gradient correction algorithm is adopted. To enforce the boundary conditions flexibly, a boundary treatment method combining boundary particles and virtual particles is developed. To eliminate the tensile instability in the flow process, the particle migration technology is applied. The improved SPH method is used to numerically simulate the impact of a droplet on the solid wall and injection molding of an F-shaped cavity. The effectiveness of the improved SPH method in solving the non-isothermal viscoelastic fluid is verified by comparing the SPH results with those obtained by the Basilisk software. Good agreement between these two numerical solutions is achieved. The numerical convergence of the improved SPH method is evaluated by using several different initial particle spacings. The different flow characteristics of non-isothermal flow compared with isothermal flow are investigated. It is found that the introduction of temperature leads to stronger contraction behavior of droplet. The influences of some different thermal rheological parameters such as the Péclet number, the Reyonlds number, the Weissenberg number, the solvent viscosity ratio, the anisotropy parameter, the relaxation time ratio and the molecular chain arm number on the flow process are deeply analyzed. The numerical results show that the improved SPH method proposed in this paper can accurately and stably describe the heat transfer mechanism, complex rheological properties, and free surface variation characteristics of non-isothermal viscoelastic fluid.

2023, 55(5): 1099-1112. doi: 10.6052/0459-1879-22-602

HTML PDF

DIRECT PREDICTION OF MAXIMUM DEFLECTION FOR PLASTICALLY DEFORMED STRUCTURES UNDER INTENSE DYNAMIC PULSE

Yu Tongxi, Tian Lanren, Zhu Ling

After years of research, the membrane factor method (MFM) and saturation analysis (SA) method proposed and developed by Chinese scholars have been proven to be effective powerful tools in analyzing and predicting the large plastic deformation behavior of structural members such as beams and plates under intense dynamic loading such as impact and explosion. Based on recent results obtained by the combination of these two sets of theoretical tools, this paper proposes a direct prediction of deflection (DPD) method to predict the maximum (saturated) deflection of beams and plates subjected to intense loading pulses. This method does not rely on the governing equations of the structure; rather, it only needs to establish elementary equations based on the balance of internal and external work, whilst the former can be directly integrated from the expressions of relevant membrane factors. While the interaction between bending moment and membrane force (i.e., exact yield locus) is considered, the predictions on the maximum deflection can be simply obtained by solving the elementary equations, thus greatly simplifying the mathematical derivation. Compared with the complete solution, which considers both the exact yield criterion and the transient response phase, as well as the upper and lower bounds resulted from modal solution, the proposed DPD method can more simply yet still accurately account for the effect of membrane force on the load-carrying capacity of the structure in large deformation. Consequently, this DPD method can provide a series of calculation formulae on the maximum plastic deflection of beams and plates, which are more concise than complete solutions, more accurate than modal solutions, and easier for the use in engineering design. Combined with a refined pulse equivalency technique, this DPD method is expected to be further extended to other structures under general pulse loading and achieve a wide range of engineering applications.

2023, 55(5): 1113-1123. doi: 10.6052/0459-1879-22-607

HTML PDF

THE MODE AND SCATTERED ENERGY DISTRIBUTION OF GUIDED WAVES PROPAGATING IN TWO COUPLED PLANE-STRAIN LAYERS WITH RIGID BASE

Shan Yao, Li Xinran, Zhou Shunhua

The dynamic stability of subgrade in transition zones has become a key problem restricting the design of high-speed railway subgrade with a speed of 400 km/h and above. It urgent to explore the amplification mechanism of system dynamic response caused by non-uniform foundation from the perspective of wave and energy. In this paper, the foundation under track is reduced to a elastic layer which has a free surface and rigid bottom. The problem of vehicle induced elastic wave propagation in the transition zones in high-speed railway is refined into the problem of wave scattering in the inhomogeneous elastic layer with rigid base. A plane-strain model of two medium coupling elastic layers with rigid base is established. Facing with the dispersion equation of elastic layer with rigid base, the paper optimizes the method of finding roots in complex plane. Then, the dispersion analyses of the elastic layers that are assigned with geotechnical medium are carried out, and the corresponding multi-mode guided wave characteristics and the distribution of scattered energy are clarified. Furthermore, in terms of the thickness of elastic layer, stiffness ratio of two elastic layers and so on, comparative analyses are carried out at last. The results indicate that all of the guided wave modes in the elastic layer with rigid base have cut-off frequencies. When the thickness of the elastic layer decreases or the Young's modulus of the medium increases, the cut-off frequency of each order guided wave mode becomes higher. In scattering, the fundamental mode of the transmitted field can occupy the main energy. And as modes are excited one by one, the proportion of energy of higher modes of the reflected field and the transmitted field shows a “trade-off” state in the full frequency range. The energy distribution law will not be significantly changed when the elastic layer materials on both sides are exchanged, or the elastic layers thickness and the stiffness ratio is changed. On the whole, the energy is more easily concentrated in the softer elastic layer, and guided wave mode is more active in the initial frequency band after excitation and distributes more energy.

2023, 55(5): 1124-1137. doi: 10.6052/0459-1879-22-573

HTML PDF

PROPAGATION OF ELASTIC WAVE IN INFINITE CABLE WITH SMALL SAG CONSIDERING DAMPING

Li Lijun, Zeng Xiaohui, Cui Zhehua, Wu Han

Cable structures are widely used in electrical, civil, marine and aviation engineering. As cable in engineering longer and longer, the high-order vibration becomes more and more obvious. Accordingly, the disturbance propagation should be considered in the study. In the existing research on the propagation of elastic waves in cables, the damping is usually not considered. However, damping has an important influence on the propagation of waves. We developed the motion equation of three-dimensional elastic cable by considering damping into equation. The free propagation characteristics of in-plane and out-of-plane waves are discussed respectively by solving the equations of motion above, including frequency relation, phase velocity, group velocity. And then, the wave propagation law of the cable is further discussed by calculating the displacement response under the initial cosine pulse. Besides, we study the wave dispersion and the influence of damping on the propagation of elastic waves in cables. The results show that both in-plane and out-plane waves are dispersive while damping is considered. In addition, the in-plane waves are highly dispersive with the curvature considered. In addition, the crest of wave dissipates in wave propagation, and the response of trailing edge is higher than the leading edge while damping is considered.

2023, 55(5): 1138-1150. doi: 10.6052/0459-1879-22-606

HTML PDF

ADAPTIVE ISOGEOMETRIC BUCKLING ANALYSIS OF STIFFENED PANELS DRIVEN BY STIFFENER PATHS

Jin Lingzhi, Wang Yu, Hao Peng, Zhang Yueyi, Wang Bo

The stiffened thin-walled structures are broadly used in the lightweight design of aerospace structures. With the increase in structure size and geometric characteristics, more refined meshes are needed to meet the requirements of analysis accuracy. The conventional isogeometric method adopts the topological structure in the form of NURBS tensor product, which makes it challenging to achieve local refinement in the analysis process, and global refinement will increase unnecessary degrees of freedom. In order to improve the accuracy and efficiency of numerical analysis of stiffened plate and shell structures, an adaptive isogeometric buckling analysis method based on RPHT-spline (rational polynomial splines over hierarchical T-meshes) for stiffened structures is presented in this paper. The spline mesh can be refined locally and adaptively along the stiffener paths, which effectively improves the accuracy of isogeometric buckling analysis of stiffened panels with low degrees of freedom. Firstly, the skins and stiffeners are modelled using RPHT-spline surfaces and NURBS curves, respectively. The geometric modeling and numerical simulation adopt a unified geometric language to achieve the integration of modelling and analysis. Secondly, the geometric projection algorithm and spline interpolation algorithm are used to achieve the high-efficiency and high-precision strong coupling between skins and stiffeners. In addition, an adaptive mesh refinement method driven by the stiffener paths is established. Finally, two numerical examples, a curve stiffened plate and a grid stiffened shell, verify the efficiency and robustness of the proposed method. Compared with NURBS-based isogeometric analysis, the proposed method can significantly reduce the total degrees of freedom of the analysis model.

2023, 55(5): 1151-1164. doi: 10.6052/0459-1879-22-508

HTML PDF

TOPOLOGY OPTIMIZATION OF THIN SHELL STRUCTURES BASED ON ADAPTIVE BUBBLE METHOD

Zhang Hualin, Yang Dong, Shi Zhijun, Cai Shouyu

Combined with the isogeometric shell analysis (IGA) method, a new optimization design framework based on the adaptive bubble method (ABM) is proposed in this work, in order to effectively solve the topology optimization design problem of thin shell structures, and meet the high standards for the accuracy of analysis models as well as the quality of optimization results. The IGA technique has its natural advantages in thin shell analysis: on one hand, precise analysis models for thin shell structures are established with IGA, and model transformation operations and the resulting errors could therefore be avoided; on the other hand, the high-order continuity of physical fields to be solved can be guaranteed without setting the rotational degrees of freedom. Thanks to the mapping relationship related to the NURBS surface (i.e., the middle surface of thin shell), the structural topology evolution of a given shell surface can be achieved easily in the 2D regular parametric domain. In view of this, the ABM is adopted to carry out topology optimization in the parametric domain, and it contains three modules: the modeling of holes with closed B-splines (CBS), the insertion of holes via the topological derivative theory, and the fixed-grid analysis based on the finite cell method (FCM). It should be noted that holes are expressed in both parametric and implicit forms with CBS. The parametric form makes it convenient to import the structural model into the CAD system exactly. The implicit form not only facilitates the merging and separating operations of holes, but also can be well combined with the FCM which is far more convenient than trimming surface analysis (TSA). Theoretical analysis and numerical examples indicate that the proposed design framework could convert the complicated thin shell structural topology optimization problem into the simple one in the 2D domain, and optimized results with clear and smooth boundaries can be obtained with relatively few design variables.

2023, 55(5): 1165-1173. doi: 10.6052/0459-1879-22-562

HTML PDF

GENERALIZED GAUSS PRINCIPLE OF LEAST COMPULSION FOR VARIABLE-ACCELERATION DYNAMICAL SYSTEMS

Zhang Yi, Song Chuanjing, Zhai Xianghua

The motion with variable acceleration is common in daily life and engineering problems. Variable acceleration dynamics, also known as Newtonian jerky dynamics, has gained wide attention due to its application in chaos theory and nonlinear dynamics. Gauss principle is a differential variational principle with extreme value characteristics. Therefore, it is of great significance to study the generalized Gauss principle of dynamical systems with variable acceleration in both theory and application. In this paper, the generalized Gauss principle for dynamical systems with variable accelerated motion is presented and studied. Firstly, we introduce the concept of the generalized Gaussian variation in the jerky space. We take the derivative of d’Alembert principle of a particle with respect to time, and then calculate its dot product with the generalized Gaussian variation. By using the condition of ideal constraints in the sense of Gauss, we establish the generalized Gauss principle for dynamical systems with variable acceleration. On this basis, the generalized Gauss principle of least compulsion is established and proved by constructing the generalized compulsion function. The Appell form, Lagrange form and Nielsen form of the principle are given. Secondly, the extension of the principle to variable mass mechanics is explored. Starting from Meshchersky equation and taking its derivative with respect to time, and then calculating its dot product with the generalized Gaussian variation, we establish the generalized Gauss principle for variable-mass variable-acceleration dynamical systems with ideal constraints. The generalized compulsion function in the case of variable mass is constructed and the generalized Gauss principle of least compulsion for variable-mass variable-acceleration mechanical systems is established and proved. We take the Kepler-Newton problem as an example, and use the approach of the generalized Gauss least compulsion principle we presented to calculate, and verify the effectiveness of the method.

2023, 55(5): 1174-1180. doi: 10.6052/0459-1879-23-030

HTML PDF

HARVESTING PERFORMANCE AND DYNAMIC RESPONSES OF THE BISTABLE HARVESTER WITH A NONLINEAR RESONANT CIRCUIT

Liang Chao, Ma Hongye, Wang Ke, Yan Bo

The bistable harvester can achieve wide band and high-efficiency energy harvesting performance under low frequency and low excitation levels. Previous studies mainly use a simple resistor circuit to capture the energy in the bistable structures. This paper proposes a two-degree-of-freedom (DOF) nonlinear system formed by coupling a three-spring bistable structure with a nonlinear RLC (resistance-inductance-capacitance) resonant circuit for energy harvesting enhancement. The nonlinear electromagnetic coupling coefficient between the circuit and structure is obtained by the special configuration between permanents and coils. The governing equation of the two DOF nonlinear systems is acquired. The analytical responses of the current and displacement are derived by the harmonic balance method, whose stability is judged by the Jacobin matrix. The analytical solution is compared with the numerical solution. Results demonstrate that introducing a nonlinear two-order resonant circuit into the bistable energy harvester can further improve the harvesting responses and broaden the energy bandwidth. With the same circuit parameters, the nonlinear resonant circuit can achieve lower frequency energy harvesting performance through frequency doubling of the current compared with the traditional linear circuit. One can enhance the energy harvester performance by decreasing the resonant ratio between the resonant circuit and bistable structure, increasing the excitation amplitude, and decreasing the distance between two static equilibrium points. The system can realize the switching of single-period response, multi-period response, and chaotic responses by adjusting the resonant ratio between circuit and bistable structure, and excitation amplitude.

2023, 55(5): 1181-1194. doi: 10.6052/0459-1879-23-048

HTML PDF

FD-PINN: FREQUENCY DOMAIN PHYSICS-INFORMED NEURAL NETWORK

Song Jiahao, Cao Wenbo, Zhang Weiwei

Physics-informed neural network (PINN) is a method for solving partial differential equations by encoding model equations into neural network, which fits solutions by simultaneously minimizing equation residuals and approximating definite solution conditions or observation data. Despite the fact that this approach has the benefits of being mesh-free and allowing easy integration of observation data, it still suffers from drawbacks such as high cost of training and limited accuracy in finding solutions. To break these limitation, Frequency domain physics-informed neural network (FD-PINN) is proposed in this paper. The approach involves using discrete Fourier transform on a partial differential equation in the periodic spatial dimension. This transforms the equation into a lower-dimensional system of differential equations in the frequency domain, which are then used to constrain FD-PINN. Due to the fact that each equation within the system of differential equations not only has fewer independent variables, but also has a lower difficulty in solving it. Therefore, compared to the classical PINN using the original partial differential equation as a constraint, the advantage of FD-PINN is that it reduces the number of input samples and the difficulty of optimization, and can improve the solution accuracy while reducing training costs. To demonstrate the effectiveness of FD-PINN, we test it on three different partial differential equations: the heat equation, the Laplace's equation for flow around a cylinder, and the Burgers equation. The results show that FD-PINN generally reduces the solution error by 1-2 orders of magnitude and improves the training efficiency by more than 6 times.

2023, 55(5): 1195-1205. doi: 10.6052/0459-1879-23-169

HTML PDF

RELIABILITY-BASED TOPOLOGY OPTIMIZATION OF FAIL-SAFE STRUCTURES USING RESPONSE SURFACE METHOD

Wang Xuan, Shi Yuankun, Yang Bo, Cheng Changzheng, Long Kai

Traditional structures are more susceptible to local stiffness loss due to the lack of redundancy and problem of ignoring the influence of uncertain factors. This paper proposes an effective reliability-based topology optimization methodology for design problem of fail-safe structures under load uncertainty basing on response surface method, to improve the structural safety and ensure that the structure can still meet the service performance and reliability requirements even when local damage occurs. To this end, a double-loop reliability-based topology optimization model of minimizing the volume fraction while satisfying the probabilistic compliance constraint is established, in which the inner loop is used for reliability analysis and the outer loop is used for topology optimization. To solve the problem of high calculation cost of the derivative of response function with respect to random variables in reliability analysis, an explicit expression of response function with respect to random variables was established based on response surface method. The analytic sensitivity formulations of the response function with respect to design variables and random variables are deduced in detail, and the method of moving asymptotes (MMA) is used to solve the optimization problem. The response surface-based reliability design method is compared with the method based on analytic derivative, and Monte Carlo simulation is also carried out to verify the effectiveness and superiority of the proposed method, discussing the influence of standard deviation of random load on the optimization results. The optimization results show that the proposed method can effectively design the fail-safe structures that meets the specified reliability level, and the relative error of the reliability index of the optimized structures does not exceed 1.3%. In addition, the response surface-based reliability design method can save about 74% of the reliability analysis time compared with the reliability design method based on analytical derivative.

2023, 55(5): 1206-1216. doi: 10.6052/0459-1879-22-591

HTML PDF

Current Issue
2023, Volume 55, Issue 5

NoticeMORE+

Exquisite ArticlesMORE+

Download Center

Author Center

Current Issue 2023, Volume 55, Issue 5

NoticeMORE+

Exquisite ArticlesMORE+

Download Center

Author Center

Current Issue
2023, Volume 55, Issue 5