应用数学和力学

Optical Measurement of Heated-Front-Surface Strains for Components in High Temperature Environments up to 1200 ℃

WU Dafang, WANG Huaitao, ZHU Fanghui

2018, 39(6): 631-644. doi: 10.21656/1000-0887.390084

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Abstract:
The external surface of a hypersonic vehicle flying in the atmosphere is facing a severe high-temperature environment due to aerodynamic heating. While in the aerodynamic thermal simulation test, the deformation measurement of heated front surface of aircraft components under high temperature conditions is extremely important and difficult. A heated-front-surface strain measurement system for hypersonic vehicle components was established, and by means of the digital image correlation method, the strain measurement for heat-resistant Al₂O₃ ceramic material with the front-surface temperature up to 1 200 ℃ was realized under the oxidizing environment. To demonstrate the correctness of the measuring method, the experimental results were compared with the calculation results from the relation between the thermal expansion coefficient and the temperature of Al₂O₃ material given by Hillman, and good agreement was obtained. The proposed 1 200 ℃ high temperature strain measurement system and the heated-front-surface strain measurement method for components under oxidation environments provide a important experimental method for the thermal strength analysis and safe reliability design of the hypersonic vehicle’s heated parts.

Research and Simulation of Mechanical Properties of GFRP Launching Tubes

HE Zepeng, BI Shihua, MA Yue, LUO Bixia

2018, 39(6): 645-656. doi: 10.21656/1000-0887.390085

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Abstract:
The launching tube is an important part of the rocket system. In the process of longterm storage, aging phenomena inevitably occur under various stress and environment factors, with important influences on the system reliability. The glass fibre reinforced plastic (GFRP) launching tube was studied through thermomechanical tests of the oneway GFRP slabs. The tests and measurements gave the basic thermodynamic performances of the oneway GFRP slab materials, including the basic mechanical properties after accelerated aging. The mechanical model for the GFRP launching tube was constructed and the thermodynamic characteristics of the GFRP launching tube under loads were analyzed. Then the creep models for the GFRP launching tubes were established, that is, the composite laminate model and the anisotropic model. With the structural model, the material parameters for the longterm performance analysis of nonmetallic directional tubes were provided.

Thermal Deformation Analysis and Structural Optimization of HighPrecision Reflector Engineering Models on Satellites

LI Yanyong, WEI Juanfang, JIANG Wenjian

2018, 39(6): 657-664. doi: 10.21656/1000-0887.390089

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Abstract:
The finite element modeling method and material parameter valuing method were presented for a 2 m diameter satellite reflector engineering model, including the honeycomb sandwich structure, the backframe tubes and the patches connecting the back frame and the reflector. The thermal deformation and the variation of pointing accuracy in unfolded work condition of the reflector under extreme high/low temperatures were analyzed. Based on the principle of minimum inorbit thermal deformation, the optimal design values of the parameters, including the section parameters of the backframe, the thickness of the backframe tubes, the connection mode and the density of patches, were obtained by means of the discrete data comparative analysis method. The structural optimization of the reflector engineering model was fulfilled.

Application of Strain-Rate-Dependent Material Models to Aero-Engine Honeycomb Casing Analysis

MENG Weihua, WANG Jianjun, MI Dong, WANG Wenjun, GUO Weiguo

2018, 39(6): 665-671. doi: 10.21656/1000-0887.390087

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Abstract:
For typical honeycomb materials used in turbine casings of aero-engines to prevent blades from scraping the casing, 2 commonly used material models, the Johnson-Cook model and the honeycomb equivalent model, and the relevant calibration methods were discussed. Then the 2 models were implemented in the simulation of a honeycomb impact test, and the simulation results were compared with the test results. It is shown that, through appropriate parameter calibrations and reasonable simplifications, the Johnson-Cook model provides satisfying results, in which the damage prediction is in good agreement with the test observation. Since the Johnson-Cook model is relatively easier to be implemented with enough prediction accuracy, it is recommended for blade-honeycomb scraping analysis of aero-engines.

An Equivalent Micropolar Beam Method for Grid Sandwich Structures Under Inhomogeneous Temperature Conditions

ZHANG Rui, FENG Ya, YANG Shuo

2018, 39(6): 672-680. doi: 10.21656/1000-0887.390086

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Abstract:
The grid sandwich structure was equivalent to a continuous micropolar elastic material with the method of cell energy equivalence, and the constitutive relation of the equivalent micropolar elastic material was obtained. Based on the geometrical relation and the equilibrium condition, the governing equations for the micropolar beam with thermal deformation were established, and the expression of the variation of the micropolar beam displacement under temperature load was given. By means of a grid sandwich cantilever beam under inhomogeneous temperature conditions, the effectiveness of the micropolar elastic equivalent was verified through comparison of the thermal bending deformation results calculated with the equivalent micropolar beam model, the sandwich beam model and the ANSYS finite element software, respectively. The results also show that, more stress and strain parameters are needed to describe the nonlocality due to the increase of constraints and the decrease of degrees of freedom when the discontinuous grid sandwich structure is equivalent to a continuous medium model.

Research on Dynamic Behavior and a Failure-Model for GH4133B Superalloy

MENG Weihua, WANG Jianjun, LI Jian, GUO Xiaojun, GUO Weiguo

2018, 39(6): 681-688. doi: 10.21656/1000-0887.390088

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Abstract:
According to the experimental results of dynamic properties of typical aero-engine casing material GH4133B at different temperatures (298～1 073K) and strain rates (10^-1～5×10³s^-1), and in view of intrinsic defects of the J-C model used in the analysis of casing acceptance in engineering applications, a more accurate revised J-C model was proposed to describe the mechanical behavior of GH4133B superalloy. In the meantime, an empirical failure model based on the J-C model was obtained based on test results of material stress triaxiality. Comparison between the model predictions and the experimental results shows that, the established constitutive model and the failure model well predict the plastic flow stress and the failure behavior of GH4133B.

Dynamic Responses of Saturated Porous Foundations Under Coupled Thermo-Hydro-Mechanical Effects

XIONG Chunbao, GUO Ying, DIAO Yu

2018, 39(6): 689-699. doi: 10.21656/1000-0887.380140

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Abstract:
Based on Lord and Shulman’s generalized thermoelastic theory with the relaxation time, the coupled thermo-hydro-mechanical problem for a poroelastic half-space foundation medium subjected to conoidal waves on its surface was investigated. Through modification of Biot’s theory of dynamic poroelasticity, the foundation medium was idealized as a uniform, fully saturated and poroelastic half-space body. The governing equations of the thermo-hydro-mechanical model were established. The analytical solutions of non-dimensional vertical displacement, excess pore water pressure, vertical stress and temperature were derived with the normal mode analysis method. In addition, the influences of different permeability coefficients and different frequencies on the non-dimensional vertical displacement, excess pore water pressure, vertical stress and temperature, were discussed.

A Multi-Level Method for Hierarchical Quadratic Discretizations of Thin-Walled Structures in 3D Heat Conduction

ZHANG Shen, XIAO Yingxiong, GUO Ruiqi

2018, 39(6): 700-713. doi: 10.21656/1000-0887.380035

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Abstract:
When the finite element method is applied to analyze the 3D thin-walled structures, some thin hexahedral elements are usually used in order to reduce the number of elements, and the corresponding higher-order elements are preferred since they have some obvious advantages in the calculation accuracy, the anti-distortion degree and so on. However, they have much higher computational complexity than the lower-order (e.g., linear) elements and the coefficient matrix of the linear algebraic equation system is severely ill-conditioned. The convergence of the commonly used solvers will deteriorate with the increasing size of the problem. An efficient and robust multi-level method was presented for the hierarchical quadratic discretizations of 3D thin-walled structures through combination of two special local block Gauss-Seidel smoothers and the DAMG algorithm based on the distance matrix. Since a hierarchical basis is used, those algebraic criteria are not needed to judge the relationships between the unknown variables and the geometric node types, and the grid transfer operators are also trivial. This makes it easy to find the coarse level (linear element) matrix derived directly from the fine level matrix, and thus the overall efficiency is greatly improved. The numerical results verify the efficiency and robustness of the proposed method.

Equivalent ThermoElasticity Analysis of 2D Lattice Structures With Periodic Unit Cells

ZHANG Zhaohui, LI Baohui, SHI Jiao

2018, 39(6): 714-727. doi: 10.21656/1000-0887.390025

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Abstract:
The thermo-elasticity of 2D lattice structures with periodic unit cells was studied. The lattice structure was homogenized as a pseudo-membrane (PM) structure and the equivalent thermal expansion coefficients (TECs) of the PM were derived. The TECs were expressed as explicit functions of the geometrical and physical parameters of the links in unit cells. Simultaneously, the elastic properties were re-defined based on the new geometry of the unit cell under thermal load. Numerical results were given to show the difference between the deformations of the structure under different thermo-mechanical loads, and a uniform pressure was applied on the top surface of the cantilever beam with or without thermal loads (the temperature increment was positive, negative or null, respectively). In simulation, the deformations of the lattice structure beams (with different sizes of unit cells) and the corresponding PM beams were calculated numerically. The theoretical solution of the beam deformation was also given with the elasticity of the PM beam. Differences between the solutions verify the correctness of the derived equivalent parameters. Results show the validity of the PM method for equivalent thermo-mechanical analysis of 2D lattice structures with periodic unit cells.

A New Method for Solving Heat Transfer Problems of Laminate Materials Based on the Differential Theory

LI Xixia, DAI Haiyan, LI Changyu

2018, 39(6): 728-736. doi: 10.21656/1000-0887.380116

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Abstract:
A new analytical method for solving heat transfer problems of laminate materials was proposed based on the differential theory. The curves of temperature variation at the interface of the laminate material were approximately linear in a small time interval. With the method of separation of variables, the analytical solution containing unknown coefficients of each layer in a small time interval was obtained. According to the continuous condition of energy at the interface, the unknown coefficients of each layer were determined. Then the temperature field in the whole time domain was obtained. Finally, the analytical method was used to solve the heat transfer problem of a 3-layer structure. The analytical results were compared with those of the finite element method, and the influences of several parameters on the temperature field were discussed, with the correctness of the proposed method verified.

2018 Vol. 39, No. 6