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2011 Vol. 32, No. 2
Published:
论文
0
A New Multiscale Computational Method for Mechanical Analysis of Periodic Truss Materials
DOI:
A new multiscale computational method is developed to study the mechanical properties of periodic lattice truss materials. The underlying idea is to construct numerically the multiscale base functions to reflect the heterogeneities of the unit cells and obtain the equivalent stiffness matrix of the unit cells of periodic truss materials. Then the problems only need to be solved on the large–scale meshes and the computational cost can be dramatically reduced. To consider the coupled effect among different directions in the multi-dimensional problems, the coupled additional terms of base functions for the interpolation of the vector fields are introduced. Numerical experiments show that the base functions constructed by the linear boundary conditions sometimes will have a strong boundary effect. While the oscillatory boundary conditions obtained by the oversampling technique and the periodic boundary conditions can greatly reduce the errors induced by the forcible deformations of the unit cells. Especially for the unit cells whose coarse-mesh scales are close to the small scales of heterogeneities, the periodic boundary conditions proposed can improve greatly the accuracy of the results. The advantage of the method developed is that the downscaling computation could be realized easily and the stress and strain in the unit cell can be obtained simultaneously in the multiscale computation. Thus the multiscale method studied here has good potential in the strength analysis of heterogeneous materials.
2011 Vol. 32 (2): 0-118 [
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1396
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Multi Geometrical Scale Optimization for Porous Structure and Material with Multi-Objective of Structural Compliance and Thermo Deformation
DOI:
Light weight is the eternal pursuit of spacecraft structures. Load carrying spacecraft structures experience severe mechanical loads and thermo environments, which lead the thermo deformation and stress to be the key issues of performance of spacecraft and equipment. Porous ceramic is one of the most competitive materials to compose this kind of structures because of its excellent mechanical properties in high temperature circumstance and potentials in multi-functional application. The authors attempt to use topology optimization technique to design the light weight structure composed of porous ceramic with uniform microstructure, which combines high stiffness with low thermal expansion in a predefined domain. A new multi-objective optimization formulation is developed for the multi geometrical scale topology optimization of structures and materials concurrently. The objective function is composed of two items. One is to minimize the structural compliance when only the mechanical loads are applied on structures, while the other is to minimize the thermal expansion of the outer spacecraft structure surface when only the thermo loads are applied. The two items are both normalized and then jointed through weighted coefficients to form a multi-objective function. The independent macro and micro densities are introduced as the design variables and penalization approaches are adopted in both scales, i.e. SIMP (Solid Isotropic Material Penalization) in micro material scale and PAMP (Porous Anisotropic Material Penalization) in macro structure scale. Optimizations of the two geometrical scales are integrated into one system through homogenization theory. In order to improve computational efficiency, the adjoint method is utilized to obtain the sensitivity. The SQP method is adopted and the volume preserving nonlinear density filtering based on Heaviside step function is used to prevent checkerboard patterns and to obtain a clear design. We apply the proposed multi-objective optimization model to a sandwich elliptically curved shell to investigate the concurrent multi-scale design of structure configuration and microstructure of porous ceramic. The numerical examples demonstrate that the porous material is conducive to enhance the multi-objective performance of curve shell structure when the available amount of material is insufficiently given. And an “optimum” material volume fraction is observed for the multi-objective optimization problem, and the performance of structures can not be improved by increasing material volume when the “optimum” volume fraction is reached. The influence of thickness of surface sheets on the optimal design is investigated at last.
2011 Vol. 32 (2): 0-132 [
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1330
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Boundary element analysis of the temperature field in coating structures
DOI:
Materials containing thin coatings are frequently used for the design of many industrial applications, profiting from its excellent physical and chemical qualities. However, due to the small size of its thickness, numerical analysis of the behavior of these structures represents a great challenge to researchers in engineering applications. The key to analyze coating structure problems by using boundary element method (BEM) is the accurate computation of nearly singular integrals. In this paper, the coating structure is divided into the substrate domain and the coating one by using a multi-domain boundary element approach, and then a general transformation method has been introduced to remove or damp out the near singularities of the kernel integrals in the coating domain. Both temperatures and fluxes are accurately computed by using the present method. Numerical examples demonstrate that the present method can effectively deal with coating structure problems even when its thickness is as small as 1E-10.
2011 Vol. 32 (2): 0-141 [
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673
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142
Research on creep experiments and rheological model of visco-plastic metal materials
The creep experiments have been done on Lc4 aluminum alloy, TC11 titanium alloy, the carbon constructional quality steels (20 steel, 35 steel) under high temperature, and on electro deposited nickel thin film under room temperature. The integral creep constitutive equation and differential stress-strain constitutive relationship can be established according to relevant rheological model named revised Burgers and the integral core of the creep has been achieved through the experiments. Comparing the calculation results conducted from the model with the experiment results, they were in good agreement. Moreover, the coefficient related with viscosity of visco-plastic materials were obtained through creep experiments’ datum. The viscosity coefficients under high temperature of the former three kind of materials were compared; and the mechanical characteristics of the loading, unloding and creep caves under room temperature of the electro deposited nickel thin film were also analyzed.
2011 Vol. 32 (2): 142-148 [
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1445
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149
Probability Density Evolution Process Analysis about the Damage of Gravity Dam based on Perturbation Theory
The research objective is to design and construct an improved method for damage reliability analysis of concrete gravity dam. Firstly, we use pseudo excitation method and Mazar damage model to analyze how to calculate damage expected value and variance excited by random earthquake loading and deterministic static load in the initial iterative step. Moreover, based on perturbation theory, we analyze probability density evolution process in other iterative steps. Finally, we give a test example to verify and analyze the convergence and stability of this method.
2011 Vol. 32 (2): 149-157 [
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663
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549
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158
DESIGN OF EXPERIMENTS AND SENSITIVITY ANALYSIS FOR ELECTROMIGRATION ON SOLDER JOINTS
This paper presents a algorithm for electromigration (EM) failure analysis based on ANSYS Multi-physics commercial software and FORTRAN codes with considering multiple driving migration mechanisms. The electromigration sensitivity analysis equation and the corresponding numerical algorithm are also proposed. The sensitivity analysis for solder joints is implemented when the involved EM sensitivity design variables are the activation energy, the initial self-diffusion coefficient and mechanical properties of the material parameters. Furthermore, the EM simulation for CSP structure is performed to get failure lifetime based on the full factorial design of experiments (DOE) by using 3D finite element analysis.
2011 Vol. 32 (2): 158-166 [
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667
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167
Nonlinear analysis of concrete wall at high temperature
A coupled elastoplastic-damage constitutive model for the numerical simulation of realistic failure in concretes at high temperature is developed in this paper. A general direct stress return mapping algorithm, using Newton-Raphson iteration, is derived. The stress vector and scalar internal state variables quantifying the incremental plasticity and damage are updated simultaneously. The consistent tangent modulus matrices for coupled chemo-thermo-hygro-mechanical analysis are formulated for use in the global Newton iterative procedure. A solution procedure with two hierarchical phases for the coupled elastoplastic-damage analysis is proposed. Numerical examples are given to demonstrate the validity of the presented algorithm and formulations, illustrate the capability of the proposed constitutive model in reproducing coupled chemo-thermo-hygro-mechanical behavior in concrete wall subjected to fire and thermal radiation.
2011 Vol. 32 (2): 167-175 [
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581
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176
Study on the Nonlinear Vibration of Axially Moving Cylindrical Shells Made from Composites
Runge-Kutta method and multiscale method were used to study nonlinear vibration characteristics of axially moving multi-Layered cylindrical shells made from composites. A nonlinear wave vibration equation of the thin cylindrical shell made from composites was established firstly, taking multilayer and axially movement into account, based on layered shell theory. The equation was discretized by Galerkin’s method and then interconnected modal equations were obtained. Runge-Kutta method was applied to analyze curves of amplitude-frequency characteristic with different parameters. The results show some nonlinear properties of the system such as the phenomenon of internal resonance due to two closed natural frequencies and soft feature. Finally, multiscale method was introduced to investigate approximate analytical solutions of the system with 1:1 internal resonance. The results indicate that excitation amplitude, damping and speed can affect response amplitude, range of interval resonance, coupling between two modes and soft feature of the system. Conclusions with different methods coincide and stability of the system is further discussed.
2011 Vol. 32 (2): 176-185 [
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676
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简报
186
APPLICATION RESEARCH OF MULTI-OBJECTIVE ROBUST OPTIMIZATION FOR DESIGH AND MANUFACTURE IN VEHICLE BODY
Conventional robust optimization design methodology is only concerned with optimization of a single response or quality characteristic. However, products are typically characterized by numerous quality characteristics and quality characteristics are often conflicted each other. Therefore, it is very important significance that to research a efficient and effective multi-objective robust optimization methodology. In this paper, we present that the mean and variance of product characteristics and constraints are constructed to use dual response surface methodology. At the foundation of that, integrating 6sigma with dual response surface methodology ,we establish a multi-objective robust optimization methodology based 6sigma. The method is applied to optimize vehicle crashworthiness and sheet metal forming. The optimal result significantly improves robust of vehicle crashworthiness and sheet metal forming. Numeral example has indicated that this method has higher precision and stronger project practicability.
2011 Vol. 32 (2): 186-196 [
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611
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197
Hygrothermal Post-Buckling of Elastic Beams under Point Space-Constraint
Li Shi-Rong
Based on the geometrically nonlinear theory for extensional Euler-Bernoulli beams and by using numerical shooting method, post-buckling behavior of elastic beams with immovable ends and a middle point space-constraint under hygrothrrmal loadings were studied. Especially, changes in the characteristics of the hygrothermal post-buckling deformation and the internal forces of the beam after its middle point deflection reaches the gap value and at the same time the constraint force arises. Curves of equilibrium paths and configurations of the beams depending on the middle point constraint force were presented.
2011 Vol. 32 (2): 197-202 [
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624
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493
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203
DIRECT FINITE ELEMENT METHOD TO A GENERALIZED TWO-DIMENSIONAL THERMO-ELASTIC COUPLED PROBLEM SUBJECT TO A THERMAL SHOCK
The direct finite element method is used to solve a L-S type generalized electromagneto-thermoelastic coupled dynamic problem of a rotating half-space. The results show that the method is very valid to obtain high calculation accuracy for L-S type generalized two-dimensional electromagneto-themoelastic coupled rotating problem subject to a thermal shock.. The L-S type generalized electromagneto-thermoelastic coupled governing equations are given, the general form of virtual displacement principle as well as the corresponding finite element equations are formulated in this paper. The distributions of dimensionless temperature, dimensionless displacement, dimensionless stress and dimensionless induced magnetic field are displayed graphically. From the distribution of temperate, the unique characteristic of heat wave front can be observed clearly in the location of heat wave front where a sharp change of temperature occurs. And it also can be found that rotation acts to decrease the magnitude of the real part of displacement, stress, induced magnetic field and insignificantly affect the magnitude of temperature.
2011 Vol. 32 (2): 203-209 [
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535
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539
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210
Multivariable Wavelet Finite Element Method for Analysis of Thin Plate
Abstract: Based on B-spline wavelet on the interval and generalized potential variational principle, a new multivariable wavelet finite element method was proposed in this study, and the new corresponding elements for square and skew thin plate were constructed. Firstly, formulations were derived from multivariable generalized potential energy functional. Then the matrix equation of thin plate was obtained by using BSWI as trial function. In this study, the generalized stress and strain were interpolated separately, so differentiation of displacement in traditional method of stress calculation was avoided, and the calculation error was reduced. Besides, the good approximation property of B-spline wavelet on the interval can further guarantee the solving accuracy. In the end, several numerical examples for bending and vibration analysis of square and skew thin plate verified the efficiency and superiority in solving generalized stress.
2011 Vol. 32 (2): 210-216 [
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1260
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487
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