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A three-dimensional dynamic thermo-mechanical coupling model (TMCM) has been developed to analyze re-entry evolution mechanism of spacecraft propulsion module subjected to aerodynamic/thermal loads. Firstly, a general dynamic thermo-mechanical coupling finite element algorithm is proposed based on TMCM. The accuracy of TMCM is verified by comparison with analytical solutions of one-dimensional problem and numerical solutions of three-dimensional problem. Then, the TMCM for a complex propulsion module is established, in which all the fuel tanks, gas cylinders, support frame and cone platform are taken into account. The external heat flux and pressure of the whole propulsion module are calculated by gas-kinetic unified algorithm (GKUA). Finally, the dynamic thermo-mechanical evolution mechanism of each component structure and the influence of radiation heat transfer are discussed separately during re-entry 90 km-75 km altitude range, and materials considered are stainless steel, carbon fiber composite and aluminum alloy. Simulation results reveal the evolution process of the temperature field, displacement field and stress field of the whole propulsion module. The TMCM provides a powerful tool for accurate prediction of disintegration failure during spacecraft re-entry through thermal and structural analysis of the structure. • A general dynamic thermo-mechanical finite element algorithm with radiation effects is presented. • A new one-way coupling method for calculating the thermo-mechanical response of aerodynamic and solid structures is established. • The evolutionary failure mechanism at different altitudes during the re-entry process of the spacecraft propulsion module can be accurately predicted. • The proposed algorithm can be widely used in numerical calculation of structures with different geometrical structures and different materials. [ABSTRACT FROM AUTHOR]

A coupled aerodynamic-thermoelastic analysis framework is presented to simulate the deformation and failure mechanism of metal truss structure for spacecraft under re-entry aerothermodynamic environment. The three-dimensional dynamic thermo-mechanical coupling finite element algorithm is developed by computable modeling of thermoelasticity and heat conduction equations to solve the thermo-mechanical coupling response of spacecraft structure. The aerodynamic boundary conditions such as temperature, heat flux and pressure distribution are computed and provided by the gas-kinetic unified algorithm (GKUA) based on the Boltzmann model equation. The linear interpolation method is designed and employed to couple the boundary conditions between the external aerodynamic flow field and the solid structure interface. The present thermo-mechanical coupling algorithm is verified on one-dimensional and two-dimensional transient heat flow problems with analytical solutions, and good consistency is achieved. The reliability of the GKUA for solving the boundary conditions of the external flow field and the dynamic thermo-mechanical coupling algorithm for the thermal response behavior of the internal structure material is verified by the consistency calculation of the internal and external temperature distribution. Then, the aerodynamic-thermoelastic analysis framework is further applied to study the deformation behavior of structural thermo-mechanical responses and failure mechanism of a hollow sphere under re-entry aerothermodynamic environment with emphasis placed on the influence of flight speeds, rarefied effects, algorithm schemes and damping effects. The numerical results obtained by the presented algorithm including the internal temperature, thermal stress and deformation distribution law are compared and analyzed. Finally, the deformation and failure mechanism of spacecraft structure during re-entry process are solved and analyzed by the present algorithm framework. The displacement, temperature and stress distribution contours of the structure are presented to make a preliminary understanding and evaluation on the process of spacecraft deformation and failure disintegration. It is indicated that the present coupled aerodynamic-thermoelastic analysis framework can provide a reliable, applicable and efficient platform for the thermo-mechanical coupling responses and failure mechanism of re-entry spacecraft in the end of life. [ABSTRACT FROM AUTHOR]

A new second-order two-scale (SOTS) analysis finite element algorithm is developed for the axisymmetric and spherical symmetric elastic problems with small periodic configurations. The axisymmetric structure considered is periodic in both radial and axial directions and homogeneous in circumferential direction, and the spherical symmetric structure is only periodic in radial direction and homogeneous in other two directions. The SOTS asymptotic expansions for the space problem, plane axisymmetric problem, and spherical symmetric problem are presented, and the main feature is that the anisotropic material is obtained by the homogenization. The analytical expressions of the cell functions and homogenized solutions for plane axisymmetric and spherical symmetric problems are obtained, and the error estimations of the expansions are established. The second-order asymptotic analysis finite-element algorithm is presented and the numerical examples are solved including the hollow cylinder, rotating disk and hollow sphere composed of periodic composite materials. The computational results demonstrate the effectiveness and accuracy of the SOTS asymptotic analysis algorithm, and the converging behavior of the asymptotic analysis algorithm agrees well with the theoretical prediction. It is also indicated that the stress distributions can be correctly computed only by adding the second-order correctors. [ABSTRACT FROM AUTHOR]

The micro-damage such as voids, inclusions, or cracks in interconnects of integrated circuits (IC) will evolve dramatically under different mass flow transport mechanisms driven by a variety of external physical fields, which will lead to the decrease of the reliability of the interconnects and the occurrence of failure in severe cases. Based on the microstructure evolution theory of solid materials, a phase field model under the mechanism of electric field-induced interface migration is constructed in this paper. The compatibility between the phase field model and the sharp interface model is proved by the asymptotic analysis. The modified theoretical solution of two-dimensional intragranular void in interconnects is derived, and the reliability of the finite element algorithm is verified by checking with the numerical results. Numerical simulation is carried out to discuss the effects of the electric field intensity χ , the initial morphological ratio β 0 , and the free energy density difference between the vapor-solid phase Δ g ˜ on the morphological evolution of the void. The results indicate that the external electric field drives the void to drift in the direction of the electric field, which is widely known as electromigration, and the morphology of the void becomes cylindrization gradually under the action of interface energy. With the increase of the external electric field, there are three morphological evolution trends of the void, including growth, equilibrium, and healing. The electric field critical value χ c r , representing the equilibrium state of the void, is used to distinguish different evolution trends. The increase of β 0 or the decrease of Δ g ˜ will lead to the acceleration of void drift velocity, the delay of cylindrization time, and the decrease of critical value, which aggravates the reliability problem of interconnects. Therefore, we should focus on the control of parameters such as χ , β 0 , and Δ g ˜ , so that the current density of the interconnects is under the condition of χ < χ c r . It can cause the intragranular void to shrink and even heal, effectively improving the reliability of IC and prolonging its service life. • A phase field model under interface migration induced by electric field is developed. • The bulk free energy and mobility are constructed by quartic double-well potential. • The electric field aggravates the drift, growth and cylindrization time of the void. • Critical electric field divides void evolution into growth, equilibrium and healing. • Critical electric field decreases as morphological ratio increases or Δ g ˜ decreases. [ABSTRACT FROM AUTHOR]

• A coupled thermo-mechanical finite element algorithm with computable model on damping effects is presented. • A new one-way coupling method for calculating the thermo-mechanical response of aerodynamic and solid structures is established. • The contribution of inertia term and coupling term to thermo-mechanical response is deeply studied. • The damping effect of re-entry process is considered for the first time. [Display omitted] A coupled thermo-mechanical finite element (TMFE) algorithm with the computable model on damping effects is proposed to simulate the thermo-mechanical coupling behavior and damping characteristics of a plate structure under re-entry aerodynamic environment. Firstly, an unconditionally stable implicit FE algorithm considering damping effects is constructed. Based on the coupled transient heat conduction problem, the proposed algorithm is verified through comparing the analytical and numerical solution. Combined with the gas-kinetic unified algorithm (GKUA), the aerodynamic force and heating are calculated as the temperature and pressure boundary conditions for the thermo-mechanical coupling calculation. The aerodynamic-structure boundary coupling verification is realized by comparing the GKUA calculated value of the flow field boundary with the TMFE results on the temperature and pressure of the plate surface. Then, the influences of element mesh density, inertia term, coupling term and damping effect on the thermo-mechanical coupling response of a plate are studied. The variation laws among temperature, displacement and stress fields are deeply revealed. The proposed algorithm offers a novel pathway to predict thermal flutter induced by thermo-mechanical coupling response of spacecraft structure. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we will discuss elliptic partial differential equation whose coefficients are constants. On basis of a new computing technique for Green function, we will propose a new effective finite element algorithm for that problem. Finally, we will give some numerical examples to investigate that finite element algorithm. [Copyright &y& Elsevier]

Abstract: On basis of He and Cui [W.-m. He, J.-z. Cui, A pointwise estimate on the 1-order approximation of , IMA Journal of Applied Mathematics 70 (2005) 241–269.], we propose two kinds of effective finite element algorithms to obtain numerical approximations of Green function defined in based on the method of multiscale asymptotic expansions; we present their pointwise error estimates and analyse their computer memory and CPU time; finally, we report results from numerical experiments. [Copyright &y& Elsevier]