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A multiscale analysis and computational method based on the Second-Order Two-Scale (SOTS) approach are proposed for the elastic quadratic eigenvalue problems in the periodic composite domain. Two typical quadratic eigenvalue problems with different damping effects are considered, and by the asymptotic expansions of both the eigenfunctions and eigenvalues, the first- and second-order cell functions, the microscale features of this heterogeneous materials are defined successively. Then, the homogenized quadratic eigenvalue problems are derived and the second-order expansions of the eigenfunctions are formed. The eigenvalues are also broadened to the second-order terms by introducing proper auxiliary elastic functions defined in the composite structure, and the nonlinear expressions of the correctors of the eigenvalues are derived. The finite element procedures are established, linearized methods are discussed for solving the quadratic eigenvalue problems and the second-order asymptotic computations are performed. Effectiveness of the asymptotic model is demonstrated by both the qualitative and quantitative comparisons between the computed SOTS approximations and the reference solutions, and the converging behavior of the eigenfunctions are numerically verified. It is also indicated that the second-order correctors are of importance to reconstruct the detailed information of the original eigenfunctions within the micro cells. [ABSTRACT FROM AUTHOR]

A multiscale analysis and computational method based on the Second-Order Two-Scale (SOTS) approach are proposed for the elastic quadratic eigenvalue problems in the periodic composite domain. Two typical quadratic eigenvalue problems with different damping effects are considered, and by the asymptotic expansions of both the eigenfunctions and eigenvalues, the first- and second-order cell functions, the microscale features of this heterogeneous materials are defined successively. Then, the homogenized quadratic eigenvalue problems are derived and the second-order expansions of the eigenfunctions are formed. The eigenvalues are also broadened to the second-order terms by introducing proper auxiliary elastic functions defined in the composite structure, and the nonlinear expressions of the correctors of the eigenvalues are derived. The finite element procedures are established, linearized methods are discussed for solving the quadratic eigenvalue problems and the second-order asymptotic computations are performed. Effectiveness of the asymptotic model is demonstrated by both the qualitative and quantitative comparisons between the computed SOTS approximations and the reference solutions, and the converging behavior of the eigenfunctions are numerically verified. It is also indicated that the second-order correctors are of importance to reconstruct the detailed information of the original eigenfunctions within the micro cells.

This article presents a novel direct Jacobian total Lagrangian explicit dynamics (DJ‐TLED) finite element algorithm for real‐time nonlinear mechanics simulation. The nodal force contributions are expressed using only the Jacobian operator, instead of the deformation gradient tensor and finite deformation tensor, for fewer computational operations at run‐time. Owing to this proposed Jacobian formulation, novel expressions are developed for strain invariants and constant components, which are also based on the Jacobian operator. Results show that the proposed DJ‐TLED consumed between 0.70× and 0.88× CPU solution times compared to state‐of‐the‐art TLED and achieved up to 121.72× and 94.26× speed improvements in tetrahedral and hexahedral meshes, respectively, using GPU acceleration. Compared to TLED, the most notable difference is that the notions of stress and strain are not explicitly visible in the proposed DJ‐TLED but embedded implicitly in the formulation of nodal forces. Such a force formulation can be beneficial for fast deformation computation and can be particularly useful if the displacement field is of primary interest, which is demonstrated using a neurosurgical simulation of brain deformations for image‐guided neurosurgery. The present work contributes towards a comprehensive DJ‐TLED algorithm concerning isotropic and anisotropic hyperelastic constitutive models and GPU implementation. [ABSTRACT FROM AUTHOR]

In this article, some second-order time discrete schemes covering parameter 𝜃 combined with Galerkin finite element (FE) method are proposed and analyzed for looking for the numerical solution of nonlinear cable equation with time fractional derivative. At time tk−𝜃, some second-order 𝜃 schemes combined with weighted and shifted Grünwald difference (WSGD) approximation of fractional derivative are considered to approximate the time direction, and the Galerkin FE method is used to discretize the space direction. The stability of second-order 𝜃 schemes is derived and the second-order time convergence rate in L2-norm is proved. Finally, some numerical calculations are implemented to indicate the feasibility and effectiveness for our schemes. [ABSTRACT FROM AUTHOR]

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]

With the forthcoming global energy crisis, the nuclear power has a broader range of the applications. At the same time, the safe operation of the nuclear turbo-generator, particularly the calculation of the rotor shaft vibration, becomes incredibly important. This paper takes a nuclear power turbo-generator as an example and the finite element calculation model has been built up. During the process of the analytic algorithm, the current vector caused by the rotating rotor is replaced by the three-phase current vector induced by the static rotor windings. When symmetrical component transform and dq0 transform employed, the impact of positive current vector and negative current vector on the constant and second harmonic part of the electromagnetic torque has been discussed. Then a novel method for second harmonic electromagnetic torque calculation has been proposed. The data of the finite element algorithm is consistent with that of analytic algorithm, verifying the correctness of the method proposed by this paper. [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]

Liquid-structure interaction problem exists widely in the important engineering field, such as cooling tank and reaction tank in nuclear power plants. At present, the effective seismic analysis and design method of this kind of structure are insufficient. In this paper, by using Housner method and velocity potential description method, the seismic response of large liquid storage structure considering liquid-structure interaction is measured, whose results are compared with those obtained by the finite element method in Zhang et al. in order to study the applicability of these two analytic algorithms. The analysis results show the natural periods and inner forces calculated by Housner method are closer to those calculated by finite element method than those by velocity potential description method. The results of analytic methods are smaller than those of finite element method, which means it should be careful to apply analytic methods in seismic response analysis of large liquid storage structures. [ABSTRACT FROM AUTHOR]

A novel consequent-pole toroidal-winding outer-rotor (CPTW) Vernier permanent-magnet (VPM) machine is proposed in this paper. Different from a regular VPM machine, the stator and rotor of the proposed machine employ the consequent-pole and toroidal-winding configurations, which can significantly reduce magnet consumption, shorten the end-winding length, and improve the torque density. It is proved by a finite-element algorithm and prototype experiments that this machine can exhibit ∼20% higher back electromotive force and electromagnetic torque than that of a regular VPM machine, whereas its magnet consumption is only ∼60% of that in a regular VPM machine. [ABSTRACT FROM PUBLISHER]

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]

The Monte Carlo-based Characteristic Basis Finite-Element Method (MC-CBFEM) is developed for predicting the statistical properties of the 2-D electromagnetic scattering from objects (such as ship- and decoy-like objects) on or above random rough sea surfaces. At each realization of the Monte Carlo technique, the 1-D rough sea surface is randomly generated by using the Pierson-Moskowitz spectrum, and the bistatic radar cross section (RCS) is computed by employing the CBFEM approach. The CBFEM is a noniterative domain decomposition finite-element algorithm, which is designed to alleviate the challenges of the conventional finite-element method in solving large-scale electromagnetic problems. The CBFEM partitions the problem into a number of nonoverlapping subdomains and generates physics-based characteristic basis functions for the representation of the fields in each subdomain. Since this approach reduces the matrix size and lends itself to convenient parallelization, it is attractive for efficiently solving large-scale problems many times in the Monte Carlo simulation with the use of direct solvers and small-sized matrices. For a number of surface realizations, each of which can be considered as a sample from the random process specifying the surface, a family of bistatic RCS values is obtained as a function of incidence angle and surface roughness (or wind speed). The coherent (mean) and incoherent (variance) components of the RCS are illustrated with particular emphasis on the effects of surface roughness and the angles near grazing. Statistical characterization is also achieved by other means, such as correlation coefficient and density functions represented by histograms. [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]