A modified alternating direction implicit algorithm is proposed to solve the full-vectorial finite-difference beam propagation method formulation based on H fields. The cross-coupling terms are neglected in the first ...A modified alternating direction implicit algorithm is proposed to solve the full-vectorial finite-difference beam propagation method formulation based on H fields. The cross-coupling terms are neglected in the first sub-step, but evaluated and doubly used in the second sub-step. The order of two sub-steps is reversed for each transverse magnetic field component so that the cross-coupling terms are always expressed in implicit form, thus the calculation is very efficient and stable. Moreover, an improved six-point finite-difference scheme with high accuracy independent of specific structures of waveguide is also constructed to approximate the cross-coupling terms along the transverse directions. The imaginary-distance procedure is used to assess the validity and utility of the present method. The field patterns and the normalized propagation constants of the fundamental mode for a buried rectangular waveguide and a rib waveguide are presented. Solutions are in excellent agreement with the benchmark results from the modal transverse resonance method.展开更多
Chaotic vibrations of flexible non-linear Euler-Bernoulli beams subjected to harmonic load and with various boundary conditions（symmetric and non-symmetric）are studied in this work.Reliability of the obtained result...Chaotic vibrations of flexible non-linear Euler-Bernoulli beams subjected to harmonic load and with various boundary conditions（symmetric and non-symmetric）are studied in this work.Reliability of the obtained results is verified by the finite difference method（FDM）and the finite element method（FEM）with the Bubnov-Galerkin approximation for various boundary conditions and various dynamic regimes（regular and non-regular）.The influence of boundary conditions on the Euler-Bernoulli beams dynamics is studied mainly,dynamic behavior vs.control parameters { ωp,q0 } is reported,and scenarios of the system transition into chaos are illustrated.展开更多
Based on the dynamic governing equation of propagating buckle on a beam on a nonlinear elastic foundation, this paper deals with an important problem of buckle arrest by combining the FEM with a time integration techn...Based on the dynamic governing equation of propagating buckle on a beam on a nonlinear elastic foundation, this paper deals with an important problem of buckle arrest by combining the FEM with a time integration technique. A new conclusion completely different from that by the quasi-static analysis about the buckle arrestor design is drawn. This shows that the inertia of the beam cannot be ignored in the analysis under consideration, especially when the buckle propagation is suddenly stopped by the arrestors.展开更多
A modified alternating direction implicit approach is proposed to discretize the three-dimensional full-vectorial beam propagation method （3D-FV-BPM） formulation along the longitudinal direction. The cross-coupling ...A modified alternating direction implicit approach is proposed to discretize the three-dimensional full-vectorial beam propagation method （3D-FV-BPM） formulation along the longitudinal direction. The cross-coupling terms （CCTs） are neglected at the first substep, and then double used at the second substep. The order of two substeps is reversed for each transverse electric field component so that the CCTs are always expressed in an implicit form, thus the calculation is efficient and stable. Based on the multinomial interpolation, a universal finite difference scheme with a high accuracy is developed to approximate the 3D-FV-BPM formulation along the transverse directions, in which the discontinuities of the normal components of the electric field across the abrupt dielectric interfaces are taken into account and can be applied to both uniform and non-uniform grids. The corresponding imaginary-distance procedure is first applied to a buried rectangular and a GaAs-based deeply-etched rib waveguide. The field patterns and the normalized propagation constants of the fundamental and the first order modes are presented and the hybrid nature of the full-vectorial guided-modes is demonstrated, which shows the validity and utility of the present approach. Then the modal characteristics of the deeply- and shallow-etched rib waveguides based on the InGaAsp/InGaAsP strained multiple quantum wells in InP substrate are investigated in detail. The results are necessary for modeling and the design of the planar lightwave circuits or photonic integrated circuits based on these waveguides.展开更多
For exact estimation of efficiency of a buckle arrestor, it is necessary to take the effect of structural inertia into account in the analysis of buckle propagation on elastic structures after meeting arrestors. Under...For exact estimation of efficiency of a buckle arrestor, it is necessary to take the effect of structural inertia into account in the analysis of buckle propagation on elastic structures after meeting arrestors. Under this consideration, this paper deals with the dynamics of buckle arrest and its numerical simulation on the basis of the beam system model used by Chater and Hutchinson (1983). The FEM combined with an improving are-length control method is adopted to solve the dynamic equations describing the arresting of buckle propagation. A new group of parameters for arrestor design which differs greatly from that by the quasi-static analysis is obtained. The present results support the conclusion that the inertia of the beam cannot be neglected in such analysis.展开更多
In this paper, we propose a method to solve coupled problem. Our computational method is mainly based on conjugate gradient algorithm. We use finite difference method for the structure and finite element method for th...In this paper, we propose a method to solve coupled problem. Our computational method is mainly based on conjugate gradient algorithm. We use finite difference method for the structure and finite element method for the fluid. Conjugate gradient method gives suitable numerical results according to some papers.展开更多
The generalized finite difference method (GFDM) used for irregular grids is first introduced into the numerical study of thelevel set equation, which is coupled with the theory of detonation shock dynamics (DSD) descr...The generalized finite difference method (GFDM) used for irregular grids is first introduced into the numerical study of thelevel set equation, which is coupled with the theory of detonation shock dynamics (DSD) describing the propagation of thedetonation shock front. The numerical results of a rate-stick problem, a converging channel problem and an arc channel prob-lem for specified boundaries show that GFDM is effective on solving the level set equation in the irregular geometrical domain.The arrival time and the normal velocity distribution of the detonation shock front of these problems can then be obtainedconveniently with this method. The numerical results also confirm that when there is a curvature effect, the theory of DSDmust be considered for the propagation of detonation shock surface, while classic Huygens construction is not suitable anymore.展开更多
The present work deals with a new problem of thermoelasticity for an infinitely long and isotropic circular cylinder of temperature dependent physical properties.The inner and outer curved surfaces of the cylinder are...The present work deals with a new problem of thermoelasticity for an infinitely long and isotropic circular cylinder of temperature dependent physical properties.The inner and outer curved surfaces of the cylinder are subjected to both the mechanical and thermal boundary conditions.A finite difference model is developed to derive the solution of the problem in which the governing equations are uncoupled linear partial differential equations.The transient solution at any time can be evaluated directly from the model.In order to demonstrate the efficiency of the present model we consider a suitable material and obtain the numerical solution of displacement,temperature,and stresses inside the cylinder for the homogeneous-dependent material properties of the medium.The results are analyzed with the help of different graphical plots.展开更多
文摘A modified alternating direction implicit algorithm is proposed to solve the full-vectorial finite-difference beam propagation method formulation based on H fields. The cross-coupling terms are neglected in the first sub-step, but evaluated and doubly used in the second sub-step. The order of two sub-steps is reversed for each transverse magnetic field component so that the cross-coupling terms are always expressed in implicit form, thus the calculation is very efficient and stable. Moreover, an improved six-point finite-difference scheme with high accuracy independent of specific structures of waveguide is also constructed to approximate the cross-coupling terms along the transverse directions. The imaginary-distance procedure is used to assess the validity and utility of the present method. The field patterns and the normalized propagation constants of the fundamental mode for a buried rectangular waveguide and a rib waveguide are presented. Solutions are in excellent agreement with the benchmark results from the modal transverse resonance method.
文摘Chaotic vibrations of flexible non-linear Euler-Bernoulli beams subjected to harmonic load and with various boundary conditions（symmetric and non-symmetric）are studied in this work.Reliability of the obtained results is verified by the finite difference method（FDM）and the finite element method（FEM）with the Bubnov-Galerkin approximation for various boundary conditions and various dynamic regimes（regular and non-regular）.The influence of boundary conditions on the Euler-Bernoulli beams dynamics is studied mainly,dynamic behavior vs.control parameters { ωp,q0 } is reported,and scenarios of the system transition into chaos are illustrated.
基金This project is supported by the National Natural Science Foundation of China(NNSF 18572029).
文摘Based on the dynamic governing equation of propagating buckle on a beam on a nonlinear elastic foundation, this paper deals with an important problem of buckle arrest by combining the FEM with a time integration technique. A new conclusion completely different from that by the quasi-static analysis about the buckle arrestor design is drawn. This shows that the inertia of the beam cannot be ignored in the analysis under consideration, especially when the buckle propagation is suddenly stopped by the arrestors.
文摘A modified alternating direction implicit approach is proposed to discretize the three-dimensional full-vectorial beam propagation method （3D-FV-BPM） formulation along the longitudinal direction. The cross-coupling terms （CCTs） are neglected at the first substep, and then double used at the second substep. The order of two substeps is reversed for each transverse electric field component so that the CCTs are always expressed in an implicit form, thus the calculation is efficient and stable. Based on the multinomial interpolation, a universal finite difference scheme with a high accuracy is developed to approximate the 3D-FV-BPM formulation along the transverse directions, in which the discontinuities of the normal components of the electric field across the abrupt dielectric interfaces are taken into account and can be applied to both uniform and non-uniform grids. The corresponding imaginary-distance procedure is first applied to a buried rectangular and a GaAs-based deeply-etched rib waveguide. The field patterns and the normalized propagation constants of the fundamental and the first order modes are presented and the hybrid nature of the full-vectorial guided-modes is demonstrated, which shows the validity and utility of the present approach. Then the modal characteristics of the deeply- and shallow-etched rib waveguides based on the InGaAsp/InGaAsP strained multiple quantum wells in InP substrate are investigated in detail. The results are necessary for modeling and the design of the planar lightwave circuits or photonic integrated circuits based on these waveguides.
基金This work was financially supported by the National Natural Science Foundation of China(No.19572029)
文摘For exact estimation of efficiency of a buckle arrestor, it is necessary to take the effect of structural inertia into account in the analysis of buckle propagation on elastic structures after meeting arrestors. Under this consideration, this paper deals with the dynamics of buckle arrest and its numerical simulation on the basis of the beam system model used by Chater and Hutchinson (1983). The FEM combined with an improving are-length control method is adopted to solve the dynamic equations describing the arresting of buckle propagation. A new group of parameters for arrestor design which differs greatly from that by the quasi-static analysis is obtained. The present results support the conclusion that the inertia of the beam cannot be neglected in such analysis.
文摘In this paper, we propose a method to solve coupled problem. Our computational method is mainly based on conjugate gradient algorithm. We use finite difference method for the structure and finite element method for the fluid. Conjugate gradient method gives suitable numerical results according to some papers.
基金supported by the National Natural Science Foundation of China (Grant No. 11002029)
文摘The generalized finite difference method (GFDM) used for irregular grids is first introduced into the numerical study of thelevel set equation, which is coupled with the theory of detonation shock dynamics (DSD) describing the propagation of thedetonation shock front. The numerical results of a rate-stick problem, a converging channel problem and an arc channel prob-lem for specified boundaries show that GFDM is effective on solving the level set equation in the irregular geometrical domain.The arrival time and the normal velocity distribution of the detonation shock front of these problems can then be obtainedconveniently with this method. The numerical results also confirm that when there is a curvature effect, the theory of DSDmust be considered for the propagation of detonation shock surface, while classic Huygens construction is not suitable anymore.
文摘The present work deals with a new problem of thermoelasticity for an infinitely long and isotropic circular cylinder of temperature dependent physical properties.The inner and outer curved surfaces of the cylinder are subjected to both the mechanical and thermal boundary conditions.A finite difference model is developed to derive the solution of the problem in which the governing equations are uncoupled linear partial differential equations.The transient solution at any time can be evaluated directly from the model.In order to demonstrate the efficiency of the present model we consider a suitable material and obtain the numerical solution of displacement,temperature,and stresses inside the cylinder for the homogeneous-dependent material properties of the medium.The results are analyzed with the help of different graphical plots.
