In this work,a new methodology is presented to mainly solve the fluid–solid interaction(FSI)equation.This methodology combines the advantages of the Newmark precise integral method(NPIM)and the dual neural network(DN...In this work,a new methodology is presented to mainly solve the fluid–solid interaction(FSI)equation.This methodology combines the advantages of the Newmark precise integral method(NPIM)and the dual neural network(DNN)method.The NPIM is employed to modify the exponential matrix and loading vector based on the DNN integral method.This involves incorporating the basic assumption of the Newmark-βmethod into the dynamic equation and eliminating the acceleration term from the dynamic equilibrium equation.As a result,the equation is reduced to a first-order linear equation system.Subsequently,the PIM is applied to integrate the system step by step within the NPIM.The DNN method is adopted to solve the inhomogeneous term through fitting the integrand and the original function with a pair of neural networks,and the integral term is solved using the Newton–Leibniz formula.Numerical examples demonstrate that the proposed methodology significantly improves computing efficiency and provides sufficient precision compared to the DNN method.This is particularly evident when analyzing large-scale structures under blast loading conditions.展开更多
The scattering of plane harmonic P and SV waves by a pair of vertically overlapping lined tunnels buried in an elastic half space is solved using a semi-analytic indirect boundary integration equation method. Then the...The scattering of plane harmonic P and SV waves by a pair of vertically overlapping lined tunnels buried in an elastic half space is solved using a semi-analytic indirect boundary integration equation method. Then the effect of the distance between the two tunnels, the stiffness and density of the lining material, and the incident frequency on the seismic response of the tunnels is investigated. Numerical results demonstrate that the dynamic interaction between the twin tunnels cannot be ignored and the lower tunnel has a significant shielding effect on the upper tunnel for high-frequency incident waves, resulting in great decrease of the dynamic hoop stress in the upper tunnel; for the low-frequency incident waves, in contrast, the lower tunnel can lead to amplification effect on the upper tunnel. It also reveals that the frequency-spectrum characteristics of dynamic stress of the lower tunnel are significantly different from those of the upper tunnel. In addition, for incident P waves in low-frequency region, the soft lining tunnels have significant amplification effect on the surface displacement amplitude, which is slightly larger than that of the corresponding single tunnel.展开更多
Extended finite element method (XFEM) implementation of the interaction integral methodology for evaluating the stress intensity factors (SIF) of the mixed-mode crack problem is presented. A discontinuous function and...Extended finite element method (XFEM) implementation of the interaction integral methodology for evaluating the stress intensity factors (SIF) of the mixed-mode crack problem is presented. A discontinuous function and the near-tip asymptotic function are added to the classic finite element approximation to model the crack behavior. Two-state integral by the superposition of actual and auxiliary fields is derived to calculate the SIFs. Applications of the proposed technique to the inclined centre crack plate with inclined angle from 0° to 90° and slant edge crack plate with slant angle 45°, 67.5° and 90° are presented, and comparisons are made with closed form solutions. The results show that the proposed method is convenient, accurate and computationally efficient.展开更多
A closed form of the title integral formula over the Gaussian-type orbitals is derived for the first time. The present closed form is analytical as the multiple hyper-geometric function of five variables.
The path integral Monte Carlo(PIMC) method is employed to study the thermal properties of C70 with one, two,and three H2 molecules confined in the cage, respectively. The interaction energies and vibrationally average...The path integral Monte Carlo(PIMC) method is employed to study the thermal properties of C70 with one, two,and three H2 molecules confined in the cage, respectively. The interaction energies and vibrationally averaged spatial distributions under different temperatures are calculated to evaluate the stabilities of(H2)n@C70(n = 1, 2, 3). The results show that(H2)2@C70is more stable than H2@C70. The interaction energy slowly changes in a large temperature range,so temperature has little effect on the stability of the system. For H2@C70and(H2)2@C70, the interaction energies keep negative; however, when three H2 molecules are in the cage, the interaction energy rapidly increases to a positive value.This implies that at most two H2 molecules can be trapped by C70. With an increase of temperature, the peak of the spatial distribution gradually shifts away from the center of the cage, but the maximum distance from the center of H2 molecule to the cage center is much smaller than the average radius of C70.展开更多
This paper is devoted to a new approach—the dynamic response of Soil-Structure System (SSS), the far field of which is discretized by decay or mapped elastodynamic infinite elements, based on scaling modified Bessel ...This paper is devoted to a new approach—the dynamic response of Soil-Structure System (SSS), the far field of which is discretized by decay or mapped elastodynamic infinite elements, based on scaling modified Bessel shape functions are to be calculated. These elements are appropriate for Soil-Structure Interaction problems, solved in time or frequency domain and can be treated as a new form of the recently proposed elastodynamic infinite elements with united shape functions (EIEUSF) infinite elements. Here the time domain form of the equations of motion is demonstrated and used in the numerical example. In the paper only the formulation of 2D horizontal type infinite elements (HIE) is used, but by similar techniques 2D vertical (VIE) and 2D corner (CIE) infinite elements can also be added. Continuity along the artificial boundary (the line between finite and infinite elements) is discussed as well and the application of the proposed elastodynamical infinite elements in the Finite element method is explained in brief. A numerical example shows the computational efficiency and accuracy of the proposed infinite elements, based on scaling Bessel shape functions.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.12072288,U2241274,and 12272319).
文摘In this work,a new methodology is presented to mainly solve the fluid–solid interaction(FSI)equation.This methodology combines the advantages of the Newmark precise integral method(NPIM)and the dual neural network(DNN)method.The NPIM is employed to modify the exponential matrix and loading vector based on the DNN integral method.This involves incorporating the basic assumption of the Newmark-βmethod into the dynamic equation and eliminating the acceleration term from the dynamic equilibrium equation.As a result,the equation is reduced to a first-order linear equation system.Subsequently,the PIM is applied to integrate the system step by step within the NPIM.The DNN method is adopted to solve the inhomogeneous term through fitting the integrand and the original function with a pair of neural networks,and the integral term is solved using the Newton–Leibniz formula.Numerical examples demonstrate that the proposed methodology significantly improves computing efficiency and provides sufficient precision compared to the DNN method.This is particularly evident when analyzing large-scale structures under blast loading conditions.
基金supported by the Tianjin Research Program of Application Foundation Advanced Technology (14JCYBJC21900)the National Natural Science Foundation of China under grants 51278327
文摘The scattering of plane harmonic P and SV waves by a pair of vertically overlapping lined tunnels buried in an elastic half space is solved using a semi-analytic indirect boundary integration equation method. Then the effect of the distance between the two tunnels, the stiffness and density of the lining material, and the incident frequency on the seismic response of the tunnels is investigated. Numerical results demonstrate that the dynamic interaction between the twin tunnels cannot be ignored and the lower tunnel has a significant shielding effect on the upper tunnel for high-frequency incident waves, resulting in great decrease of the dynamic hoop stress in the upper tunnel; for the low-frequency incident waves, in contrast, the lower tunnel can lead to amplification effect on the upper tunnel. It also reveals that the frequency-spectrum characteristics of dynamic stress of the lower tunnel are significantly different from those of the upper tunnel. In addition, for incident P waves in low-frequency region, the soft lining tunnels have significant amplification effect on the surface displacement amplitude, which is slightly larger than that of the corresponding single tunnel.
基金Projects(41172244,41072224) supported by the National Natural Science Foundation of ChinaProject(2009GGJS-037) supported by the Foundation of Youths Key Teacher by the Henan Educational Committee,China
文摘Extended finite element method (XFEM) implementation of the interaction integral methodology for evaluating the stress intensity factors (SIF) of the mixed-mode crack problem is presented. A discontinuous function and the near-tip asymptotic function are added to the classic finite element approximation to model the crack behavior. Two-state integral by the superposition of actual and auxiliary fields is derived to calculate the SIFs. Applications of the proposed technique to the inclined centre crack plate with inclined angle from 0° to 90° and slant edge crack plate with slant angle 45°, 67.5° and 90° are presented, and comparisons are made with closed form solutions. The results show that the proposed method is convenient, accurate and computationally efficient.
文摘A closed form of the title integral formula over the Gaussian-type orbitals is derived for the first time. The present closed form is analytical as the multiple hyper-geometric function of five variables.
基金supported by the National Natural Science Foundation of China(Grant Nos.11474207 and 11374217)
文摘The path integral Monte Carlo(PIMC) method is employed to study the thermal properties of C70 with one, two,and three H2 molecules confined in the cage, respectively. The interaction energies and vibrationally averaged spatial distributions under different temperatures are calculated to evaluate the stabilities of(H2)n@C70(n = 1, 2, 3). The results show that(H2)2@C70is more stable than H2@C70. The interaction energy slowly changes in a large temperature range,so temperature has little effect on the stability of the system. For H2@C70and(H2)2@C70, the interaction energies keep negative; however, when three H2 molecules are in the cage, the interaction energy rapidly increases to a positive value.This implies that at most two H2 molecules can be trapped by C70. With an increase of temperature, the peak of the spatial distribution gradually shifts away from the center of the cage, but the maximum distance from the center of H2 molecule to the cage center is much smaller than the average radius of C70.
文摘This paper is devoted to a new approach—the dynamic response of Soil-Structure System (SSS), the far field of which is discretized by decay or mapped elastodynamic infinite elements, based on scaling modified Bessel shape functions are to be calculated. These elements are appropriate for Soil-Structure Interaction problems, solved in time or frequency domain and can be treated as a new form of the recently proposed elastodynamic infinite elements with united shape functions (EIEUSF) infinite elements. Here the time domain form of the equations of motion is demonstrated and used in the numerical example. In the paper only the formulation of 2D horizontal type infinite elements (HIE) is used, but by similar techniques 2D vertical (VIE) and 2D corner (CIE) infinite elements can also be added. Continuity along the artificial boundary (the line between finite and infinite elements) is discussed as well and the application of the proposed elastodynamical infinite elements in the Finite element method is explained in brief. A numerical example shows the computational efficiency and accuracy of the proposed infinite elements, based on scaling Bessel shape functions.
