应用数学和力学

2017 Vol. 38, No. 9

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A Time Domain Identification Method for Distributed Dynamic Loads on 1D Spatial Structures

WAN Cheng, YAN Bo

2017, 38(9): 967-978. doi: 10.21656/1000-0887.380006

Abstract(1119) PDF(808)

Abstract:
A time domain identification method for distributed dynamic loads on 1D spatial structures was proposed. Based on the idea of spatial and temporal divisions, the formula and process for load time history identification were derived. The load identification program was compiled by means of MATLAB, and the identification method was verified through 2 examples: a simply supported beam subjected to distributed dynamic loads and a power line subjected to stochastic wind loads. Moreover, the effect of noise on the load identification was investigated through numerical simulation. It is shown that the distributed loads can be accurately identified for linear problems and approximately identified for weakly nonlinear problems with the presented method, which provides an efficient way to identify distributed loads on engineering structures.

An Improved Adaptive Chaos Control Method for Inverse Reliability Analysis

LI Bin, HAO Peng, MENG Zeng, LI Gang

2017, 38(9): 979-987. doi: 10.21656/1000-0887.380001

Abstract(1232) PDF(1461)

Abstract:
The adaptive chaos control (ACC) method was an efficient and robust method for inverse reliability analysis. However, for strongly nonlinear concave performance functions, the computational efficiency of ACC still needs to be enhanced. Moreover, it might be trapped in the local optimum. Through revision of the update strategy for the chaos control factors, an improved adaptive chaos control method was presented for the inverse reliability analysis. Numerical results show that the proposed method effectively improves the rationality of adaptive selection of chaos control factors, so as to get better convergence and higher efficiency in computation. Furthermore, it makes a more efficient and robust approach for the reliability analysis and reliabilitybased design optimization.

A Symplectic Approach for Boundary-Value Problems of Linear Hamiltonian Systems

JIANG Xian-hong, DENG Zi-chen, ZHANG Kai, WANG Jia-qi

2017, 38(9): 988-998. doi: 10.21656/1000-0887.370365

Abstract(1241) PDF(898)

Abstract:
A symplectic approach based on canonical transformation and generating functions was proposed to solve boundary-value problems of linear Hamiltonian systems. According to the relationship between the generating function and the state-transition matrix, an interval merge recursive algorithm was constructed to calculate the coefficient matrices of the 2nd-type generating function for linear homogeneous Hamiltonian systems, which was further extended to nonhomogeneous cases. Then the properties of the generating function were used to transform the boundary-value problems to initial-value problems. Finally, the general initial-value problems were solved with the symplectic numerical method to preserve the geometric structure of the Hamiltonian system. Numerical simulations show the validity of the presented approach for linear homogeneous and nonhomogeneous problems, and the advantages of the symplectic numerical method to preserve the intrinsic properties of Hamiltonian systems.

A Modified Gradient Elastic Theory Considering Damage

ZHAO Bing, LIU Tao, HE Jian-hui, ZHU Hao-rui, LI Wei

2017, 38(9): 999-1008. doi: 10.21656/1000-0887.370285

Abstract(1040) PDF(954)

Abstract:
To describe the material mechanics behaviors depending on microstructure, the gradient elastic theory with significant advantages was investigated. The gradient elastic theory was combined with the damage theory to consider the influence of microstructure on material failure. Then a modified gradient elasticity damage theory was proposed, based on which the basic law of thermodynamics, the strain tensor, the damage variable and the scalar strain gradient tensor were taken as the state variables of the Helmholtz free energy. The Taylor expansion of the Helmholtz free energy function was conducted near the natural state, and the general expressions of the modified gradient elasticity damage constitutive functions were derived. The finite element code was programmed to simulate the development process of damage localization in soil specimens. The results show that, the traditional mesh dependence in numerical simulation can be removed under the modified gradient elasticity damage theory. The band of the damage localization does not concur with the damage, but occurs after the damage development to some extent.

The Explicit Expression of Erdogan’s Fundamental Solution for Plane Problems With Cracks

XU Zhi, FAN Xue-ming

2017, 38(9): 1009-1020. doi: 10.21656/1000-0887.370253

Abstract(1199) PDF(487)

Abstract:
The fundamental solution plays an essential role in many numerical methods such as the boundary element method (BEM), the method of fundamental solution and the boundarytype meshless methods. For fracture problems, application of fundamental solutions in domains with cracks can avoid deeming the crack surface as boundary condition and simplify the problems significantly. Based on the complex variable expression of Erdogan’s fundamental solution (EFS) for plane problems, the application conditions for EFS were noted, some faults in EFS were corrected and the explicit expression of the displacement in EFS was obtained. The computer program of the spline fictitious boundary element method (SFBEM) based on EFS was compiled to calculate the numerical solutions to mixed boundary condition problems. Numerical examples prove the correctness and accuracy of the derived explicit expression of EFS.

Stress Distribution Analysis of the Casings Under Suspended Packer Slips

HE Xia, LI Ming, WANG Guo-rong, ZHANG Min

2017, 38(9): 1021-1028. doi: 10.21656/1000-0887.370271

Abstract(1069) PDF(928)

Abstract:
The slips in a suspended packer are very important components to ensure success of the horizontal well reconstruction technology. They can support and fasten the packer and lock the rubber when they are anchored. But the casing is liable to failure under the effect of slips since it’s a thinwall cylinder, so it is very important to conduct mechanical analysis of casings under the effect of slips. The stress distribution of the casing under actions of slips was determined with an established mathematical model. The results show that the setting force of the packer increases the hoop stress of the casing and the suspended weight magnifies the axial stress, which jointly make the casing stress much higher and even cause failure of the casing. The theoretical model provides some useful references for evaluation of the casing stress state under the effect of packer slips for the horizontal well reconstruction technology.

Numerical Analysis of Geometrically Nonlinear Problems Based on the S-R Decomposition Theorem

SONG Yan-qi, HAO Liang-jun, LI Xiang-shang

2017, 38(9): 1029-1040. doi: 10.21656/1000-0887.370229

Abstract(1188) PDF(495)

Abstract:
To explore the numerical solution method for geometrically nonlinear problems, the theoretical derivation, the MATLAB programming and the finite element simulation were used together. Based on the S-R decomposition theorem, the interpolated element-free Galerkin method was applied to deduce the incremental variational equations through the updated co-moving coordinate formulation, which were solved with the 4-point Gauss integration method and the fixed point iteration method. Finally, the large deformations of exemplary elastic and elastoplastic planar cantilever beams were calculated and the results agreed well with those from the ANSYS simulation. The examples illustrate the correctness and rationality of the proposed geometrically nonlinear mechanics theory and the present numerical calculation method. The work provides a new basis for the solutions to geometrically nonlinear problems.

Study of Kilometer Drilling Stability at Different Strata Beneath the Floor

SHI Zhan-shan, LIANG Bing, WANG Yan, QIN Bing

2017, 38(9): 1041-1052. doi: 10.21656/1000-0887.370234

Abstract(764) PDF(880)

Abstract:
The stability of gas drainage drilling affects the quality of extraction engineering. Under the action of mining, underfloor kilometer drillings distributed at different horizons have different loading and unloading paths. To get the influence of mining on borehole stability, the loading and unloading paths of drillings located at different horizons were analyzed and accordingly the hole destruction area and the wall displacement at different loading and unloading rates and timevarying loading and unloading rates were numerically simulated. Through 10 numerical simulation schemes, the distribution of plastic zones and the loading and unloading displacement curves of the hole wall were obtained. Based on the numerically simulated relationship between the unloading rate and the hole deformation hysteresis, the shear stress calculation model around the borehole was built in view of the unloading rate. The results indicate that, during the loading process, the loading rate hardly inflences the destruction area arround the borehole; during the unloading process, the destruction area arround the borehole is related to the initial unloading stress and the unloading rate. The stress and the unloading rate at the hole location shall be synthetically considered in the placing of bedding boreholes.

The Nonlinear KdV Equation Under External Forcing With the Complete Coriolis Force

YIN Xiao-jun, YANG Lian-gui, SONG Jian, ZHANG Rui-gang, YANG Hong-li>, LIU Quan-sheng

2017, 38(9): 1053-1060. doi: 10.21656/1000-0887.370297

Abstract(1102) PDF(481)

Abstract:
The nonlinear KdV equation under external forcing was deduced from the potential vorticity equation involving both the vertical and the horizontal components of the Coriolis force with the perturbation method near the equatorial Rossby waves. Then the periodic solution of the model was obtained by means of the Jacobi elliptic functions. It is shown that the horizontal components of the Coriolis force play an important role in the structures of the Rossby waves.

Classical Solutions of Motion for Dyon Systems

XU Xue-yan, CHEN Hai-bo, ZHANG Hong-bin, DING Guang-tao

2017, 38(9): 1061-1070. doi: 10.21656/1000-0887.380046

Abstract(1216) PDF(514)

Abstract:
According to the mechanics theories and the classical electromagnetism, the motion of 2-dyon systems was studied. Some integrals of motion, including the energy integral, the total angular momentum integral and the Runge-Lenz-like integral, were derived from the differential equations of motion for the system, then the SO(4) symmetry of the system was exposed. With the inverse problem method of variational calculus, the Lagrangian function and the Hamiltonian function for the 2-dyon system were constructed. The classical motion of the system is completely integrable, the equations of the orbit and the relation between radial distance r and time t are solvable.

Modified Halpern Iteration and Viscosity Approximation Methods for Split Feasibility Problems in Hilbert Spaces

YANG Li, LI Jun

2017, 38(9): 1072-1080. doi: 10.21656/1000-0887.380106

Abstract(1059) PDF(466)

Abstract:
In infinitedimensional Hilbert spaces, the modified Halpern iteration and viscosity approximation methods for solving the split feasibility problems (SFPs) were proposed. When the parameters satisfy certain conditions, it is proved that the sequences generated with the proposed algorithms converge strongly to a solution to the split feasibility problem. The main findings improve and extend some recent results by Deepho and Kumam.