应用数学和力学

Simulation of Water Waves Based on the Inter-Belt Finite Element Method

WU Feng, ZHONG Wan-xie

2015, 36(12): 1219-1227. doi: 10.3879/j.issn.1000-0887.2015.12.001

Abstract(1189) PDF(759)

Abstract:
Here the displacement method for the simulation of water waves was studied. Under the physical coordinate system, the displacements were taken as the unknown variables. Under the assumption of small deformation, the water incompressibility was satisfied through introduction of the flow function. Hence the variational principle of the analytic mechanics can be applied and the numerical results can be more conveniently got by efficient means of the interbelt finite element method, the canonical transformation and the symplectic conservation integration. 2 numerical examples show the correctness and potential of the proposed method.

A Fast POD-Based Method for Predicting Oil and Water Flow in Water-Drive Reservoir

SUN Xian-hang, XU Ming-hai, GONG Liang, JIA Xin-xin, ZHOU Hui

2015, 36(12): 1228-1237. doi: 10.3879/j.issn.1000-0887.2015.12.002

Abstract(1420) PDF(528)

Abstract:
A fast method based on the proper orthogonal decomposition (POD) technique for predicting oil and water flow in water-drive reservoir was proposed. The reduced order model of oil and water flow in water-drive reservoir was generated with the POD. An ensemble of 100 samples of pressure and water saturation snapshots in the time range of [0 d, 500 d] with an interval step of 5 d for the 2D water-drive reservoir model was obtained through numerical reservoir simulation, and the POD was applied to extract a reduced set of POD basis functions from these snapshots. After the injection and production parameters were changed continuously, the obtained POD basis functions combined with the reduced order model were used to predict the new physical fields. The research results show that fast and accurate predictions can be achieved with the proposed POD-based method, for the given example, the prediction errors of pressure and water saturation are less than 1.2% and 1.5%, respectively. What’s more, this POD-based method is 50 times faster in calculation than the traditional numerical reservoir simulation.

Research Progress and Development Trend of Numerical Simulation Technology for Unconventional Wells

GAO Da-peng, LIU Tian-yu, WANG Tian-jiao, YUAN He, WANG Dong>, LI Yong, LIU Ying-bo

2015, 36(12): 1238-1256. doi: 10.3879/j.issn.1000-0887.2015.12.003

Abstract(1351) PDF(764)

Abstract:
Compared with the numerical simulation of conventional wells, the numerical simulation of unconventional wells focuses on the characterization of multiphase flow in vertical and horizontal wellbores, the explanation of the velocity difference between different phases and the pressure loss due to friction, hydrostatic force, acceleration and slip of each phase, and the simulation of the downhole flow control equipment and other complex phenomena. The research progress and existing defects of the numerical simulation techniques for unconventional wells were summarized from 7 aspects including the flow equations for complex-structure wells, the multiphase pipe flow and well-reservoir coupling simulation, the multi-segment well model, the downhole flow control device simulation, the near-wellbore area coarsening, the downhole complex phenomena simulation and the embedded discrete fracture model. The wellbore-reservoir numerical coupling simulation based on the multi-segment well model, the extended well model and the reservoir model coupling simulation, the fluid-structure coupling numerical simulation, the downhole monitoring control equipment simulation, and the multi-segment fracture complex-structure well simulation, make the development trend in the future.

Elasticity Solutions for Cylindrical Bending of Functionally Graded Plates

YANG Yun-fang, YANG Bo, CHEN Wei-qiu, DING Hao-jiang

2015, 36(12): 1257-1264. doi: 10.3879/j.issn.1000-0887.2015.12.004

Abstract(1303) PDF(649)

Abstract:
The cylindrical bending of functionally graded rectangular plates under different loads was studied based on a generalization of the England-Spencer theory. The expansion formulae for displacements and the assumption that the material parameters can vary along the thickness direction in an arbitrary fashion were adopted. The elasticity solutions were obtained for an orthotropic functionally graded plate in cylindrical bending with an infinite length in y-direction. The effects of the boundary conditions, the material gradient and the thickness-to-span ratio on the static responses of the functionally graded plates were investigated through a numerical example. The proposed solutions are useful for the validation of various numerical methods or approximate plate theories.

Analysis of Circular Tunnel Stability Based on the Limit Strain Method

ABI Erdi, ZHENG Ying-ren, FENG Xia-ting, XIANG Yu-zhou

2015, 36(12): 1265-1273. doi: 10.3879/j.issn.1000-0887.2015.12.005

Abstract(1240) PDF(701)

Abstract:
The material yield and failure bear different mechanisms. There have been substantial research on yield criteria, but few strict rules about failure criteria. The ideal elastic-plastic model in the expression of stress was difficult to be used to differ between yield and failure, so the limit strain failure criterion was put forward, which was intended to predict the material local and overall failure. Compared with the slip-line field theory and the model experiment, the limit strain method was applied to a circular tunnel to analyze the damage process of the tunnel, including the damage depths of surrounding rock and the related safety coefficients. The work shows that the limit strain method helps to successfully predict the failure process and ultimate state of the circular tunnel, and obtain accurate safety coefficients. The present results are in good agreement with those out of the slip-line field method and the model experiment, which verifies the feasibility and effectiveness of this limit strain method. The limit strain criterion with clear mechanical meanings reflects the holistic process of material failure, and provides a promising method for the geotechnical material limit analysis.

An Effective Meshfree Method for Bending and Vibration Analyses of Laminated Composite Plates

WANG Wei, YI Shi-chao, YAO Lin-quan

2015, 36(12): 1274-1284. doi: 10.3879/j.issn.1000-0887.2015.12.006

Abstract(1611) PDF(598)

Abstract:
Numerical analysis of laminated plates’ bending and vibration problems was presented based on the high order shear and normal deformation plate theory (HOSNDPT) with the meshless method. For the usual radial point interpolation method (RPIM), the inverses of the moment matrices are required for each Gauss point or calculation point, and are limited by the radius of the domain. For the weighted node radial point interpolation method (WN-RPIM), the number of the inverses of the system matrices is equal to the number of nodes in the problem domain, which is far less than the number of Gauss points, so the WN-RPIM can greatly reduce the computation complexity of the moment matrices and overcome the limitations on the RPIM. First, the 3D plate displacement was decomposed into the product of the thickness-direction and in-plane displacements, and the orthogonal Legendre polynomials were used as basis functions in the thickness direction, the WN-RPIM was employed in plane to construct the shape functions. Then, the numerical calculation of the bending problems of laminated plates verified the accuracy and stability of the WN-RPIM. At last, the proposed method was extended to the numerical calculation of the vibration problems of laminated plates with different boundary conditions, different thickness-to-span ratios and different laying patterns. The numerical results show the applicability and effectiveness of the proposed method.

Study on Symmetries and Conserved Quantities of Vehicle Body Vibration Systems

ZHAI Xiao-yang, FU Jing-li

2015, 36(12): 1285-1293. doi: 10.3879/j.issn.1000-0887.2015.12.007

Abstract(1284) PDF(545)

Abstract:
Symmetries and conserved quantities of vehicle body vibration systems were studied with the Lie group method. The vertical translational vibration and the pitching vibration around the mass center were addressed by means of the Lagrangian functions to construct the vehicle body vibration model. According to this vibration system, the Noether symmetry theory and the Lie symmetry theory were derived via the introduction of the Lie group method. The existence of the Noether symmetries and the Lie symmetries of the system were proved with the corresponding conserved quantities obtained. This work provides a new symmetry solution to the vehicle body vibration problem, and meanwhile expands the application scope of the Lie group method.

A Unified Bond-Slip Model for HB-FRP Strengthened Concrete Structures

ZHANG Feng, XU Xiang-feng, LI Shu-cai

2015, 36(12): 1294-1305. doi: 10.3879/j.issn.1000-0887.2015.12.008

Abstract(1353) PDF(631)

Abstract:
In order to simplify the bond-slip models for the HB-FRP strengthening technology, the expression of a unified bond-slip model for HB-FRP strengthened concrete structures was assumed based on a previously built partition bond-slip model. The distribution of bond stress was deduced. The bond force of the HB-FRP was divided into 2 parts: one from the EB-FRP and the other from the steel fasteners. The relationship between load on FRP and slip was derived based on the energy method. The interfacial slip was investigated with the theoretical and numerical methods. The undetermined coefficients in the bond-slip model were formulated based on the model test results. The research results show that, the unified bond-slip model for HB-FRP strengthened concrete structures can effectively predict the bond strength and effective bond length of HB-FRP.

A Meso-Micromechanics Approach to the Strength Criteria for Particle-Reinforced Radiation-Shielding Materials

HE Zheng, WANG Xu-wei, Djimedo Kondo

2015, 36(12): 1306-1314. doi: 10.3879/j.issn.1000-0887.2015.12.009

Abstract(1416) PDF(641)

Abstract:
Based on the micromechanics homogenization theory, the macroscopic mechanical strength properties of radiation-shielding composite materials were investigated according to their meso-microstructures and local physical properties at micro-scale. Ductile micro-porous materials reinforced with rigid particles were studied. The strength criteria in view of the impacts of porosity and particle volume fraction were derived for metal matrix composites containing hard inclusions as well as other engineering composite materials (polymer matrix composites or geomaterials). Under the framework of the plastic limit analysis approach, the velocity field jump at meso-scale was introduced to describe the interfacial mechanical behavior between the matrix phase and the inclusion phase, and the rigid core unit cell model was applied in solution. In the end the velocity field in which the interfacial velocity equalled 0 was chosen for calculation, and the effects of the interfacial properties on the material strengths were discussed. The results show the effectiveness of the proposed multi-scale analysis framework.

New Iterative Judging Criteria for H-Tensors and Some Applications

WANG Feng, SUN De-shu

2015, 36(12): 1315-1323. doi: 10.3879/j.issn.1000-0887.2015.12.010

Abstract(1482) PDF(706)

Abstract:
H-tensors have wide applications in science and engineering, but it is difficult to determine whether a given tensor is an H-tensor or not in practice. Several new iterative judging criteria were given for H-tensors through construction of different positive diagonal matrices and introduction of some techniques of inequalities. For application, some sufficient conditions of the positive definiteness for an even-order real symmetric tensor were given. Results of the numerical examples illustrate the effectiveness of the presented criteria.

2015 Vol. 36, No. 12