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Rock fracture mechanism of buffer blasting with cushion layer at the borehole bottom

International Journal of Minerals,Metallurgy and Materials 2025年第2期32卷 325-334页

作者： Xinguang Zhu Chenxi Ding Zhe Sui Hong Su Xu Guo School of Civil and Resources Engineering University of Science and Technology BeijingBeijing 100083China Key Laboratory for mechanics in Fluid solid Coupling Systems Institute of MechanicsChinese Academy of SciencesBeijing 100190China School of mechanics and Civil Engineering China University of Mining and Technology(Beijing)Beijing 100083China School of Chemical and Blasting Engineering Anhui University of Science and TechnologyHuainan 232001China

This study primarily investigates the rock fracture mechanism of bottom cushion layer blasting and explores the effects of the bottom cushion layer on rock *** involves analyses of the evolution patterns of blasting stress,characteristics of crack distribution,and rock fracture features in the ***,blasting model experiments were carried out using the dynamic caustics principle to investigate the influence of bottom cushion layers and initiation methods on the integrity of the bottom rock *** experimental results indicate that the combined use of bottom cushion layers and inverse initiation effectively protects the integrity of the bottom rock ***,the process of stress wave propagation and dynamic crack propagation in rocks was simulated using the continuum-discontinuum element method(CDEM)and the Landau explosion source model,with varying thicknesses of bottom cushion *** numerical simulation results indicate that with increasing cushion thickness,the absorption of energy generated by the explosion becomes more pronounced,resulting in fewer cracks in the bottom rock *** illustrates the positive role of the cushion layer in protecting the integrity of the bottom rock mass.

关键词： bottom cushion layer blasting crack propagation continuum-discontinuum element method dynamic stress intensity factor

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Inverse problem of elastica of a variable-arc-length beam subjected to a concentrated load

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Acta Mechanica Sinica 2005年第5期21卷 444-450页

作者： Xiaowei Zhang Jialing Yang solid mechanics research centre Beijing University of Areonauticsand Astronautics Beijing 100083 China

An inverse problem of elastica of a variable-arclength beam subjected to a concentrated load is investigated. The beam is fixed at one end, and can slide freely over a hinge support at the other end. The inverse problem is to determine the value of the load when the deflection of the action point of the load is given. Based on the elasitca equations and the elliptic integrals, a set of nonlinear equations for the inverse problem are derived, and an analytical solution by means of iterations and Quasi-Newton method is presented. From the results, the relationship between the loads and deflections of the loading point is obtained.

关键词： Inverse problem. Elastica. Variable-arc-length beam-. Quasi-Newton method

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Exact Geometric Relationships, Symmetry Breaking and Structural Stability for Single-Walled Carbon Nanotubes

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Nano-Micro Letters 2011年第4期3卷 228-235页

作者： Tong Zhang Ze Shuai Yuan Li Hao Tan research Center for solid mechanics Beihang University

We pioneered a study about how the geometric relationship of single-walled carbon nanotubes(SWCNT) is influenced by curvature factor and non-planar geometry factor in cylindrical coordinate system based on the assumption of complete symmetry. The bond length and angle of every carbon-carbon bonds are determined by using the principle of the minimum energy. The results of the paper include(1) From the calculation result, the symmetry breaking appears for chiral carbon nanotubes, while the part symmetry appears for achiral carbon nanotubes with increasing curvature.(2) The synergistic effect of bond lengths and bond angles is first found.(3) We conclude that the influence of non-planar geometry factor can be completely ignored on bond lengths and bond angles when the curvature parameter has been included in the model.(4)The two fractal dimensions are given from the nanoscale to the macroscale for zigzag topology and armchair topology respectively. Fractal dimensions of SWCNT show special characteristics, varying with the length of SWCNT until the lengths approach infinity. The close and inevitable correlations among curvature, symmetry breaking and stability of SWCNTs can be summed up as: the increase of curvature causes symmetry breaking,and such symmetry breaking will further reduce the structural stability.

关键词： Geometry Structural Stability Symmetry Breaking Fractal Dimension

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Analytical dynamic model of elastic-plastic pipe-on-pipe impact

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Applied Mathematics and mechanics(English Edition) 2013年第6期34卷 731-746页

作者：闫冬梅孙玉鑫杨嘉陵 solid mechanics research Center Beihang University

Abstract The dynamic response of pipe-on-pipe impact is described by an analytical model. The model considers the impact of a whipping pipe with one end hinged and the other end free on a simply-supported target pipe at its midpoint. Combining with the contact theory, the Laplace transformation, and the inverse Laplace transformation method, an analytical model based on the tubular beam theory is proposed to study the elastic-plastic behavior of a target pipe laterally impacted by a whipping pipe. Numerical simulations using the explicit finite element code MSC/DYTRAN are also performed. The results are coincident with the theoretical prediction.

关键词： pipe impact dynamic response Laplace transformation analytical model

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INFLUENCE OF THE MIDDLE WEAK LAYER ON THE IMPACT BEHAVIOR OF LAMINATED STRUCTURES

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Acta Mechanica solida Sinica 2013年第3期26卷 263-276页

作者： Dongfang Wang Jialing Yang Yuxin Sun The solid mechanics research Center Beijing University of Aeronautics and Astronautics

In this paper, a calculation model based on the subsection displacement theory and the large deflection analysis is developed to describe the dynamic response of isotropic laminated circular plates impacted by a soft body. The model takes into account the interlaminar shear effect induced by the middle weak layer. It is proved by numerical examples that the difference between the model developed in this paper and that based on the classical laminated theory mainly depends on three factors, the elastic modulus of the glue, the radius of the circular plate and the impact force.

关键词： laminated glass interlaminar shear stress subsection displacement theory lami-nated circular plate

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Closed form solutions for free vibrations of rectangular Mindlin plates

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Acta Mechanica Sinica 2009年第5期25卷 689-698页

作者： Yufeng Xing Bo Liu The solid mechanics research Center, Beihang University,100191 Beijing, China The solid mechanics research Center Beihang University 100191 Beijing China

A new two-eigenfunctions theory, using the amplitude deflection and the generalized curvature as two fundamental eigenfunctions, is proposed for the free vibration solutions of a rectangular Mindlin plate. The three classical eigenvalue differential equations of a Mindlin plate are reformulated to arrive at two new eigenvalue differential equations for the proposed theory. The closed form eigensolutions, which are solved from the two differential equations by means of the method of separation of variables are identical with those via Kirchhoff plate theory for thin plate, and can be employed to predict frequencies for any combinations of simply supported and clamped edge conditions. The free edges can also be dealt with if the other pair of opposite edges are simply supported. Some of the solutions were not available before. The frequency parameters agree closely with the available ones through pb-2 Rayleigh-Ritz method for different aspect ratios and relative thickness of plate.

关键词： Mindlin plate Free vibration Closed form solution Separation of variable

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An eigenelement method and two homogenization conditions

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Acta Mechanica Sinica 2009年第3期25卷 345-351页

作者： Yufeng Xing Xingming Wang The solid mechanics research Center, Beihang University, 100083 Beijing, China The solid mechanics research Center Beihang University 100083 Beijing China

Under inspiration from the structure-preserving property of symplectic difference schemes for Hamiltonian systems, two homogenization conditions for a representative unit cell of the periodical composites are proposed, one condition is the equivalence of strain energy, and the other is the deformation similarity. Based on these two homogenization conditions, an eigenelement method is presented, which is characteristic of structure-preserving property. It follows from the frequency comparisons that the eigenelement method is more accurate than the stiffness average method and the compliance average method.

关键词： Composites Homogenization ,The equivalence of strain energy Deformation similarityEigenelement method

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Differential quadrature time element method for structural dynamics

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Acta Mechanica Sinica 2012年第3期28卷 782-792页

作者： Yu-Feng Xing Jing Guo The solid mechanics research Center Beihang University100191 BeijingChina

An accurate and efficient differential quadrature time element method （DQTEM） is proposed for solving ordi- nary differential equations （ODEs）, the numerical dissipation and dispersion of DQTEM is much smaller than that of the direct integration method of single/multi steps. Two methods of imposing initial conditions are given, which avoids the tediousness when derivative initial conditions are imposed, and the numerical comparisons indicate that the first method, in which the analog equations of initial displacements and velocities are used to directly replace the differential quadra- ture （DQ） analog equations of ODEs at the first and the last sampling points, respectively, is much more accurate than the second method, in which the DQ analog equations of initial conditions are used to directly replace the DQ analog equations of ODEs at the first two sampling points. On the contrary to the conventional step-by-step direct integration schemes, the solutions at all sampling points can be obtained simultaneously by DQTEM, and generally, one differential quadrature time element may be enough for the whole time domain. Extensive numerical comparisons validate the effi- ciency and accuracy of the proposed method.

关键词： Differential quadrature rule Direct integrationmethod Time element Phase error. Artificial damping

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New exact solutions for free vibrations of rectangular thin plates by symplectic dual method

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Acta Mechanica Sinica 2009年第2期25卷 265-270页

作者： Y. Xing B. Liu The solid mechanics research Center, Beihang University, 100083 Beijing, China The solid mechanics research Center Beihang University 100083 Beijing China

The separation of variables is employed to solve Hamiltonian dual form of eigenvalue problem for transverse free vibrations of thin plates, and formulation of the natural mode in closed form is performed. The closed-form natural mode satisfies the governing equation of the eigenvalue problem of thin plate exactly and is applicable for any types of boundary conditions. With all combinations of simplysupported （S） and clamped （C） boundary conditions applied to the natural mode, the mode shapes are obtained uniquely and two eigenvalue equations are derived with respect to two spatial coordinates, with the aid of which the normal modes and frequencies are solved exactly. It was believed that the exact eigensolutions for cases SSCC, SCCC and CCCC were unable to be obtained, however, they are successfully found in this paper. Comparisons between the present results and the FEM results validate the present exact solutions, which can thus be taken as the benchmark for verifying different approximate approaches.

关键词： Classical theory of thin plate Frequency Free vibrations Symplectic dual method Exact solution

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Response analysis based on smallest interval-set of parameters for structures with uncertainty

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Applied Mathematics and mechanics(English Edition) 2012年第9期33卷 1153-1166页

作者：王晓军王磊邱志平 Institute of solid mechanics Beihang University

An integral analytic process from quantification to propagation based on limited uncertain parameters is investigated to deal with practical engineering problems. A new method by use of the smallest interval-set/hyper-rectangle containing all exper- imental data is proposed to quantify the parameter uncertainties. With the smallest parameter interval-set, the uncertainty sponse and the least favorable response propagation evaluation of the most favorable re- of the structures is studied based on the interval analysis. The relationship between the proposed interval analysis method （IAM） and the classical IAM is discussed. Two numerical examples are presented to demonstrate the feasibility and validity of the proposed method.

关键词： quantification analysis smallest interval-set/hyper-rectangle uncertain structural response most favorable response least favorable response

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