In view of the occurrence of the coal and gas, outburst coal body separates in series of layer form, and tosses in a series of coal shell, and the morphological characteristics of the holes that formed in the coal lay...In view of the occurrence of the coal and gas, outburst coal body separates in series of layer form, and tosses in a series of coal shell, and the morphological characteristics of the holes that formed in the coal layers are very similar to some iterative morphological characteristics of the system state under highly nonlinear condition in chaos theory. Two kinds of morphology as well as their starting and end states are comparatively studied in this paper. The research results indicate that the outburst coal and rock system is in a chaotic state of lower nested hierarchy before outburst, and the process that lots of holes form owing to continuous outburst of a series of coal shells in a short time is in a rhythmical fast iterative stage of intermittent chaos state. And the state of the coal-gas system is in a stable equilibrium state after outburst. The behaviors of outburst occurrence, development and termination, based on the universal properties of various nonlinear mappings in describing complex problems, can be described by iterative operation in mathematics which uses the Logistic function f (x,μ)=μx(1-x) and the composite function F(3, x) = f(3)(x, μ) as kernel function. The primary equation of relative hole depth x and outburst parameter l in kernel function are given in this paper. The given results can deepen and enrich the understanding of physical essence of outburst.展开更多
Based on Donnell's shallow shell equation, a new method is given in this paper to analyze theoretical solutions of stress concentrations about cylindrical shells with large openings. With the method of complex var...Based on Donnell's shallow shell equation, a new method is given in this paper to analyze theoretical solutions of stress concentrations about cylindrical shells with large openings. With the method of complex variable function, a series' of conformal mapping functions are obtained from different cutouts' boundary curves in the developed plane of a cylindrical shell to the unit circle. And, the general expressions for the equations of a cylindrical shell, including the solutions of stress concentrations meeting the boundary conditions of the large openings' edges, are given in the mapping plane. Furthermore, by applying the orthogonal function expansion technique, the problem can be summarized into the solution of infinite algebraic equation series. Finally, numerical results are obtained for stress concentration factors at the cutout's edge with various opening's ratios and different loading conditions. This new method, at the same time, gives a possibility to the research of cylindrical shells with large non-circular openings or with nozzles.展开更多
Accurate boundary conditions of composite material plates with different holes are founded to settle boundary condition problems of complex holes by conformal mapping method upon the nonhomogeneous anisotropic elastic...Accurate boundary conditions of composite material plates with different holes are founded to settle boundary condition problems of complex holes by conformal mapping method upon the nonhomogeneous anisotropic elastic and complex function theory. And then the two stress functions required were founded on Cauchy integral by boundary conditions. The final stress distributions of opening structure and the analytical solution on composite material plate with rectangle hole and wing manholes were achieved. The influences on hole-edge stress concentration factors are discussed under different loads and fiber direction cases, and then contrast calculates are carried through FEM.展开更多
According to the mapping theory in complex plane, the geometric features of eigen frequency loci of systems undergoing free vibrations are investigated. It is concluded that the phenomena of curve coalescence and veer...According to the mapping theory in complex plane, the geometric features of eigen frequency loci of systems undergoing free vibrations are investigated. It is concluded that the phenomena of curve coalescence and veering can be described in a unified manner from the singularities of mapping from the complex parameter plane onto the complex frequency plane. The formation of a branch point in the parameter Space is the foundation of explaining localization and veering phenomena. By the use of condensation to reduce the dimension of a system, the scope of application of the geometric theory is widely expanded. The theory is applied to examples to verify the validity of the proposed approach. The present work is an improvement and extension of recent work by M. S. Traintafyllou et al..展开更多
In this paper, based on the theory of thick shells including effects of transverse shear deformations, a complex variables analytic method to solve stress concentrations in circular cylindrical shells with a small cut...In this paper, based on the theory of thick shells including effects of transverse shear deformations, a complex variables analytic method to solve stress concentrations in circular cylindrical shells with a small cutout is established A general solution and expression satisfying the boundary conditions on the edge of arbitrary cutouts are obtained. The stress problem can be reduced to the solution of an infinite algebraic equation series, and can be normalized by means of this method. Numerical results for stress concentration factors of the shell with a small circular and elliptic cutout are presented.展开更多
In this paper a complex variable analytic method for solving stress concentrations in the circular cylindrical shell is proposed. The problem to be solved can be summarized into the solution of an infinite algebraic e...In this paper a complex variable analytic method for solving stress concentrations in the circular cylindrical shell is proposed. The problem to be solved can be summarized into the solution of an infinite algebraic equation series. The solution can be normal and effective by means of this method. Numerical results for stress concentrations in the shell with a circular, elliptic cutout are graphically presented.展开更多
In this paper, based on complex variables and conformal mapping methods, using the refined dynamic equation of plates, elastic wave scattering and dynamic stress concentrations in plates with two cutouts were studied....In this paper, based on complex variables and conformal mapping methods, using the refined dynamic equation of plates, elastic wave scattering and dynamic stress concentrations in plates with two cutouts were studied. Applying the orthogonal function expansion method, the problem to be solved can be reduced into the solution of a set of infinite algebraic equations. According to free boundary conditions, numerical results of dynamic moment concentration factors in thick plates with two circular cutouts analyze that: there will be more complex interaction changes between two-cutout situation than single cutout situation. In the case of low frequency or high frequency and thin plate, the hole-spacing in the absence of coupling interactions was larger or smaller. The numerical results and method can be used to analyze the dynamics and strength of plate-like structures.展开更多
Purpose-This paper aims to describe a recently proposed algorithm in terrain-based cooperative UAV mapping of the unknown complex obstacle in a stationary environment where the complex obstacles are represented as cur...Purpose-This paper aims to describe a recently proposed algorithm in terrain-based cooperative UAV mapping of the unknown complex obstacle in a stationary environment where the complex obstacles are represented as curved in nature.It also aims to use an extended Kalman filter(EKF)to estimate the fused position of the UAVs and to apply the 2-D splinegon technique to build the map of the complex shaped obstacles.The path of the UAVs are dictated by the Dubins path planning algorithm.The focus is to achieve a guaranteed performance of sensor based mapping of the uncertain environments using multiple UAVs.Design/methodology/approach–An extended Kalman filter is used to estimate the position of the UAVs,and the 2-D splinegon technique is used to build the map of the complex obstacle where the path of the UAVs are dictated by the Dubins path planning algorithm.Findings-The guaranteed performance is quantified by explicit bounds of the position estimate of the multiple UAVs for mapping of the complex obstacles using 2-D splinegon technique.This is a newly proposed algorithm,the most efficient and a robust way in terrain based mapping of the complex obstacles.The proposed method can provide mathematically provable and performance guarantees that are achievable in practice.Originality/value-The paper describes the main contribution in mapping the complex shaped curvilinear objects using the 2-D splinegon technique.This is a new approach where the fused EKF estimated positions are used with the limited number of sensors’measurements in building the map of the complex obstacles.展开更多
Recently, Ye et al.[2] proved that the predictor-corrector method proposed by Mizuno et al[1] maintains O( L)-iteration complexity while exhibiting the quadratic convergence of the dual gap to zero under very mild con...Recently, Ye et al.[2] proved that the predictor-corrector method proposed by Mizuno et al[1] maintains O( L)-iteration complexity while exhibiting the quadratic convergence of the dual gap to zero under very mild conditions. This impressive result becomes the best-known in the interior point methods. In this paper, we modify the predictor-corrector method and then extend it to solving the nonlinear complementarity problem. We prove that the new method has a ( log(1/ε))-iteration complexity while maintaining the quadratic asymptotic convergence.展开更多
文摘In view of the occurrence of the coal and gas, outburst coal body separates in series of layer form, and tosses in a series of coal shell, and the morphological characteristics of the holes that formed in the coal layers are very similar to some iterative morphological characteristics of the system state under highly nonlinear condition in chaos theory. Two kinds of morphology as well as their starting and end states are comparatively studied in this paper. The research results indicate that the outburst coal and rock system is in a chaotic state of lower nested hierarchy before outburst, and the process that lots of holes form owing to continuous outburst of a series of coal shells in a short time is in a rhythmical fast iterative stage of intermittent chaos state. And the state of the coal-gas system is in a stable equilibrium state after outburst. The behaviors of outburst occurrence, development and termination, based on the universal properties of various nonlinear mappings in describing complex problems, can be described by iterative operation in mathematics which uses the Logistic function f (x,μ)=μx(1-x) and the composite function F(3, x) = f(3)(x, μ) as kernel function. The primary equation of relative hole depth x and outburst parameter l in kernel function are given in this paper. The given results can deepen and enrich the understanding of physical essence of outburst.
文摘Based on Donnell's shallow shell equation, a new method is given in this paper to analyze theoretical solutions of stress concentrations about cylindrical shells with large openings. With the method of complex variable function, a series' of conformal mapping functions are obtained from different cutouts' boundary curves in the developed plane of a cylindrical shell to the unit circle. And, the general expressions for the equations of a cylindrical shell, including the solutions of stress concentrations meeting the boundary conditions of the large openings' edges, are given in the mapping plane. Furthermore, by applying the orthogonal function expansion technique, the problem can be summarized into the solution of infinite algebraic equation series. Finally, numerical results are obtained for stress concentration factors at the cutout's edge with various opening's ratios and different loading conditions. This new method, at the same time, gives a possibility to the research of cylindrical shells with large non-circular openings or with nozzles.
基金This project is supported by National Natural Science Foundation of China(No.50175031).
文摘Accurate boundary conditions of composite material plates with different holes are founded to settle boundary condition problems of complex holes by conformal mapping method upon the nonhomogeneous anisotropic elastic and complex function theory. And then the two stress functions required were founded on Cauchy integral by boundary conditions. The final stress distributions of opening structure and the analytical solution on composite material plate with rectangle hole and wing manholes were achieved. The influences on hole-edge stress concentration factors are discussed under different loads and fiber direction cases, and then contrast calculates are carried through FEM.
基金This work was partially supported by the NNSFC and the ASFC.
文摘According to the mapping theory in complex plane, the geometric features of eigen frequency loci of systems undergoing free vibrations are investigated. It is concluded that the phenomena of curve coalescence and veering can be described in a unified manner from the singularities of mapping from the complex parameter plane onto the complex frequency plane. The formation of a branch point in the parameter Space is the foundation of explaining localization and veering phenomena. By the use of condensation to reduce the dimension of a system, the scope of application of the geometric theory is widely expanded. The theory is applied to examples to verify the validity of the proposed approach. The present work is an improvement and extension of recent work by M. S. Traintafyllou et al..
文摘In this paper, based on the theory of thick shells including effects of transverse shear deformations, a complex variables analytic method to solve stress concentrations in circular cylindrical shells with a small cutout is established A general solution and expression satisfying the boundary conditions on the edge of arbitrary cutouts are obtained. The stress problem can be reduced to the solution of an infinite algebraic equation series, and can be normalized by means of this method. Numerical results for stress concentration factors of the shell with a small circular and elliptic cutout are presented.
文摘In this paper a complex variable analytic method for solving stress concentrations in the circular cylindrical shell is proposed. The problem to be solved can be summarized into the solution of an infinite algebraic equation series. The solution can be normal and effective by means of this method. Numerical results for stress concentrations in the shell with a circular, elliptic cutout are graphically presented.
文摘In this paper, based on complex variables and conformal mapping methods, using the refined dynamic equation of plates, elastic wave scattering and dynamic stress concentrations in plates with two cutouts were studied. Applying the orthogonal function expansion method, the problem to be solved can be reduced into the solution of a set of infinite algebraic equations. According to free boundary conditions, numerical results of dynamic moment concentration factors in thick plates with two circular cutouts analyze that: there will be more complex interaction changes between two-cutout situation than single cutout situation. In the case of low frequency or high frequency and thin plate, the hole-spacing in the absence of coupling interactions was larger or smaller. The numerical results and method can be used to analyze the dynamics and strength of plate-like structures.
文摘Purpose-This paper aims to describe a recently proposed algorithm in terrain-based cooperative UAV mapping of the unknown complex obstacle in a stationary environment where the complex obstacles are represented as curved in nature.It also aims to use an extended Kalman filter(EKF)to estimate the fused position of the UAVs and to apply the 2-D splinegon technique to build the map of the complex shaped obstacles.The path of the UAVs are dictated by the Dubins path planning algorithm.The focus is to achieve a guaranteed performance of sensor based mapping of the uncertain environments using multiple UAVs.Design/methodology/approach–An extended Kalman filter is used to estimate the position of the UAVs,and the 2-D splinegon technique is used to build the map of the complex obstacle where the path of the UAVs are dictated by the Dubins path planning algorithm.Findings-The guaranteed performance is quantified by explicit bounds of the position estimate of the multiple UAVs for mapping of the complex obstacles using 2-D splinegon technique.This is a newly proposed algorithm,the most efficient and a robust way in terrain based mapping of the complex obstacles.The proposed method can provide mathematically provable and performance guarantees that are achievable in practice.Originality/value-The paper describes the main contribution in mapping the complex shaped curvilinear objects using the 2-D splinegon technique.This is a new approach where the fused EKF estimated positions are used with the limited number of sensors’measurements in building the map of the complex obstacles.
文摘Recently, Ye et al.[2] proved that the predictor-corrector method proposed by Mizuno et al[1] maintains O( L)-iteration complexity while exhibiting the quadratic convergence of the dual gap to zero under very mild conditions. This impressive result becomes the best-known in the interior point methods. In this paper, we modify the predictor-corrector method and then extend it to solving the nonlinear complementarity problem. We prove that the new method has a ( log(1/ε))-iteration complexity while maintaining the quadratic asymptotic convergence.
