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non-linear buckling analysis of imperfect thin spherical pressure hull for manned submersible

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Journal of Ocean Engineering and Science 2017年第4期2卷 293-300页

作者： SB.Pranesh Deepak Kumar V.Anantha Subramanian D.Sathianarayanan GA.Ramadass Department of Ocean Engineering Indian Institute of Technology MadrasChennai 600036India National Institute of Ocean Technology Ministry of Earth SciencesChennai 600100India

Thin spherical pressure hulls are used as a human occupancy in deep water applications.DNV and other standards specify the imperfection allowed for pressure hulls.Numerical analyses are carried out to find the buckling pressure for both perfect and imperfect thin spherical pressure hulls,considering the geometric and material non-linearities.It is observed that there is a huge variation in the elastic and inelastic buckling pressure in perfect spherical pressure hulls.Moreover,if the manufacturing imperfections are considered in the inelastic numerical analysis,still there is a reduction in the buckling pressure.Design criteria,for deep water pressure hulls,is that both buckling pressure and yield pressure must be greater than the design pressure.In the elastic analysis,if t/D>0.006 buckling pressure is always greater than the yield pressure whereas in the inelastic analysis,the buckling pressure is falling below the yield pressure for all t/D ratios.Hence,inelastic numerical analysis with manufacturing imperfection has to considered in the design of deep water spherical pressure hulls of manned submersibles.

关键词： Manned submersible Spherical pressure hull non-linear Buckling Imperfection Numerical analysis

Modelling of the Vortex-Induced Motion of A Single-Column Platform with non-linear Mooring Stiffness Using the Coupled Wake Oscillators

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China Ocean Engineering 2019年第4期33卷 459-467页

作者： HU Xiao-feng ZHANG Xin-shu YOU Yun-xiang DUAN Jin-long State Key Laboratory of Ocean Engineering School of Naval Architecture Ocean and Civil Engineering Shanghai Jiao Tong University Shanghai 200240 China Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration (CISSE) School of Naval Architecture Ocean and Civil Engineering Shanghai Jiao Tong University Shanghai 200240 China

A phenomenological model for predicting the vortex-induced motion (VIM) of a single-column platform with non- linear stiffness has been proposed. The VIM model is based on the couple of the Duffing-van der Pol oscillators and the motion equations with non-linear terms. The model with liner stiffness is presented for comparison and their results are compared with the experiments in order to calibrate the model. The computed results show that the predicted VIM amplitudes and periods of oscillation are in qualitative agreements with the experimental data. Compared with the results with linear stiffness, it is found that the application of non-linear stiffness causes the significant reductions in the in-line and transverse motion amplitudes. Under the non-linear stiffness constraint, the lock-in behavior is still identified at 8non-linear geometrically parameters show that both in-line and transverse non-linear characteristics can significantly affect the predict in-line and transverse motion amplitudes. Furthermore, the computed results for different aspect ratios indicate that the in-line and transverse motion amplitudes increase with the growth of aspect ratio, and the range of lock-in region is enlarged for the large aspect ratio.

关键词： vortex-induced motion single-column platform wake oscillators non-linear stiffness

Study of the internal characteristics of the stall in a centrifugal pump with a cubic non-linear SGS model

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Journal of Hydrodynamics 2019年第4期31卷 788-799页

作者： Xian-bei Huang Zhu-qing Liu Yao-jun Li Wei Yang Qiang Guo School of Hydraulic Energy and Power Engineering Yangzhou University Yangzhou 225127 China College of Water Resources and Civil Engineering China Agricultural University Beijing 100083 China

The stall in a centrifugal pump impeller under a quarter-load condition is investigated by using a third-order SGS model named the DCNM, for a better understanding of the rotation effect on the stall phenomenon. The study of the distributions of the Reynolds stresses, the production tei*m and the rotation term reveals that the production and the rotation jointly result in the non-uniform Reynolds stress distribution. Further study of the two components of the production and the rotation shows that they jointly transport a certain energy from the Reynolds component R、to Ruu.

关键词： Centrifligal pump large-eddy simulation non-linear model OpenFOAM stall

STABILITY OF GLOBAL MAXWELLIAN FOR non-linear VLASOV-POISSON-FOKKER-PLANCK EQUATIONS

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Acta Mathematica Scientia 2019年第1期39卷 127-138页

作者：廖杰王倩蓉杨雄锋 Department of Mathematics East China University of Science and Technology School of Mathematical Sciences Key Laboratory of Scientific and Engineering Computing (MOE) Shanghai Jiao Tong University

In this article, we establish the exponential time decay of smooth solutions around a global Maxwellian to the non-linear Vlasov–Poisson–Fokker–Planck equations in the whole space by uniform-in-time energy estimates. The non-linear coupling of macroscopic part and Fokker–Planck operator in the model brings new difficulties for the energy estimates, which is resolved by adding tailored weighted-in-v energy estimates suitable for the Fokker–Planck operator.

关键词： non-linear Vlasov–Poisson–Fokker–Planck equation global Maxwellian global a priori estimates exponential convergence

VALUE DISTRIBUTION OF MEROMORPHIC SOLUTIONS OF CERTAIN non-linear DIFFERENCE EQUATIONS

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Acta Mathematica Scientia 2019年第4期39卷 1173-1184页

作者：陈敏风高宗升张继龙 School of Mathematics and Statistics Guangdong University of Foreign Studies Guangzhou 510006 China LMIB and School of Mathematics and Systems Science Beihang University Beijing 100191 China

In this article, we consider the non-linear difference equation(f(z + 1)f(z)-1)(f(z)f(z-1)-1) =P(z, f(z))/Q(z, f(z)),where P(z, f(z)) and Q(z, f(z)) are relatively prime polynomials in f(z) with rational coefficients. For the above equation, the order of growth, the exponents of convergence of zeros and poles of its transcendental meromorphic solution f(z), and the exponents of convergence of poles of difference △f(z) and divided difference △f(z)/f(z)are estimated. Furthermore, we study the forms of rational solutions of the above equation.

关键词： non-linear difference equation meromorphic solution rational solution value dist ribution

The “Endogenous” Planning and Design Strategy of the Park Under the non-linear Thinking

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Journal of Landscape Research 2019年第6期11卷 40-44页

作者： HAN Guihong WU Wei Shanghai Institute of Technology Shanghai 200234China Shanghai Yingxiang Architectural Design Co. LtdShanghai 200235China Shanghai International Institute of Design&Innovation Tongji UniversityShanghai 200092China

Shanghai is in the period of urban transformation, so it is urgent to focus on building urban cultural brand, improving the quality of urban environment, and actively promoting urban fine design. The study combined the planning and design scheme of Chuansha Software Park, and used the non-linear thinking method to pay attention to the spatial practice of public significance from the aspects of planning spatial pattern, sharing community construction and site spirit, so as to explore the "endogenous" industrial park planning and design strategy, in order to provide reference for the planning and design of the park and decision-making consultation.

关键词： non-linear thinking Sharing community Site spirit “Endogenous” space

Unconditionally Explicit Stable Difference Schemes for Solving Some linear and non-linear Parabolic Differential Equation

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Journal of Applied Mathematics and Physics 2015年第11期3卷 1506-1521页

作者： Masaharu Nakashima Kagoshima-shi Taniyama Chuou 1-4328 891-0141 Japan

We present the numerical method for solution of some linear and non-linear parabolic equation. Using idea [1], we will present the explicit unconditional stable scheme which has no restriction on the step size ratio k/h2 where k and h are step sizes for space and time respectively. We will also present numerical results to justify the present scheme.

关键词： Runge-Kutta Methods Method of Lines Difference Equation non-linear PDE

non-linear Forces and Irreversibility Problem in Classical Mechanics

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Journal of Modern Physics 2014年第1期5卷 17-22页

作者： Vyacheslav Mikhaylovich Somsikov Alexey Igorevich Mokhnatkin Institute of Ionosphere Kamenskoe Plato Almaty Kazakhstan

Restrictions of classical mechanics which take place because of holonomic constraints hypothesis used for obtaining canonical Lagrange equation are analyzed. As it was shown that this hypothesis excludes non-linear terms in the expression for forces which are responsible for energy exchange between different degrees of freedom of a many-body system. An oscillator passing a potential barrier is considered as an example which demonstrated this fact. It was found that the oscillator can pass the barrier even if kinetic energy of its mass center is below the potential barrier’s height due to non-linear terms. This effect is lost because of holonomic constraints hypothesis. We also explained how one can derive a system’s motion equation without the use of holonomic constraints hypothesis. This equation can be used to describe non-linear irreversible processes within the frames of Newton’s laws.

关键词： non-linear Forces and Irreversibility Problem in Classical Mechanics

A non-linear finite element model of human L4-L5 lumbar spinal segment with three-dimensional solid element ligaments

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Theoretical & Applied Mechanics Letters 2011年第6期1卷 75-80页

作者： Zhitao Xiao,1 Liya Wang,1 He Gong,1, ) Dong Zhu,2, ) and Xizheng Zhang3 1)Department of Engineering Mechanics, Jilin University, Changchun 130012, China 2)Department of Orthopaedic Trauma No.1, Hospital of Jilin University, Changchun 130012, China 3)Institute of Medical Equipment, Academy of Military Medical Sciences, Tianjin 300161, China Jilin Univ Dept Engn Mech Changchun 130012 Jilin Peoples R China Hosp Jilin Univ Dept Orthopaed Trauma 1 Changchun 130012 Jilin Peoples R China Acad Mil Med Sci Inst Med Equipment Tianjin 300161 Peoples R China

This paper establishes a non-linear finite element model (NFEM) of L4-L5 lumbar spinal segment with accurate three-dimensional solid ligaments and intervertebral disc. For the purpose, the intervertebral disc and surrounding ligaments are modeled with four-nodal three-dimensional tetrahedral elements with hyper-elastic material properties. Pure moment of 10 N·m without preload is applied to the upper vertebral body under the loading conditions of lateral bending, backward extension, torsion, and forward flexion, respectively. The simulate relationship curves between generalized forces and generalized displacement of the NFEM are compared with the in vitro experimental result curves to verify NFEM. The verified results show that: (1) The range of simulated motion is a good agreement with the in vitro experimental data; (2) The NFEM can more effectively reffect the actual mechanical properties than the FE model using cable and spring elements ligaments; (3) The NFEM can be used as the basis for further research on lumbar degenerative diseases.

关键词： lumbar spine non-linear ligaments finite element analysis