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作者： Hui Xu School of Mathematics and Physics Mianyang Teachers’ College

Accurately tracking the propagation process of a wave front is important for studying the propagation law of shock *** this study,a novel arc-length numerical algorithm to effectively calculate the interruption of shock waves is proposed,and a systematic theoretical analysis and application of this research are ***,the arc-length numerical method is proposed based on the hyperbolic conservation model equation,and the basic concept of the arc-length numerical method of hyperbolic problems is ***,an introduction method for arc-length in multidimensional space is described from the perspective of tensor analysis,and the mathematical model of shock wave propagation problems in arc-length space is *** discrete solution of the spatial mathematical model of arc length is given,and control and smoothing factors are added to ensure shock wave propagation without ***,the numerical calculation of the Lax and double Mach reflection problems shows that the arc-length numerical algorithm can be widely used as a new calculation method for shock interruption problems.

关键词： arc-length Shock interruption Numerical method

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Nonlinear vibration analysis of a circular composite plate harvester via harmonic balance

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Acta Mechanica Sinica 2019年第4期35卷 912-925页

作者： Tian-Chen Yuan Jian Yang Li-Qun Chen Shanghai Institute of Applied Mathematics and Mechanics Shanghai University Shanghai 200072 China School of Urban Railway Transportation Shanghai University of Engineering Science Shanghai 201620 China Department of Mechanics Shanghai University Shanghai 200444 China Shanghai Key Laboratory of Mechanics in Energy Engineering Shanghai University Shanghai 200072 China

Alumped parameter transversevibration model of a composite plate harvester is analyzed via harmonic balance approaches. The harvester is mainly composed of a piezoelectriccircular composite clamped by two steel rings and a proof mass on the *** lumped parameter model is a 1.5 degree-of-freedom strongly nonlinear system with a higher order polynomial stiffness. Aharmonic balance approach is developed to analyze the system, and the resulting algebraic equations are numerically solved by adopting an arc-length continuation technique. Anincremental harmonic balance approach is also developedfor the lumped parameter model. The two approaches yieldthe same *** amplitude-frequency responses produced by the harmonic balance approach are validated by the numericalintegrations and the experimental data. The investigation reveals that there coexist hardening and softening characteristics in the amplitude-frequency response curves under sufficiently large excitations. The harvester with thecoexistenceof hardening and softening nonlinearitiescan outperform not only linear energy harvesters but also typical hardening nonlinear energy harvesters.

关键词： Piezoelectricenergy harvester Circular composite plate Transverse nonlinear vibration Harmonic balance arc-length continuation

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Explorations and Expectations of Equidistribution Adaptations for Nonlinear Quenching Problems

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Advances in Applied Mathematics and Mechanics 2013年第4期5卷 407-422页

作者： Matthew A.Beauregard Qin Sheng Department of Mathematics Baylor UniversityTX 76798-7328USA

Finite difference computations that involve spatial adaptation commonly employ an equidistribution *** these cases,a new mesh is constructed such that a given monitor function is equidistributed in some *** choices of the monitor function involve the solution or one of its many *** straightforward concept has proven to be extremely effective and ***,selections of core monitoring functions are often challenging and crucial to the computational *** paper concerns six different designs of the monitoring function that targets a highly nonlinear partial differential equation that exhibits both quenching-type and degeneracy *** the first four monitoring strategies are within the so-called primitive regime,the rest belong to a later category of the modified type,which requires the priori knowledge of certain important quenching solution *** examples are given to illustrate our study and conclusions.

关键词： Degeneracy quenching singularity adaptive differencemethod arc-length monitoring function splitting method

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Study on Key Issues of the One-step Inverse Method

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武汉理工大学学报 2006年第S1期28卷 116-120页

作者： HUANG Ying 1,2 ,RUAN Yi1,DU Ruxu2 (1.College of Logistic Engineering,Wuhan University of Technology,Wuhan 430070,China 2.Department of Automation & Computer-Aided Engineering,The Chinese University of Hong Kong,Hong Kong,China) College of Logistic Engineering Wuhan University of TechnologyWuhan 430070China Department of Automation & Computer-Aided Engineering The Chinese University of Hong KongHong KongChina College of Logistic Engineering Wuhan University of TechnologyWuhan 430070China Department of Automation & Computer-Aided Engineering The Chinese University of Hong KongHong KongChina

Even though the inverse method is less accurate than that of the incremental one,it has great potential in the conceptual design stage for its less calculation load and quick speed. However,it faces a number of unsolved problems,which limit its application. The first question is how to find a suitable initial solution while the other one is how to deal with the numerical problems caused by the vertical walls. In this paper,new methods have been proposed to solve above two questions. The methods have also been coded and applied to two parts to test its feasibility.

关键词： sheet metal forming inverse method modified arc-length method

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Post-Buckling Behavior of Laminated Composite Cylindrical Shells Subjected to Axial, Bending and Torsion Loads

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World Journal of Engineering and Technology 2015年第4期3卷 185-194页

作者： Yengula Venkata Narayana Jagadish Babu Gunda Ravinder Reddy Pinninti Markandeya Ravvala Department of Mechanical Engineering Sreenidhi Institute of Science and Technology Hyderabad India Advanced Systems Laboratory Kanchan Bagh Hyderabad India Department of Mechanical Engineering Chaitanya Bharathi Institute of Science and Technology Hyderabad India Department of Metallurgical Engineering JNTUH Hyderabad India

In present work, post-buckling behavior of imperfect (of eigen form) laminated composite cylindrical shells with different L/D and R/t ratios subjected to axial, bending and torsion loads has been investigated by using an equilibrium path approach in the finite element analysis. The Newton-Raphson approach as well as the arc-length approach is used to ensure the correctness of the equilibrium paths up to the limit point load. Post-buckling behavior of imperfect cylindrical shells with different L/D and R/t ratios of interest is obtained and the theoretical knock-down factors are reported for the considered cylindrical shells.

关键词： Post-Buckling Cylindrical Shells Eigen Imperfection Shapes Axial Compressive Load Bending Load Torsion Load arc-length Method Knock-Down Factor

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