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Energy conserving and decaying algorithms for corotational finite element nonlinear dynamic responses of thin shells

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Science China(Technological Sciences) 2012年第1期55卷 3311-3321页

作者： YANG JinSong XIA PinQi College of Aerospace Engineering Nanjing University of Aeronautics and AstronauticsNanjing 210016China

On the basis of the finite element corotational formulation for geometric nonlinear static analysis of thin shells with large rota- tion and small strain established before and from the generalized-a time integration algorithm, the energy conserving and de- caying algorithms for corotational formulation nonlinear dynamic response analysis of thin shells are established in this paper. Responses are solved by means of a predictor-corrector procedure. In the case of ignoring the structural damping, the conserv- ing or decaying total energy of structure and the controllable numerical damping for high frequency responses can ensure the numerical stability of the algorithm. The inertial parts are linearly interpolated directly in the fixed global coordinate system by using the element nodal displacement in the global coordinate system for obtaining the constant mass matrix, while the elastic parts adopt the corotational formulation. Hence, the whole formulation obtained in this paper is element independent. Through three typical numerical examples, the performances of the algorithm in this paper were compared with those of the classical Newmak and HHT-a algorithms to indicate that the algorithm in this paper could accurately solve nonlinear dynamic respons- es of thin shells with large displacements and large rotations.

关键词： thin shell nonlinear dynamics corotational formulation finite elements energy conserving and decaying algorithms

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Finite element corotational formulation for geometric nonlinear analysis of thin shells with large rotation and small strain

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Science China(Technological Sciences) 2012年第11期55卷 3142-3152页

作者： YANG JinSong XIA PinQi College of Aerospace Engineering Nanjing University of Aeronautics and AstronauticsNanjing 210016China

Based on the consistent symrnetrizable equilibrated （CSE） corotational formulation, a linear triangular flat thin shell element with 3 nodes and 18~ of freedom, constructed by combination of the optimal membrane element and discrete Kirchhoff trian- gle （DKT） bending plate element, was extended to the geometric nonlinear analysis of thin shells with large rotation and small strain. Through derivation of the consistent tangent stiffness matrix and internal force vector, the corotational nonlinear finite element equations were established. The nonlinear equations were solved by using the Newton-Raphson iteration algorithm combined with an automatic load controlled technology. Three typical case studies, i.e., the slit annular thin plate, top opened hemispherical shell and cylindrical shell, validated the accuracy of the formulation established in this paper.

关键词： thin shell geometric nonlinearity corotational formulation finite element

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Innovation for forming aluminum alloy thin shells at ultra-low temperature by the dual enhancement effect

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International Journal of Extreme Manufacturing 2022年第3期4卷 99-103页

作者： Fan Xiaobo Yuan Shijian School of Mechanical Engineering Dalian University of TechnologyDalianPeople’s Republic of China School of Materials Science and Engineering Harbin Institute of TechnologyHarbinPeople’s Republic of China

Integral thin shells made of high strength aluminum alloys are urgently needed in new generation transportation equipment. There are challenges to overcoming the co-existing problems of wrinkling and splitting by the cold forming and hot forming processes. An innovative technology of ultra-low temperature forming has been invented for aluminum alloy thin shells by the new phenomenon of ‘dual enhancement effect’. That means plasticity and hardening are enhanced simultaneously at ultra-low temperatures. In this perspective, the dual enhancement effect is described, and the development, current state and prospects of this new forming method are introduced. This innovative method can provide a new approach for integral aluminum alloy components with large size, ultra-thin thickness, and high strength. An integral tank dome of rocket with 2 m in diameter was formed by using a blank sheet with the same thickness as the final component, breaking through the limit value of thickness-diameter ratio.

关键词： aluminum alloy thin shell ultra-low temperature forming dual enhancement effect

Investigation of temperature effect on stress of flexspline

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Applied Mathematics and Mechanics(English Edition) 2014年第6期35卷 791-798页

作者：项青尹征南 Shanghai Institute of Applied Mathematics & Mechanics Shanghai Key Laboratory of Mechanics in Energy Engineering Shanghai University

The effect of temperature loading on the stress of a flexspline is investigated. Based on the geometric and mechanical characteristics of the harmonic gear flexspline, a circular thin shell model is presented in this paper. The theoretical solution for the flexspline under different displacement loads and different temperature fields is derived. Meanwhile, an impact factor formula, which reflects the effect of the temperatures of the inner and outer surfaces of the flexspline on the stress of the flexspline, is presented. Finally, numerical calculations by the finite element method （FEM） are adopted to verify the corresponding conclusions.

关键词： thermal stress harmonic flexspline thin shell finite element method (FEM)

The Time-Dependent Von Kármán shell Equation as a Limit of Three-Dimensional Nonlinear Elasticity

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Journal of Systems Science & Complexity 2021年第2期34卷 465-482页

作者： QIN Yizhao YAO Peng-Fei Department of Mathematical Science Tsinghua UniversityBeijing 100084China Key Laboratory of Systems and Control Institute of Systems ScienceAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049China

The asymptotic behaviour of solutions of three-dimensional nonlinear elastodynamics in a thin shell is considered,as the thickness h of the shell tends to *** the appropriate scalings of the applied force and of the initial data in terms of h,it’s verified that three-dimesional solutions of the nonlinear elastodynamic equations converge to solutions of the time-dependent von Kármán equations or dynamic linear equations for shell of arbitrary geometry.

关键词： Nonlinear elasticity thin shell time-dependent von Kármán equations

Multi-objective design optimization of composite submerged cylindrical pressure hull for minimum buoyancy and maximum buckling load capacity

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Defence Technology（防务技术） 2021年第4期17卷 1190-1206页

作者： Muhammad Imran Dong-yan Shi Li-li Tong Ahsan Elahi Hafiz Muhammad Waqas Muqeem Uddin College of Mechanical and Electrical Engineering Harbin Engineering University Harbin 150001China College of Aerospace and Civil Engineering Harbin Engineering University Harbin 150001China Pakhtunkhwa Energy Development Organization(PEDO) Khyber PakhtunkhwaPakistan

This paper presents the design optimization of composite submersible cylindrical pressure hull subjected to 3 MPa hydrostatic *** design optimization study is conducted for cross-ply layups[0_(s)/90_(t)/0_(u)],[0_(s)/90_(t)/0_(u)]s,[0_(s)/90_(t)]s and[90_(s)/0_(t)]s considering three uni-directional composites,***/Epoxy,Glass/Epoxy,and Boron/*** optimization study is performed by coupling a Multi-Objective Genetic Algorithm(MOGA)and Analytical *** the buoyancy factor and maximizing the buckling load factor are considered as the objectives of the optimization *** objectives of the optimization are achieved under constraints on the Tsai-Wu,Tsai-Hill and Maximum Stress composite failure criteria and on buckling load *** verify the optimization approach,optimization of one particular layup configuration is also conducted in ANSYS with the same objectives and constraints.

关键词： Multi-objective genetic algorithm Optimization Composite submersible pressure hull thin shell Material failure shell buckling

PERFORATION OF PLASTIC SPHERICAL shellS UNDER IMPACT BY CYLINDRICAL PROJECTILES

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Applied Mathematics and Mechanics(English Edition) 2006年第2期27卷 235-240页

作者：宁建国宋卫东 State Key Laboratory of Explosion Science and Technology Beijing Institute of Technology Beijing 100081 P. R. China

The objective is to study the perforation of a plastic spherical shell impacted by a cylindrical projectile. First, the deformation modes of the shell were given by introducing an isometric transformation. Then, the perforation mechanism of the shell was analyzed and an analytical model was advanced. Based on Hamilton principle, the governing equation was obtained and solved using Runge-Kuta method. Finally, some important theoretical predictions were given to describe the perforation mechanism of the shell. The results will play an important role in understanding the perforation mechanism of spherical shells impacted by a projectile.

关键词： thin shell impact perforation

Numerical simulation of the parabolic shell surface under blast wave loading

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Journal of Beijing Institute of Technology 2012年第4期21卷 427-433页

作者：侯俊亮蒋建伟房玉军 State Key Laboratory of Explosion Science and Technology Beijing Institute of Technology China South Industry Research Academy

Deformation of parabolic shell surface under explosion shock waves is a complex dynamic problem. Because of reflection and interference of blast wave, it＇s hard to analytically delineate the dynamic responds of radar parabolic shell surface on blast wave. To gain the characteristics of thin shell deformation under impulsive loading of blast wave, numerical simulation methods for blast load on the shell structure was studied and analyzed. Euler-Lagrange numerical simulation was implemen- ted by AUTODYN code to simulate the problem. Through analysis on deflection feature of radial po- sition under different explosive mass and detonation height, an equation was founded by fitting the deflection results from numerical simulation results of shockwave loading. Experiments were ar- ranged to confirm the validity of the formula. The results gained by simulation are consistent with experiments, and the formula can be used to delineate the deflection of aluminum alloy parabolic shell under blast loading.

关键词： blast wave thin shell simulation deflection

Hydrodynamic Interaction of Elastic Capsules in Bounded Shear Flow

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Communications in Computational Physics 2014年第9期16卷 1031-1055页

作者： D.V.Le Zhijun Tan Institute of High Performance Computing Agency for ScienceTechnology and Research1 Fusionopolis Way#16-16 ConnexisSingapore 138632 School of Mathematics and Computational Science Sun Yat-sen UniversityGuangzhou 510275China Province Key Laboratory of Computational Science Sun Yat-sen UniversityGuangzhou 510275China.

This paper presents a modified Loop’s subdivision algorithm for studying the deformation of a single capsule,the hydrodynamic interaction between two capsules and the hydrodynamic diffusion of a suspension of capsules in bounded shear flow.A subdivision thin-shell model is employed to compute the forces generated on the surface of the elastic capsule during *** capsule surface is approximated using the modified Loop’s subdivision scheme which guarantees bounded curvature and C1 continuity everywhere on the limit *** present numerical technique has been validated by studying the deformation of a spherical capsule in shear *** are also performed for a biconcave capsule over a wide range of shear rates and viscosity ratios to investigate its *** addition,the hydrodynamic interaction between two elastic capsules in bounded shear flow is *** on the wall separation distance,the trajectory-bifurcation points that separate reversing and crossing motions for both spherical and biconcave capsules can be *** to the spherical capsules,the biconcave capsules exhibit additional types of interaction such as rotation and head-on *** head-on collision results in a large trajectory shift which contribute to the hydrodynamic diffusion of a suspension.A suspension of a large number of biconcave capsules in shear flow is also simulated to show the ability of the modified scheme in running a large-scale simulation over a long period of time.

关键词： thin shell elastic capsules red-blood cells subdivision surfaces immersed boundary method Navier-Stokes equations.