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FINITE DEFORMATION OF A CLASS OF RECTANGULAR RUBBER RINGS SUBJECTED TO END AXIAL LOADS

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Acta Mechanica Solida Sinica 2012年第2期25卷 144-151页

作者： Wenzheng Zhang Xuegang Yuan Hongwu Zhang jiusheng ren State Key Laboratory of Structural Analysis for Industrial Equipment Department of Engineering MechanicsFaculty of Vehicle Engineering and MechanicDalian University of TechnologyDalian 116024China School of Science Dalian National UniversityDalian 116600China Shanghai Institute of Applied Mathematics and Mechanics Shanghai UniversityShanghai 200072China

The problem of finite deformation of an incompressible rectangular rubber ring with an internal rigid body, where the ring is subjected to equal axial loads at its two ends, is examined. A reasonable mathematical model is formulated by using the nonlinear field theory and the implicit analytical solutions are derived. Then numerical simulations are implemented to further illustrate the results and obtain some meaningful conclusions. The deformation of the lateral surface of the ring becomes larger with the increasing axial loads, the decreasing ratio of the inner and outer radii and the increasing height of the ring.

关键词： neo-Hookean material rectangular rubber ring axial load finite deformation implicit analytical solution

DYNAMIC CHARACTERISTICS IN INCOMPRESSIBLE HYPERELASTIC CYLINDRICAL MEMBRANES

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Acta Mechanica Solida Sinica 2010年第5期23卷 420-427页

作者： Datian Niu Xuegang Yuan Changjun Cheng jiusheng ren School of Science Dalian Nationalities University Dalian 116600 China Shanghai Institute of Applied Mathematics and Mechanics Shanghai University Shanghai 200072 China

In this paper, the dynamic characteristics are examined for a cylindrical membrane composed of a transversely isotropic incompressible hyperelastic material under an applied uniform radial constant pressure at its inner surface. A second-order nonlinear ordinary differential equation that approximately describes the radial oscillation of the inner surface of the membrane with respect to time is obtained. Some interesting conclusions are proposed for different materials, such as the neo-Hookean material, the Mooney-Rivlin material and the Rivlin-Saunders material. Firstly, the bifurcation conditions depending on the material parameters and the pressure loads are determined. Secondly, the conditions of periodic motion are presented in detail for membranes composed of different materials. Meanwhile, numerical simulations are also provided.

关键词： incompressible hyperelastic material cylindrical membrane dynamical character- istic nonlinear periodic oscillation

COUPLING EFFECTS OF VOID SHAPE AND VOID SIZE ON THE GROWTH OF AN ELLIPTIC VOID IN A FIBER-REINFORCED HYPER-ELASTIC THIN PLATE

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Acta Mechanica Solida Sinica 2012年第3期25卷 312-320页

作者： jiusheng ren Hanhai Li Changjun Cheng Xuegang Yuan Department of Mechanics Shanghai UniversityShanghai 200444China Shanghai Key Laboratory of Mechanics in Energy and Environment Engineering Shanghai 200444China College of Science Dalian Nationalities UniversityDalian 116600China

The growth of a prolate or oblate elliptic micro-void in a fiber reinforced anisotropic incompressible hyper-elastic rectangular thin plate subjected to uniaxial extensions is studied within the framework of finite elasticity. Coupling effects of void shape and void size on the growth of the void are paid special attention to. The deformation function of the plate with an isolated elliptic void is given, which is expressed by two parameters to solve the differential equation. The solution is approximately obtained from the minimum potential energy principle. Deformation curves for the void with a wide range of void aspect ratios and the stress distributions on the surface of the void have been obtained by numerical computation. The growth behavior of the void and the characteristics of stress distributions on the surface of the void are captured. The combined effects of void size and void shape on the growth of the void in the thin plate are discussed. The maximum stresses for the void with different sizes and different void aspect ratios are compared.

关键词： fiber reinforced hyper-elastic material rectangular thin plate with void void shapeand void size potential energy principle growth of void

梅里雪山植物稳定碳同位素组成及其内在水分利用效率随海拔梯度的变化

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生态学杂志 2024年第6期43卷 1558-1565页

作者：蔡锦枫薛子静黄康祥张远袁博森任久生史晓宜蒲焘石福习江西农业大学林学院鄱阳湖流域森林生态系统保护与修复国家林业与草原局重点实验室南昌330045 东华理工大学水资源与环境工程学院南昌330013 浙江师范大学地理与环境科学学院金华321000 中国科学院西北生态环境资源研究院丽江玉龙雪山冰冻圈与可持续发展国家野外科学观测站兰州730000

为了探究海拔对我国西南高寒地区植物稳定碳同位素组成特征及水分利用效率的影响,本研究以梅里雪山东坡不同海拔(2200、2500、2700、3000、3200和4200 m)上不同功能型植物为对象,分析了不同光合途径(C3和Crassulacean acid metabolism,C... 详细信息

为了探究海拔对我国西南高寒地区植物稳定碳同位素组成特征及水分利用效率的影响,本研究以梅里雪山东坡不同海拔(2200、2500、2700、3000、3200和4200 m)上不同功能型植物为对象,分析了不同光合途径(C3和Crassulacean acid metabolism,CAM)植物和C3植物中不同生活型(灌木、阔叶乔木和针叶乔木)植物叶片稳定碳同位素组成特征(δ^(13)C_(p))及内在水分利用效率(intrinsic water use efficiency,iWUE)随海拔梯度的变化。结果表明:(1)梅里雪山东坡C3植物叶片的δ^(13)C_(p)值分布范围在-26.72‰~-31.67‰,均值为-29.12‰,而CAM植物的δ^(13)C_(p)值分布范围在-13.24‰~-14.59‰,均值为-13.77‰;(2)CAM植物δ^(13)C_(p)值和iWUE显著高于C3植物,其中,C3植物中不同生活型植物δ^(13)C_(p)和iWUE值呈现灌木>阔叶乔木>针叶乔木的变化规律;(3)海拔3200 m以下乔木和灌木植物δ^(13)C_(p)和iWUE值随海拔升高而降低,主要受土壤水分的影响,3200 m以上灌木植物δ^(13)C_(p)和iWUE值随海拔升高有增大的趋势,可能受温度的调控。梅里雪山东坡不同功能型植物水分利用效率对海拔梯度的响应反映了不同植物对高寒山地气候不同的适应性。

关键词： C3植物 CAM植物土壤水分温度植物功能型

Finite elastic torsional instability of incompressible thermo-hyperelastic cylinder

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Acta Mechanica Sinica 2006年第2期22卷 156-161页

作者： jiusheng ren Changjun Cheng Department Of Mechanics.Shanghai Institute of Applied Mathematics and Mechanics Shanghai University Shanghai 200444 China

Torsional instability of an incompressible thermo-hyperelastic cylindrical rod, subjected to axial stretching and large torsions, is examined within the framework of finite elasticity. When the cylinder is stretched and twisted by a sufficiently large degree, a knot may form suddenly at one point. This inherent elastic instability is analyzed with the minimum potential energy principle and the critical values of torsion are obtained. The distribution of stresses as well as the tensile force and the torque are studied. Effect of tem- perature change is specifically discussed.

关键词： Incompressible thermo-hyperelastic material Torsional instability Effect of temperature Finite elastic

CAVITATED BIFURCATION FOR COMPOSED COMPRESSIBLE HYPER-ELASTIC MATERIALS

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Acta Mechanica Solida Sinica 2002年第3期15卷 208-213页

作者： ren jiusheng Cheng Changjun Shanghai Univ Shanghai Inst Appl Math & Mech Dept Mech Shanghai 200072 Peoples R China

The cavitated bifurcation problem in a solid sphere composed oftwo compressible hyper-elas- tic materials is examined. Thebifurcation solution for the composed sphere under a uniform radialtensile boundary dead-load is obtained. The bifurcation curves andthe stress contributions subsequent to the cavita- tion are given.The right and left bifurcation as well as the catastrophe andconcentration of stresses are ana- lyzed. The stability of solutionsis discussed through an energy comparison.

关键词： composed compressible hyper-elastic material void bifurcation catastropheand concentra- tion of stress energy comparion

Dynamical cavitation and oscillation of an anisotropic incompressible hyper-elastic sphere

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Science China(Physics,Mechanics & Astronomy) 2012年第5期55卷 822-827页

作者： ren jiusheng LI HanHai YUAN XueGang CHENG ChangJun Department of Mechanics Shanghai Key Laboratory of Mechanics in Energy and Environment EngineeringShanghai UniversityShanghai 200444China College of Science Dalian Nationalities UniversityDalian 116600China

Dynamical cavitation and oscillation of an anisotropic two-family fiber-reinforced incompressible hyper-elastic sphere subjected to a suddenly applied constant boundary dead load are examined within the framework of finite elasto-dynamics.An exact differential equation between the radius of the cavity and the applied load is obtained.The curves for the variation of the maximum radius of the cavity with the load and the phase diagrams are obtained by vibration theories and numerical computation.It is shown that there exists a critical value for the applied load.When the applied load is larger than the critical value,a spherical cavity will suddenly form at the center of the sphere.It is proved that the evolution of the cavity radius with time follows that of nonlinear periodic oscillation,and oscillation of the anisotropic sphere is not the same as that of the isotropic sphere.

关键词：周期振荡各向异性不可压缩超弹性球体最大半径塑性动力学纤维增强

Deformation analysis of an incompressible composite cylindrical tube subjected to end axial loads and internal constraint

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Science China(Physics,Mechanics & Astronomy) 2014年第1期57卷 113-121页

作者： ZHANG WenZheng YUAN XueGang ZHANG HongWu ren jiusheng State Key Laboratory of Structural Analysis for Industrial Equipment Department of Engineering Mechanics Faculty of Vehicle Engineering and Mechanic Dalian University of Technology School of Science Dalian Nationalities University Shanghai Institute of Applied Mathematics and Mechanics Shanghai University

In this paper,the problem of axially symmetric deformation is examined for a composite cylindrical tube under equal axial loads acting on its two ends,where the tube is composed of two different incompressible neo-Hookean materials.Significantly,the implicit analytical solutions describing the deformation of the tube are proposed.Numerical simulations are given to further illustrate the qualitative properties of the solutions and some meaningful conclusions are obtained.In the tension case,with the increasing axial loads or with the decreasing ratio of shear moduli of the outer and the inner materials,it is proved that the tube will shrink more along the radial direction and will extend more along the axial direction.Under either tension or compression,the deformation along the axial direction is obvious near the two ends of the tube,while in the rest,the change is relatively small.Similarly,for a large domain of the middle part,the axial elongation is almost constant;however,the variation is very fast near the two ends.In addition,the absolute value of the axial displacement increases gradually from the central cross-section of the tube and achieves the maximum at the two endpoints.

关键词：复合材料变形分析轴向载荷不可压缩圆柱管轴对称变形轴向负荷定性性质

A FAS approach for stabilization of generalized chained forms: part 1. Discontinuous control laws

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Science China(Information Sciences) 2024年第2期67卷 118-143页

作者： Guang-ren DUAN Center for Control Theory and Guidance Technology Harbin Institute of Technology Center for Control Science and Technology Southern University of Science and Technology

In this paper, a type of general nonholonomic systems is proposed, which contains both the Brockett’s two example systems, and their extended n-dimensional chained forms, as special cases. For the stabilization of such systems, a stabilizing controller is proposed based on the fully actuated system(FAS)approach, which is discontinuous at the origin but time-invariant when the open-loop system is time-invariant,and drives the feasible trajectories of the system to the origin exponentially. Furthermore, the proposed FAS approach is also extended to the sub-normal system case and the time-delay system case.

关键词： nonholonomic systems feedback stabilization exponential convergence sub-fully actuated systems time-delay systems