热超弹性薄板非对称拉伸的分岔和稳定性

本文应用超弹性材料的有限变形理论分析了在面内等双向拉伸死载荷作用下不可压热超弹性方形薄板发生非对称变形的分岔及其稳定性问题.给出了方板变形的分岔曲线和临界载荷,发现对受面内等双向拉伸载荷作用的均匀方板,当拉伸载荷值较小时,方板双向等伸长变形,发生对称的拉伸变形;但当此载荷值大于某一临界值时,从方板的对称拉伸变形中分岔出非对称的变形,方板在两个方向的变形不再相等.通过变形发生分岔前后的能量比较发现,分岔后的对称变形是不稳定的,而非对称变形是稳定的.同时,给出了板中的应力分布曲线,并由不同温度下变形的分岔曲线和应力分布曲线讨论了温度对方板变形和板中的应力分布的影响.     

燃料舱增压对整体变形的影响研究

基于弹性力学理论,获得了内压和侧向外载共同作用下燃料舱结构整体变形与内压之间变化关系的解析解,并进行了有限元分析验证和燃料舱静力试验验证。结果表明:内压对结构整体侧向变形有一定的影响,通过增大内压来减小侧向变形需要圆筒材料的轴向与环向弹性模量、泊松比之间满足一定的关系条件;内压对弹性模量小、截面惯性矩小的燃料舱结构的整体变形影响较为显著,但对弹性模量较大、截面惯性矩较大的结构可挖掘潜力较小。燃料舱静力试验结果表明:当结构的弹性模量和泊松比不满足一定关系时,有内压下的结构整体变形大于无内压下的。     

SIMULATION OF TRANSVERSE VIBRATION OF SLENDER ROD STRING IN THE VERTICAL CYLINDER UNDER BUCKLING DISPLACEMENT EXCITATION1)

对于铅直圆筒内受交变拉压轴向载荷作用的细长杆柱,当杆柱底端所受到的轴向压力大于杆柱屈曲的临界载荷时,细长杆柱在圆筒内将产生螺旋屈曲,杆柱的屈曲变形将激励杆柱在圆筒内产生横向振动。以细长杆在圆筒内的瞬时屈曲构型作为杆柱横向振动的位移激励,建立了屈曲位移激励下的细长杆在圆筒内横向振动与杆管碰撞规律的仿真模型。采用有限差分法对井深进行离散,Newmark 法对时间进行离散,以恢复系数法建立了细长杆和圆筒的碰撞条件,对细长杆在圆筒内的横向振动数学模型进行了数值仿真。仿真结果表明,细长杆和圆筒内壁的碰撞现象主要发生在细长杆底端受压发生屈曲后,且几乎沿整个圆筒都有发生,从圆筒顶部至底部的碰撞力峰值逐渐增大;而在杆柱底端受拉时碰撞现象很少,碰撞力也较小。     

铅直圆筒内细长杆柱在屈曲位移激励下的横向振动仿真

对于铅直圆筒内受交变拉压轴向载荷作用的细长杆柱,当杆柱底端所受到的轴向压力大于杆柱屈曲的临界载荷时,细长杆柱在圆筒内将产生螺旋屈曲,杆柱的屈曲变形将激励杆柱在圆筒内产生横向振动。以细长杆在圆筒内的瞬时屈曲构型作为杆柱横向振动的位移激励,建立了屈曲位移激励下的细长杆在圆筒内横向振动与杆管碰撞规律的仿真模型。采用有限差分法对井深进行离散,Newmark法对时间进行离散,以恢复系数法建立了细长杆和圆筒的碰撞条件,对细长杆在圆筒内的横向振动数学模型进行了数值仿真。仿真结果表明,细长杆和圆筒内壁的碰撞现象主要发生在细长杆底端受压发生屈曲后,且几乎沿整个圆筒都有发生,从圆筒顶部至底部的碰撞力峰值逐渐增大;而在杆柱底端受拉时碰撞现象很少,碰撞力也较小。     

生长对超弹性球壳变形和稳定性的影响

应用连续介质力学有限变形理论建立受内压作用不可压超弹性球壳大变形问题的力学模型, 且运用基于变形梯度张量极分解的弹性体积生长理论分析生长对不可压超弹性球壳变形和稳定性的影响. 通过对球壳变形与内压关系式的数值计算得到不同生长条件下球壳的变形曲线和应力分布曲线及由生长引起的残余变形和残余应力分布. 计算结果表明生长对球壳变形特性有明显的影响, 生长影响球壳可产生不稳定变形的临界壁厚和临界内压, 且在某些情况下可改变球壳的稳定性. 生长在球壳中可产生一定的残余变形和残余应力, 对球壳中的应力分布有一定的影响. 另外当生长的程度足够大时, 即便没有外力作用,球壳仅在生长引起的残余应力作用下也可产生不稳定变形.      

苹果树枝力学特性试验研究

为避免采摘机器进行水果采摘时机械臂对树枝的损伤,并为采摘机械臂设计和驱动电机功率选择提供依据,以苹果成熟时枝条为研究对象,在微型电子万能力学试验机上对其拉压、弯曲变形的弹性模量等力学性能进行试验确定。通过试验得出:树枝枝条轴向拉伸状态下弹性模量平均值为54.2228MPa;轴向压缩状态下弹性模量平均值为32.5580MPa;弯曲变形弹性模量平均值为90.4343MPa。此结果表明苹果树枝在承受轴向拉压和弯曲等不同载荷作用下具有不同的力学特性,进一步对其产生的原因进行分析。依据材料力学理论建立了树枝弯曲变形弹性模量与轴向拉压弹性模量的关系,给出中性面偏移量计算表达式。由于中性层偏移,树枝受压侧承受的最大应力大于受拉侧,且树枝本身轴向压缩弹性模量比拉伸弹性模量小,因此在承受弯曲变形时,受压侧早于受拉侧达到强度极限而发生破坏。     

内压载荷作用下薄膜椭球的稳定性分析

超弹性橄榄状和南瓜状薄膜椭球在内压载荷作用下存在不同的分岔形式.对橄榄状薄膜椭球来说,细长比大于某一临界值时,在一定内压作用下会发生梨形分岔;小于该临界值时,薄膜椭球的分岔行为与圆管的局部起鼓现象相类似.对南瓜状薄膜椭球,无论圆扁,当内压达到某载荷值时都会发生梨形分岔.本文采用能量判据,分析了在压强控制和质量控制两种加载方式作用下,不同形状的薄膜椭球的均匀解及分岔解的稳定性.通过计算要考察的平衡状态及施加小扰动之后状态的能量差来判断当前状态是否稳定,结果表明,在压强控制下,P-V曲线下降段的均匀解和分岔解均为不稳定解.但在质量控制下,在P-V曲线下降段中只有均匀解出现时,均匀解为稳定解;而在均匀解和分岔解共存的区间内,均匀解为不稳定解,分岔解为稳定解.另外,P-V曲线两个上升段的均匀解则均为稳定解.     

正常及病态下静脉壁的力学特性分析

本文应用多束纤维加强超弹性复合材料应变能函数及厚壁圆筒模型,通过有限变形弹性理论研究了正常及病态下静脉壁在静脉压及轴向预拉伸作用下的变形和应力分布等力学特性,着重分析了静脉移植后自适应变化静脉壁在动脉压下的力学特性.首先利用超弹性材料厚壁圆筒模型得到了静脉壁在静脉压下的变形方程,给出了静脉压下静脉壁的变形和应力分布曲线,讨论了静脉壁的力学特性.给出了静脉移植后,正常和自适应变化静脉壁在动脉压下的变形和应力分布曲线,讨论了静脉移植后静脉壁的力学特性及其自适应性变化.然后给出了各种病态静脉壁的变形和应力分布曲线,讨论了材料参数的变化对静脉壁力学特性的影响规律.     

热超弹性材料中空穴增长的分岔问题

研究了受外加均布拉伸死载荷作用的不可压热超弹性材料中空穴突然快速增长的分岔问题.不同于外载荷较小的情况,不可压热超弹性材料球体中的预存微空在外载荷足够大时可以发生突然的快速增长,可视为一类分岔问题.给出了不同温度场下,不同初始半径的微空的增长曲线.预存微空的增长曲线相应于初始半径的极限是实心球体中空穴突然生成的分岔曲线.讨论了均匀和非均匀,升高或降低的温度场对空穴增长问题的影响;给出了预存微空能够发生突然的快速增长的临界载荷,得到了临界载荷与实心球体中空穴突然生成时的临界载荷之间的关系及临界载荷与温度变化之间的关系.     

受外压厚壁圓管压溃过程的有限元分析

用有限元数值方法研究受外压厚壁圆管的非轴对称分支现象,假定圆管变形满足平面应变,稳定变形一直持续到外压达最大值,其后发生压溃过程.随着压力减少,数值计算中可能出现两种平衡路径,即全面弹性卸载和继续非轴对称变形.为避免前者,采用了降阶法.     

New universal relations for nonlinear isotropic elastic materials

A nonlinear isotropic elastic block is subjected to a homogeneous deformation consisting of simple shear superposed on triaxial extension. Two new relations are established for this deformation which are valid for all nonlinear elastic isotropic materials, and hence are universal relations. The first is a relation between the stretch ratios in the plane of shear and the amount of shear when the deformation is supported only by shear tractions. The second relation is established for a thin-walled cylinder under combined extension, inflation and torsion. Each material element of the cylinder undergoes the same local homogeneous deformation of shear superposed on triaxial extension. The properties of this deformation are used to establish a relation between pressure, twisting moment, angle of twist and current dimensions when no axial force is applied to the cylinder. It is shown that these relations also apply for a mixture of a nonlinear isotropic solid and a fluid.     

边界受限下的轴向压缩超弹性圆管的失稳分析

橡胶制品广泛应用于社会生产和日常生活。本文主要研究外边界受限的超弹性圆管受轴向压缩时的稳定性问题,在非线性弹性理论框架下推导控制方程,对其进行线性分岔分析。考虑沿轴向对称分布的失稳模态,得到临界模态以及对应的临界主伸长,同时刻画出临界主伸长以及临界应力与壁厚之间的关系。结果表明,圆管壁越薄,发生分岔时的临界主伸长更小,更不容易发生失稳。此外,结合封隔器的密封原理,推导出封隔器圆筒在进行油液密封时轴向应力与接触应力的表达式,修正了此前的推导结果,为封隔器在密封性能的判断上提供理论依据。     

Finite elastic deformations of transversely isotropic circular cylindrical tubes

We consider the finite radially symmetric deformation of a circular cylindrical tube of a homogeneous transversely isotropic elastic material subject to axial stretch, radial deformation and torsion, supported by axial load, internal pressure and end moment. Two different directions of transverse isotropy are considered: the radial direction and an arbitrary direction in planes normal locally to the radial direction, the only directions for which the considered deformation is admissible in general. In the absence of body forces, formulas are obtained for the internal pressure, and the resultant axial load and torsional moment on the ends of the tube in respect of a general strain-energy function. For a specific material model of transversely isotropic elasticity, and material and geometrical parameters, numerical results are used to illustrate the dependence of the pressure, (reduced) axial load and moment on the radial stretch and a measure of the torsional deformation for a fixed value of the axial stretch.     

电活性聚合物球壳的力电不稳定性

应用连续介质力学有限变形理论,分析了不可压电活性聚合物球壳在外加电场及内压作用下发生非对称变形的力电不稳定性问题。文中给出了不同外加电场下球壳的变形曲线和应力分布曲线, 结果表明对壁厚小于临界壁厚值的薄壁球壳,当内压大于临界内压值时,球壳可以产生不稳定的非对称变形。文中求得了球壳发生不稳定变形的临界壁厚及临界内压,探讨了外加电场对两个临界值的影响规律,同时讨论了外加电场对球壳中应力分布的影响。     

Mechanical performance and negative pressure instability for venous walls

Mechanical properties, such as the deformation and stress distributions for venous walls under the combined load of transmural pressure and axial stretch, are examined within the framework of nonlinear elasticity with one kind of hyper-elastic strain energy functions. The negative pressure instability problem of the venous wall is explained through energy comparison. First, the deformation equation of the venous wall under the combined loads is obtained with a thin-walled circular cylindrical tube. The deformation curves and the stress distributions for the venous wall are given under the normal transmural pressure, and the regulations are discussed. Then, the deformation curves of the venous wall under the negative transmural pressure or the internal pressure less than the external pressure are given. Finally, the negative pressure instability problem is discussed through energy comparison.     

薄壁钢管再生混凝土轴压实验研究

通过对9个薄壁圆钢管再生混凝土短柱和9个薄壁方钢管再生混凝土短柱进行的轴压试验研究,比较了三种方法测定试件轴向变形的差异,分析了不同取代率和不同截面形式薄壁钢管再生混凝土的破坏变形特征,并运用不同设计规程对薄壁钢管再生混凝土的承载力强度进行了计算分析。得出薄壁钢管再生混凝土的变形破坏形式与普通薄壁钢管混凝土相似,及再生混凝土取代率对试件极限承载力和变形能力有一定影响的结论。另外根据计算比较,得到各规程在计算薄壁钢管再生混凝土极限承载力时的适用性。     

Electromechanical responses and instability of electro-active polymer cylindrical shells

Based on the theories of finite deformation elasticity, electromechanical responses and instability of an incompressible electro-active polymer (EAP) cylindrical shell, which is subjected to an internal pressure and a static electric field, are studied. Deformation curves and distribution of stresses are obtained. It is found that an internal pressure together with an electric field may cause the unstable non-monotonic deformation of the shell. It is also shown that a critical thickness for the shell exists, and the shell may undergo the unstable deformation if its thickness is less than this critical value. In addition, the effects of the electric field, axial stretch, thickness, and internal pressure on the instability of the shell are discussed.     

Localized bulging in an inflated cylindrical tube of arbitrary thickness – the effect of bending stiffness

We study localized bulging of a cylindrical hyperelastic tube of arbitrary thickness when it is subjected to the combined action of inflation and axial extension. It is shown that with the internal pressure P and resultant axial force F viewed as functions of the azimuthal stretch on the inner surface and the axial stretch, the bifurcation condition for the initiation of a localized bulge is that the Jacobian of the vector function $(P,F)$ should vanish. This is established using the dynamical systems theory by first computing the eigenvalues of a certain eigenvalue problem governing incremental deformations, and then deriving the bifurcation condition explicitly. The bifurcation condition is valid for all loading conditions, and in the special case of fixed resultant axial force it gives the expected result that the initiation pressure for localized bulging is precisely the maximum pressure in uniform inflation. It is shown that even if localized bulging cannot take place when the axial force is fixed, it is still possible if the axial stretch is fixed instead. The explicit bifurcation condition also provides a means to quantify precisely the effect of bending stiffness on the initiation pressure. It is shown that the (approximate) membrane theory gives good predictions for the initiation pressure, with a relative error less than 5%, for thickness/radius ratios up to 0.67. A two-term asymptotic bifurcation condition for localized bulging that incorporates the effect of bending stiffness is proposed, and is shown to be capable of giving extremely accurate predictions for the initiation pressure for thickness/radius ratios up to as large as 1.2.     

轴向拉伸作用下超弹性管充气失稳的内压和形貌研究

超弹性管充气局部失稳现象与生物工程中动脉瘤形成机理相似。本文以两端密封的超弹性管为研究对象,从实验和理论两方面研究其在轴向拉伸作用下充气时的失稳现象。实验采用高频压力传感器测量充气过程中超弹性管内部压力的变化,高速摄像系统同步记录形貌变化的图像,分析超弹性管的几何尺寸和轴向拉力的改变对失稳临界压力的影响。基于连续介质力学理论,建立超弹性管充气时的控制方程并运用打靶法求解,理论分析轴向拉力与几何尺寸对超弹性管充气失稳的影响,并与实验结果比较;同时,预测超弹性管在任意时刻的形貌变化,分析特征点的变化趋势。     

Uniqueness of deformation of thin-walled rigid-plastic cylinders under internal pressure,tension and torque

Uniqueness of deformation of a long thin-walled rigid-plastic cylinder is examined under three types of load combination: (i) axial tension and torque, (ii) internal pressure and torque, (iii) internal pressure and axial tension. In each case, the critical rate of hardening, above which uniqueness in guaranteed, is calculated by using Hill's [1] sufficient condition for uniqueness. The effect of torque, applied at the ends of the cylinder, on lower bounds to the critical pressure and to the critical axial-load is also discussed.