Quantitative fractography for estimating whole bone properties of manatee rib bones

The goals of this study were to estimate the stress at failure and the fracture toughness of whole manatee ribs fractured in impact; and to determine whether typical watercraft are capable of generating enough energy to break manatee ribs upon impact. The unique construction of manatee ribs enabled us to apply quantitative fractographic techniques to measure some fracture mechanics parameters. Adult manatee bone behaves more like a ceramic than other types of bone. Due to this, we were able to see many of the features observed for brittle fracture in ceramics. We were able to identify crack origins, and make quantitative measurements of crack size. Failure stress was constant across body size despite the increase in rib size as the animals grow. Similarly, flaw size was the same for all animals regardless of body size. Fracture toughness for whole ribs (measured as the critical stress intensity factor, K _C) calculated from strain gage data was 8 MPa m^1/2. This value was greater than that reported for small sample specimens, suggestive of R-curve behavior in this bone. There were no differences between the sexes in their ability to resist fracture. Kinetic energy calculations indicated that recreational boats commonly found in Florida waters are capable of generating sufficient energy to fracture manatee ribs upon impact.     

Dynamic axial crushing of circular tubes

A series of axial crushing tests on steel circular cylindrical shells loaded either statically or dynamically is reported and compared with various theoretical predictions and empirical relations. A modified version of Alexander's theoretical analysis for axisymmetric, or concertina, deformations gives good agreement with the experimental results when the effective crushing distance is considered and provided that the influence of material strain rate sensitivity is retained in the dynamic crushing case.     

薄壁开孔圆管在轴向荷载作用下的理论研究

研究薄壁开孔圆管的轴向耐撞性有助于其在缓冲、吸能领域的广泛应用。通过分别考虑开孔区域和未开孔区域的能量吸收特征并引入材料的应变强化效应,根据塑性铰理论建立了轴向荷载下开孔圆管轴对称压溃模式的理论模型,得到了弯曲应变能、拉伸应变能、平均压溃力、比吸能的解析表达式。分析结果表明:该理论模型的预测结果与数值和实验结果相吻合;正则化平均压溃力会随半皱褶长细比的降低而显著增加;单层孔数对正则化平均压溃力的影响会随管壁厚度的增加或孔半径的减小而降低;比吸能可通过减少单层孔数或减小孔半径提高。     

非轴对称多元载荷条件下管道中纵向模态导波激励

轴对称载荷是管道中轴对称模态导波激励的有效方法。然而,受换能器安装误差等因素的影响,激励载荷多会变为非轴对称载荷,进而使激励出的导波模态变得复杂。对非轴对称多元载荷条件下纵向模态导波的激励问题进行了深入研究。考虑两种典型的非轴对称载荷,采用简正模态展开技术,建立了导波激励声场与边界载荷的量化关系,进而分析了各模态导波的产生机理及载荷阵列对纵向导波激励的影响。采用有限元数值模拟验证了理论预测结果。考虑实际管道检测中出现的非轴对称载荷,提出了一种载荷补偿策略并进行了实验验证。结果表明,该方法能够有效抑制弯曲模态导波的产生,同时也有助于改善导波信号的噪声水平。     

Dynamic axial crushing of square tubes

Eighty-four dynamic tests on thin-walled square steel tubes having two different cross-sections with c/h = 30.25 and c/h = 32.18 and various lengths were crushed axially on a drop hammer rig. Approximate theoretical predictions were developed for the axial progressive crushing of square box columns using a kinematically admissible method of analysis. This theoretical study predicts four deformation modes which govern the behaviour for different ranges of the parameter c/h. New asymmetric deformation modes were predicted theoretically and confirmed in the experimental tests. These asymmetric modes cause an inclination of a column which could lead to collapse in the sense of Euler even for relatively short columns. The effective crushing distance is considered in the approximate theoretical analysis together with the influence of material strain rate sensitivity, which is important for steel even when the loadings are quasi-static. The simple equations presented herein for the design of axially crushed spuare box columns give reasonable agreement with the corresponding experimental results.     

Elastic postbuckling analysis via finite element and perturbation techniques part II: Application to shells of revolution

The general theory developed in Part 1 of this paper for the finite element stability analysis of structural systems, using perturbation expansions in the vicinity of a critical point, is applied here to the analysis of shells of revolution. The discretization of the shell is performed by means of a semianalytical approximation, and the matrices required for the evaluation of critical points and postcritical equilibrium paths are obtained. Two cases are presented: bifurcation in axisymmetric and in asymmetric buckling modes. The derivatives required for an imperfection analysis are also obtained. A technique of switching between two paths using continuation methods is also discussed, in which the switch is performed using derivatives of the perturbation expansion. Results are presented for bifurcation in axisymmetric and in non-axisymmetric modes, and compared with known solutions or with results from changing the path using continuation methods; good correlation is shown. For structures displaying unstable bifurcation, the influence of load and geometric imperfections is evaluated.     

Free vibration analysis of non-axisymmetric and axisymmetric structures by the dual reciprocity BEM

The dual reciprocity boundary element method (DR/BEM) is employed for the free vibration analysis of three-dimensional non-axisymmetric and axisymmetric elastic solids. The method uses the elastostatic fundamental solution in the integral formulation of elastodynamics and as a result of that, an inertial volume integral is created in addition to the boundary ones. This volume integral is transformed into a surface integral by invoking the reciprocal theorem and expanding of the displacement field into a series involving seven different approximation functions. The approximation functions used are local radial basis functions (RBFs) and are applied in combination (or not) with global basis functions (augmentation). All these functions are compared in terms of the accuracy they provide. The axisymmetric case is efficiently treated with the aid of the fast Fourier transform (FFT) algorithm in order to provide even non-axisymmetric vibration modes. Two representative numerical examples involving the determination of natural frequencies and modal shapes of an elastic cube and an elastic cylinder serve to investigate in detail the potentiality of each of the seven approximation functions tested to provide results of high accuracy and to reach useful practical conclusions.     

Non-Axisymmetric Matrix Cracking and Interface Debonding with Friction in Ceramic Composites

A three-dimensional analytical model based on the principle of minimum potential energy is developed and applied to determine the stress state in a discrete fiber/matrix composite cylinder subjected to axial tensile loading in the fiber direction and containing a non-axisymmetric transverse matrix crack and an interface debond. The friction over the debonded interface is incorporated into the analysis. The strain energy release rates associated with the matrix crack and the interface debonding under the combination of the applied load and the interface frictional force are computed. The strain energy release rate criterion has been employed to evaluate the critical applied loads for the two fracture modes and to assess the competition between propagation of a matrix crack and growth of interface debonding. A parametric study has been carried out. The computed results show that the interface friction plays an important role in the failure of brittle matrix composites.     

Guided Wave Tuning Principles for Defect Detection in Tubing

Dispersion diagrams for longitudinal modes and several flexural modes are given. A partial loading oblique incidence technique was introduced for non-axisymmetric guided wave generation. Acoustic fields for partially loaded generation of guided waves were obtained along a sample Inconel steam generator tube surface. The axial field and the circumferential fields were non uniform. Even though the acoustic field was much more complicated than in the case of axisymmetric modes, the study of non-axisymmetric mode cannot be avoided; excitation of a single symmetric mode is often difficult due to limited access and transducer efficiency and there is also mode conversion after scattering from defects. For 100% inspection coverage of tubing and piping, three dimensional tuning (distance, frequency, and incident angle tuning), was employed. A single combination of incident angle, position, and frequency may miss defects in blind spots. However, complete inspection coverage of a whole cross sectional area over a certain distance of tubing was successfully demonstrated through a multi crack detection experiment by using the three dimensional tuning concepts. Also, the use of non-axisymmetric guided waves for a large distance inspection capability was successfully demonstrated.     

Stability of ferrofluid flow between concentric rotating cylinders with an axial magnetic field

A linear stability analysis for the ferrofluid flow between two concentric rotating cylinders in the presence of an axial magnetic field is implemented in this study. Both of the wide-gap and small-gap cases are considered and the governing equations with respect to three-dimensional disturbances including axisymmetric and non-axisymmetric modes are derived and solved by a direct numerical procedure. A parametric study covering wide ranges of ?, the volume fraction of colloidal particles; ξ, the strength of axial magnetic field; μ, the ratio of angular velocity of the outer cylinder to that of the inner cylinder; and ε, the ratio of radius of the inner cylinder to that of the outer cylinder, is conducted. Results show that the stability characteristics depend heavily on these factors. It is found that the increases of ? and ξ, and decrease of ε tend to stabilize the basic flow for an assigned value of μ. The variations of the onset mode with these parameters are discussed in detail. An example for the practical application of present results is given to help the understanding of stability behaviour of this flow.     

Analytical Model for Energy Absorption and Plastic Collapse of Thin-Walled Grooved Frusta Tubes

In the present study, an analytical model for axisymmetric axial crushing of thin-walled frusta tubes containing annular grooves is presented. In this innovative geometrical design model, to encourage axisymmetric collapsing mode, circumferential grooves are cut from the outer and inner surfaces of frusta at determined intervals. Theoretical formulations are presented for predicting the energy absorption and mean crushing load. In order to verify these analytical results, quasi-static compression tests are performed. The results of this research indicate good agreement between the theory and experimental findings. The proposed method could be a good candidate as a controllable shock absorber in impact applications.     

多层UV形瓦楞纸板的准静态轴向压溃模型研究

目的 对多层UV型瓦楞纸板轴向压溃后的变形机理和抗压性能进行探究,以助于多层瓦楞纸箱和缓冲包装的设计。方法 采用理论分析和试验研究相结合的方式,对UV形多层瓦楞纸板轴向压溃后的平台应力进行理论建模和准静态试验研究。结果 在UV形瓦楞生产工艺的基础上,假设楞纸与相邻层之间的相互作用为面黏合;提出了一种新的折叠元件以及波纹芯的3种变形模式;此外,分别提出了五层瓦楞纸板和七层瓦楞纸板平台应力理论模型;多层瓦楞纸板平台应力的理论预测结果与试验结果吻合良好。结论 所提出的多层UV形瓦楞纸板理论模型是有效的,这将有助于波纹结构刚度设计和参数选择,以满足不同的强度要求。     

A theoretical and experimental study on metal hexagonal honeycomb crushing under quasi-static and low velocity impact loading

In the study of honeycomb crushing under quasi-static loading, two parameters are important; the mean crushing stress and the wavelength of the folding mode. On the other hand, the kinetic energy absorbed by the honeycomb is investigated in the impact loading. In this paper, through fully considering the cylindrical curvature effects and implementing the energy method, a new theoretical model for the estimation of the mean crushing stress and the wavelength of the folding mode of the metal hexagonal honeycomb is presented. Afterwards, developing this static model to the dynamic state, a theoretical model for study of the behavior of these energy absorbers, in the low velocity impact loading, is proposed and the required initial velocity of the impactor, for creation of the desired folding length in these structures, is determined, analytically. The presented theoretical models have been compared with experimental results obtained from experiments on three kinds of honeycomb with the various minor diameters and thicknesses of the cell walls under quasi-static and low velocity impact loading in the axial direction. Excellent correlation has been observed between the theoretical and experimental results.     

锈胀钢筋混凝土拱肋承载力试验与模拟

为研究锈胀损伤对钢筋混凝土拱肋极限承载力的影响,制作了4片钢筋混凝土圆弧拱肋,通过电化学快速锈蚀使其表面产生不同程度的锈胀裂缝,讨论了初始锈胀裂缝的分布情况,研究了锈胀拱肋的裂缝发展、不同位置处位移和应变、极限承载力及失效模式。试验结果表明：锈胀削弱了混凝土截面尺寸和刚度,降低了钢筋与混凝土间的粘结性,是承载力退化的主要原因之一;锈胀导致的拱肋极限承载力下降率约为60%;锈胀未改变拱肋的失效模式,所有拱肋均在一侧拱脚发生脆性破坏。在试验的基础上,建立了锈胀钢筋混凝土拱肋的有限元计算模型,由于RC拱肋存在大面积锈胀,模型中未考虑混凝土保护层的影响,计算结果和试验值较为接近,为日后有限元建模提供一定参考。     

泡沫变形模式对泡沫填充圆管压溃行为的影响

将泡沫填充圆管的平均压溃载荷视为圆管、泡沫及圆管与泡沫相互作用三部分之和, 基于作者提出的直链塑性铰改进模型, 研究了两种泡沫变形模式对泡沫填充圆管准静态压溃行为的影响, 得到了新的最优屈曲半波长和平均压溃载荷的理论计算公式, 并研究了两种泡沫变形模式下, 偏心率和塑性角参数对最优屈曲半波长和平均压溃载荷的影响。结果表明, 泡沫变形模式 Ⅰ 下的平均压溃载荷略高于泡沫变形模式 Ⅱ 下的相应值, 泡沫变形模式对最优屈曲半波长影响较大; 与文献[14]相比, 所得平均压溃载荷理论预测值与试验结果吻合得更好。      

Shear-horizontal vibration modes of an oblate elliptical cylinder and energy trapping in contoured acoustic wave resonators

We study shear-horizontal free vibrations of an elastic cylinder with an oblate elliptical cross section and a traction-free surface. Exact vibration modes and frequencies are obtained. The results show the existence of thickness-shear and thickness-twist modes. The energy-trapping behavior of these modes is examined. Trapped modes are found wherein the vibration energy is largely confined to the central portion of the cross section and little vibration energy is found at the edges. It is also shown that face-shear modes are not allowed in such a cylinder. The results are useful for the understanding of the energy trapping phenomenon in contoured acoustic wave resonators.     

Free vibration of shells with axisymmetric dimples and bulges under axial compression

We present a procedure of analytical calculation of minimum natural frequencies of cylindrical shells stiffened with stringers and ribs. A new approach is put forward which allows for the presence of some axisymmetric imperfections in shells and a longitudinal compressive load. In the general case, one can analyze 17 vibration modes corresponding to possible types of deformation and pick out a minimum frequency parameter. Smooth, stringered, and stringer-rib stiffened shells are studied. The calculated data are compared to experimental results for the case of no longitudinal compressive forces. The influence of initial deflections and compressive loads on the minimum vibration parameters is assessed. The proposed approach makes it possible to define more precisely the parameters of critical loads and frequencies, thus bridging the gap between calculated and experimental data. Translated from Problemy Prochnosti, No. 2, pp. 125–138, March–April, 2009.     

Current-induced instabilities of hydromagnetic flow in a small gap between rotating conducting cylinders

Summary.  In considering the stability of an electrically conducting fluid between rotating perfectly conducting cylinders with a current-induced pressure gradient acting in the azimuthal direction and with an applied axial magnetic field, the assumption of small-gap approximation is made and the governing equations with respect to both axisymmetric and non-axisymmetric disturbances are solved by a direct numerical procedure. A parametric study covering wide ranges of Q, the Hartmann number which represents the strength of the axial magnetic field, and β, a parameter characterizing the ratio of current-induced and rotation velocities, is conducted for the situation where the outer cylinder is stationary and the inner cylinder is rotating. It is found that the stability characteristics are thoroughly different from those of the case of weakly conducting walls. The variation of the onset mode is shown in the (β, Q)-plane, and the transition of the corresponding neutral curves is discussed in detail. Results for the critical Taylor number and wavenumber pertaining to the critical disturbances are presented. The critical values of radial current density required for the onset of instability are also determined. Received May 8, 2002; revised November 11, 2002 Published online: May 8, 2003 The financial support for this work from National Science Council of Taiwan, ROC, through Grant No. NSC 89-2212-E-132-006 is gratefully acknowledged.     

Aluminium foam sandwiches collapse modes under static and dynamic three-point bending

Static and dynamic three-point bending tests were carried out in order to investigate the structural response (collapse modes, energy dissipation, strain rate sensitivity) of two different typologies of aluminium foam sandwich (AFS) panels, consisting of a closed-cell aluminium foam core with either two integral (Schunk) or two glued (Alulight) faces. Impact measurements were performed by a bi-pendulum testing machine designed by the authors. It was found that different collapse modes can be obtained for samples with identical nominal dimensions, depending on the support span distance and on the own AFS properties. Simplified theoretical collapse models were introduced to explain the observed experimental behaviour, showing good agreement between predicted and experimental limit loads. As far as energy dissipation is concerned, no strain rate sensitivity was found for initial impact velocity up to about 1.2 m/s.     

Experimental and numerical investigation of the crushing response of an open section composite energy absorbing element

The quasi-static crushing response of carbon epoxy composite hat-shaped crush elements is described herein. A steeple-type triggering mechanism was used to ensure the specimens exhibited a continuous stable crushing mode of failure. The explicit finite element software PAM-CRASH was used to predict the crushing failure of these energy absorbing elements. A four-layer, stacked-shell model of the composite hat-shaped element, after calibration against experimental test data, was found to be capable of closely approximating the failure modes and provide agreement with the load vs. displacement behaviour observed during the experiments. The predicted steady state load and specific energy absorption were respectively within 1.5 and 0.2% of the experimental average. With further validation, the developed stacked-shell methodology could help provide a predictive tool to characterise the energy absorption of open section crush elements and significantly reduce the cost associated with an extensive experimental material characterisation test program.