Buckling Equation

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Hai Chao Han - One of the best experts on this subject based on the ideXlab platform.

  • Artery Buckling analysis using a four-fiber wall model.
    Journal of biomechanics, 2014
    Co-Authors: Qin Liu, Qi Wen, Mohammad Mottahedi, Hai Chao Han
    Abstract:

    Artery bent Buckling has been suggested as a possible mechanism that leads to artery tortuosity, which is associated with aging, hypertension, atherosclerosis, and other pathological conditions. It is necessary to understand the relationship between microscopic wall structural changes and macroscopic artery Buckling behavior. To this end, the objectives of this study were to develop arterial Buckling Equations using a microstructure-based 4-fiber reinforced wall model, and to simulate the effects of vessel wall microstructural changes on artery Buckling. Our results showed that the critical pressure increased nonlinearly with the axial stretch ratio, and the 4-fiber model predicted higher critical Buckling pressures than what the Fung model predicted. The Buckling Equation using the 4-fiber model captured the experimentally observed reduction of critical pressure induced by elastin degradation and collagen fiber orientation changes in the arterial wall. These results improve our understanding of arterial stability and its relationship to microscopic wall remodeling, and the model provides a useful tool for further studies.

  • THE EFFECT OF COLLAGENASE ON THE CRITICAL Buckling PRESSURE OF ARTERIES
    Molecular & cellular biomechanics : MCB, 2012
    Co-Authors: Ricky Martinez, Hai Chao Han
    Abstract:

    The stability of arteries is essential to normal arterial functions and loss of stability can lead to arterial tortuosity and kinking. Collagen is a main extracellular matrix component that modulates the mechanical properties of arteries and collagen degradation at pathological conditions weakens the mechanical strength of arteries. However, the effect of collagen degradation on the mechanical stability of arteries is unclear. The objective of this study was to investigate the effects of collagen degradation on the critical Buckling pressure of arteries. Arterial specimens were subjected to pressurized inflation testing and fitted with nonlinear thick-walled cylindrical model Equations to determine their stress strain relationships. The arteries were then tested for the critical Buckling pressure at a set of axial stretch ratios. Then, arteries were divided into three groups and treated with Type III collagenase at three different concentrations (64, 128, and 400U/ml). Mechanical properties and Buckling pressures of the arteries were determined after collagenase treatment. Additionally, the theoretical Buckling pressures were also determined using a Buckling Equation. Our results demonstrated that the Buckling pressure for arteries was lower after collagenase treatment. The difference between pre- and post- treatment was statistically significant for the highest concentration of 400U/ml but not at the lower concentrations. The Buckling Equation was found to yield a fair estimation to the experimental critical pressure measurements. These results shed light on the role of matrix remodeling on the mechanical stability of arteries and developments of tortuous arteries.

  • a nonlinear thin wall model for vein Buckling
    Cardiovascular Engineering and Technology, 2010
    Co-Authors: Hai Chao Han, Avione Y Lee
    Abstract:

    Tortuous or twisted veins are often seen in the retina, cerebrum, and legs (varicose veins) of one-third of the aged population, but the underlying mechanisms are poorly understood. While the collapse of veins under external pressure has been well documented, the bent Buckling of long vein segments has not been studied. The objectives of this study were to develop a biomechanical model of vein Buckling under internal pressure and to predict the critical pressure. Veins were modeled as thin-walled nonlinear elastic tubes with the Fung exponential strain energy function. Our results demonstrated that veins buckle due to high blood pressure or low axial tension. High axial tension stabilized veins under internal pressure. Our Buckling model estimated the critical pressure accurately compared to the experimental measurements. The Buckling Equation provides a useful tool for studying the development of tortuous veins.

  • Determination of the Critical Buckling Pressure of Blood Vessels Using the Energy Approach
    Annals of biomedical engineering, 2010
    Co-Authors: Hai Chao Han
    Abstract:

    The stability of blood vessels under lumen blood pressure is essential to the maintenance of normal vascular function. Differential Buckling Equations have been established recently for linear and nonlinear elastic artery models. However, the strain energy in bent Buckling and the corresponding energy method have not been investigated for blood vessels under lumen pressure. The purpose of this study was to establish the energy Equation for blood vessel Buckling under internal pressure. A Buckling Equation was established to determine the critical pressure based on the potential energy. The critical pressures of blood vessels with small tapering along their axis were estimated using the energy approach. It was demonstrated that the energy approach yields both the same differential Equation and critical pressure for cylindrical blood vessel Buckling as obtained previously using the adjacent equilibrium approach. Tapering reduced the critical pressure of blood vessels compared to the cylindrical ones. This energy approach provides a useful tool for studying blood vessel Buckling and will be useful in dealing with various imperfections of the vessel wall.

  • The theoretical foundation for artery Buckling under internal pressure.
    Journal of biomechanical engineering, 2009
    Co-Authors: Hai Chao Han
    Abstract:

    The stability of blood vessels under the lumen blood pressure is essential to the maintenance of normal arterial function. Buckling Equations have been established recently for linear and nonlinear elastic artery models with assumed sinusoidal mode shapes. However, the theoretical base for the assumption is not clear. This study established differential Equations of artery Buckling and then proved that straight arteries bifurcated into sinusoidal mode shapes when Buckling occurs. These results set the Buckling Equation on a solid theoretical foundation.

Avione Y Lee - One of the best experts on this subject based on the ideXlab platform.

  • a nonlinear thin wall model for vein Buckling
    Cardiovascular Engineering and Technology, 2010
    Co-Authors: Hai Chao Han, Avione Y Lee
    Abstract:

    Tortuous or twisted veins are often seen in the retina, cerebrum, and legs (varicose veins) of one-third of the aged population, but the underlying mechanisms are poorly understood. While the collapse of veins under external pressure has been well documented, the bent Buckling of long vein segments has not been studied. The objectives of this study were to develop a biomechanical model of vein Buckling under internal pressure and to predict the critical pressure. Veins were modeled as thin-walled nonlinear elastic tubes with the Fung exponential strain energy function. Our results demonstrated that veins buckle due to high blood pressure or low axial tension. High axial tension stabilized veins under internal pressure. Our Buckling model estimated the critical pressure accurately compared to the experimental measurements. The Buckling Equation provides a useful tool for studying the development of tortuous veins.

Lihua Cai - One of the best experts on this subject based on the ideXlab platform.

  • Buckling analysis of the shell of a refuge chamber in a coal mine under uniform axial compression
    International Journal of Mining Science and Technology, 2012
    Co-Authors: Haifeng Fang, Lihua Cai
    Abstract:

    Abstract A stiffened cylindrical shell is normally used in refuge chambers of a coal mine. Based on the method of application and shape characteristics of a refuge chamber, we simplified its shell as an orthotropic cylinder. The basic Buckling Equation of the stiffened cylindrical shell under uniform axial compression was deduced by using a Donnell function. The factors affecting its Buckling capacity were studied by theoretical analysis and numerical calculations. The results reveal that the torsional rigidity of the longitudinal stiffener had little effect on the Buckling capacity of the shell and that the critical load of an externally stiffened cylindrical shell is higher than that of an internally stiffened cylindrical shell.

Bai Xiang-zhong - One of the best experts on this subject based on the ideXlab platform.

  • Magneto-elasticity Buckling Bifurcation of a Thin Current Carrying Plate Fixed at Four Edges
    Science Technology and Engineering, 2008
    Co-Authors: Bai Xiang-zhong
    Abstract:

    For a thin current carrying plate fixed at edges, the dynamic Buckling Equation was derived by using Galerkin method on the basis of the nonlinear magneto-elastic Equations of motion, physical Equations, expression of Lorentz forces and the electrodynamics Equations. The bifurcation points, bifurcation conditions and the type of bifurcation are gotten through discussing the existence and stability of equilibrium when considering the thin plate applied static load.

  • MAGNETIC-ELASTISITY STABILITY CRITERION OF THIN CURRENT PLATE SIMPLY SUPORTED AT EACH EDGE
    Chinese Journal of Mechanical Engineering, 2007
    Co-Authors: Wang Zhi-ren, Bai Xiang-zhong, Bian Yu-hong
    Abstract:

    For a current carrying rectangular plate which is simply supported at two opposite boundaries and the other two are fixed,the magnetic-elasticity steady problem is studied. Based on deriving the magnetic-elasticity dynamic Buckling Equation of the plate applied mechanical load in a magnet field, the Buckling Equation is changed into the standard form of the Mathieu Equation by using Galerkin method.Thus,the Buckling problem comes down to solve the Mathien Equation.The crite- rion Equation of the plate at the critical state of magnetic elas- ticity Buckling is obtained with the analysis on the eigen value relations between the coefficientsλandηin the Mathieu equa- tion.The map and the boundary lines of the steady areas of the Mathieu Equation are shown whenηis small exciter.At last,the curves of the relations among the critical state of magnetic elastic- ity dynamic Buckling problem of the plate and the relative pa- rameters are drawn out through a calculating example.The con- clusions show that the electrical and magnetic forces may be con- trolled by changing the parameters of the current and the magnetic field so that the aim for controlling the deformation,stress,strain and the stability of the current canying plate is achieved.

Ciprian D. Coman - One of the best experts on this subject based on the ideXlab platform.

  • Global asymptotic approximations for wrinkling of polar orthotropic annular plates in tension
    International Journal of Solids and Structures, 2010
    Co-Authors: Ciprian D. Coman
    Abstract:

    The role of polar orthotropy is investigated in relation to an elastic wrinkling problem for annular thin plates in tension. An appealing feature of this generalised constitutive framework is the possibility of allowing the radial and circumferential directions to have different bending stiffnesses. By suitably rescaling the Buckling Equation, three main parameters are identified as being responsible for the behaviour of the linear wrinkling mechanism. We conduct a number of singular-perturbation analyses in order to capture the dependence of the critical loads and mode numbers on the various physical parameters that enter in the description of the problem.