Techno Press


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CONTENTS
Volume 35, Number 6, August20 2010
 

Abstract
An energy-based fatigue life prediction framework was previously developed by the authors for prediction of axial and bending fatigue life at various stress ratios. The framework for the prediction of fatigue life via energy analysis was based on a new constitutive law, which states the following: the amount of energy required to fracture a material is constant. In this study, the energy expressions that construct the new constitutive law are integrated into minimum potential energy formulation to develop new finite elements for uniaxial and bending fatigue life prediction. The comparison of finite element method (FEM) results to existing experimental fatigue data, verifies the new finite elements for fatigue life prediction. The final output of this finite element analysis is in the form of number of cycles to failure for each element in ascending or descending order. Therefore, the new finite element framework can provide the number of cycles to failure for each element in structural components. The performance of the fatigue finite elements is demonstrated by the fatigue life predictions from Al6061-T6 aluminum and Ti-6Al-4V. Results are compared with experimental results and analytical predictions.

Key Words
bending; cycles; fatigue; finite element analysis; structures; uniaxial.

Address
Wasim Tarar: Department of Mechanical and Aerospace Engineering, The Ohio State University, 2036 Neil Ave. Bolz Hall, Room 328, Columbus, OH 43210, USA
Onome Scott-Emuakpor: Department of Mechanical and Aerospace Engineering, The Ohio State University, 2036 Neil Ave. Bolz Hall, Room 328, Columbus, OH 43210, USA
M.-H. Herman Shen: Department of Mechanical and Aerospace Engineering, The Ohio State University, 2036 Neil Ave. Bolz Hall, Room 328, Columbus, OH 43210, USA

Abstract
This paper focuses on geometrically non-linear static analysis of a simply supported beam made of hyperelastic material subjected to a non-follower transversal uniformly distributed load. As it is known, the line of action of follower forces is affected by the deformation of the elastic system on which they act and therefore such forces are non-conservative. The material of the beam is assumed as isotropic and hyperelastic. Two types of simply supported beams are considered which have the following boundary conditions: 1) There is a pin at left end and a roller at right end of the beam (pinned-rolled beam). 2) Both ends of the beam are supported by pins (pinned-pinned beam). In this study, finite element model of the beam is constructed by using total Lagrangian finite element model of two dimensional continuum for a twelve-node quadratic element. The considered highly non-linear problem is solved by using incremental displacement-based finite element method in conjunction with Newton-Raphson iteration method. In order to use the solution procedures of Newton-Raphson type, there is need to linearized equilibrium equations, which can be achieved through the linearization of the principle of virtual work in its continuum form. In the study, the effect of the large deflections and rotations on the displacements and the normal stress and the shear stress distributions through the thickness of the beam is investigated in detail. It is known that in the failure analysis, the most important quantities are the principal normal stresses and the maximum shear stress. Therefore these stresses are investigated in detail. The convergence studies are performed for various numbers of finite elements. The effects of the geometric non-linearity and pinned-pinned and pinned-rolled support conditions on the displacements and on the stresses are investigated. By using a twelve-node quadratic element, the free boundary conditions are satisfied and very good stress diagrams are obtained. Also, some of the results of the total Lagrangian finite element model of two dimensional continuum for a twelve-node quadratic element are compared with the results of SAP2000 packet program. Numerical results show that geometrical nonlinearity plays very important role in the static responses of the beam.

Key Words
geometrical non-linearity; simply supported beams; finite element analysis; total lagrangian finite element model; two dimensional solid continuum.

Address
T. Kocaturk: Yildiz Technical University, Davutpasa Campus, Department of Civil Engineering, 34210 Esenler- stanbul, Turkey
S.D. Akbas: Yildiz Technical University, Davutpasa Campus, Department of Civil Engineering, 34210 Esenler- stanbul, Turkey

Abstract
This paper investigates the structural responses of axially restrained steel beams under fire conditions by a nonlinear finite element method. The axial restraint is represented by a linear elastic spring. Different parameters which include beam slenderness ratio, external load level and axial restraint ratio are investigated. The process of forming a mid-span plastic hinge at the mid-span under a rising temperature is studied. In line with forming a fully plastic hinge at mid-span, the response of a restrained beam under rising temperature can be divided into three stages, viz. no plastic hinge, hinge forming and rotating, and catenary action stage. During catenary action stage, the axial restraint pulls the heated beam and prevents it from failing. This study introduces definitions of beam limiting temperature Tlim, catenary temperature Tctn and warning time twn. Influences of slenderness ratio, load level and axial restraint ratio on Tlim, Tctn and twn are examined.

Key Words
steel; fire; numerical analysis; axial restraint; limiting temperature; catenary action.

Address
Zhan-fei Huang: AECOM Singapore Pte Ltd., BLK. 289G, Bukit Batok St. 25, #07-108, Singapore 656289
Kang-hai Tan: School of Civil & Environmental Engineering, Nanyang Technological University, Singapore 639798
George L. England: Department of Civil Engineering, Imperial College, Imperial College Road, London SW7 2BU, United Kingdom

Abstract
The dynamic stiffness matrix is formulated for an axially loaded slender double-beam element in which both beams are homogeneous, prismatic and of the same length by directly solving the governing differential equations of motion of the double-beam element. The Bernoulli-Euler beam theory is used to define the dynamic behaviors of the beams and the effects of the mass of springs and axial force are taken into account in the formulation. The dynamic stiffness method is used for calculation of the exact natural frequencies and mode shapes of the double-beam systems. Numerical results are given for a particular example of axially loaded double-beam system under a variety of boundary conditions, and the exact numerical solutions are shown for the natural frequencies and normal mode shapes. The effects of the axial force and boundary conditions are extensively discussed.

Key Words
double-beam system; Bernoulli-Euler beam; axial force; free vibration; dynamic stiffness matrix.

Address
Li Jun: Vibration, Shock & Noise Institute, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, People

Abstract
The paper proposes two methodologies for damage identification from measured natural frequencies of a contiguously damaged reinforced concrete beam, idealised with distributed damage model. The first method identifies damage from Iso-Eigen-Value-Change contours, plotted between pairs of different frequencies. The performance of the method is checked for a wide variation of damage positions and extents. The method is also extended to a discrete structure in the form of a five-storied shear building and the simplicity of the method is demonstrated. The second method is through smeared damage model, where the damage is assumed constant for different segments of the beam and the lengths and centres of these segments are the known inputs. First-order perturbation method is used to derive the relevant expressions. Both these methods are based on distributed damage models and have been checked with experimental program on simply supported reinforced concrete beams, subjected to different stages of symmetric and un-symmetric damages. The results of the experiments are encouraging and show that both the methods can be adopted together in a damage identification scenario.

Key Words
damage identification; Iso-eigen-change; smeared damage model.

Address
N. Lakshmanan: Structural Engineering Research Centre, CSIR Campus, Taramani, Chennai 600113, India
B.K. Raghuprasad: Department of Civil Engineering, Indian Institute of Science, Bangalore 560012, India
N. Gopalakrishnan: Structural Engineering Research Centre, CSIR Campus, Taramani, Chennai 600113, India
R. Sreekala: Structural Engineering Research Centre, CSIR Campus, Taramani, Chennai 600113, India
G.V. Rama Rao: Structural Engineering Research Centre, CSIR Campus, Taramani, Chennai 600113, India

Abstract
Seismic isolation is a well-known method to mitigate the earthquake effects on structures by increasing their fundamental natural periods at the expense of larger displacements in the structural system. In this paper, the seismic response of isolated and fixed base vertical, cylindrical, liquid storage tanks is investigated using a Finite Element Model (FEM), taking into account fluid-structure interaction effects. Three vertical, cylindrical tanks with different ratios of height to radius (H/R = 2.6, 1.0 and 0.3) are numerically analyzed and the results of response-history analysis, including base shear, overturning moment and free surface displacement are reported for isolated and non-isolated tanks. Isolated tanks equipped by lead rubber bearings isolators and the bearing are modeled by using a non-linear spring in FEM model. It is observed that the seismic isolation of liquid storage tanks is quite effective and the response of isolated tanks is significantly influenced by the system parameters such as their fundamental frequencies and the aspect ratio of the tanks. However, the base isolation does not significantly affect the surface wave height and even it can causes adverse effects on the free surface sloshing motion.

Key Words
liquid storage tank; seismic analysis; numerical analysis; base isolation.

Address
Mohammad Ali Goudarzi: Civil Engineering Department, Lorestan University, Khoramabad, Iran
Saeed Alimohammadi: Civil Engineering, University of Science and Culture, Tehran, Iran

Abstract
It is well known that the analytical vibration characteristic of a cracked beam depends largely on the crack model. In the forward analysis, an improved and simplified approach in modeling discrete open cracks in beams is presented. The effective length of the crack zone on both sides of a crack with stiffness reduction is formulated in terms of the crack depth. Both free and forced vibrations of cracked beams are studied in this paper and the results from the proposed modified crack model and other existing models are compared. The modified crack model gives very accurate predictions in the modal frequencies and time responses of the beams particularly with overlaps in the effective lengths with reduced stiffness. In the inverse analysis, the response sensitivity with respect to damage parameters (the location and depth of crack, etc.) is derived. And the dynamic response sensitivity is used to update the damage parameters. The identified results from both numerical simulations and experiment work illustrate the effectiveness of the proposed method.

Key Words
multiple cracks; dynamic response; crack identification; inverse problem.

Address
Z.Y. He: School of Civil and Transportation Engineering, South China University of Technology, Guangzhou 510641, P.R. China
Z.R. Lu: School of Engineering, Sun Yat-sen University, Guangzhou 510275, P.R. China

Abstract


Key Words


Address
Yudong Chen: Department of Mechanics, Nanling Campus, Jilin University, Changchun, 130025, China
Suhuan Chen: Department of Mechanics, Nanling Campus, Jilin University, Changchun, 130025, China


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