Abstract
Numerical solution to linear bending analysis of circular plates is obtained by the method of harmonic differential quadrature (HDQ). In the method of differential quadrature (DQ), partial space derivatives of a function appearing in a differential equation are approximated by means of a polynomial expressed as the weighted linear sum of the function values at a preselected grid of discrete points. The method of HDQ that was used in the paper proposes a very simple algebraic formula to determine the weighting coefficients required by differential quadrature approximation without restricting the choice of mesh grids. Applying this concept to the governing differential equation of circular plate gives a set of linear simultaneous equations. Bending moments, stresses values in radial and tangential directions and vertical deflections are found for two different types of load. In the present study, the axisymmetric bending behavior is considered. Both the clamped and the simply supported edges are considered as boundary conditions. The obtained results are compared with existing solutions available from analytical and other numerical results such as finite elements and finite differences methods. A comparison between the HDQ results and the finite difference solutions for one example plate problem is also made. The method presented gives accurate results and is computationally efficient.
Abstract
A rational and simple analytical model to predict the time varying cracking moment of reinforced concrete sections under sustained loading is developed. The modeling procedure is based on equilibrium and compatibility requirements and takes into account the interdependent effects of creep and shrinkage as well as the presence of axial loading. A parametric study is conducted in which particular consideration is given to the effects of reinforcement ratio, level of loading, and creep and shrinkage characteristics of concrete. It is concluded that the reduction in cracking moment is mainly attributed to shrinkage. The effect of shrinkage is more pronounced at low levels of sustained loading and at high reinforcement ratios. This effect is lessened by the compression steel and creep particularly when the applied moment is near the cracking moment.
Key Words
cracking; creep; reinforced concrete; shrinkage; sustained loading.
Address
Civil Engineering Department, College of Engineering, P.O. Box 800, King Saud University, Riyadh 11421, Saudi Arabia
Abstract
A total life model was developed to assess the service life of aging aircraft. The primary focus of this paper is the development of crack growth life projection using the response surface method. Crack growth life projection is a necessary component of the total life model. The study showed that the number of load cycles N needed for a crack to propagate to a specified size can be linearly related to the geometric parameter, material, and stress level of the component considered when all the variables are transformed to logarithmic values. By the Central Limit theorem, the ln N was approximated by Gaussian distribution. This Gaussian model compared well with the histograms of the number of load cycles generated from simulated crack growth curves. The outcome of this study will aid engineers in designing their crack growth experiments to develop the stochastic crack growth models for service life assessments.
Key Words
crack growth; fatigue; aging aircraft; response surface method; central limit theorem; structural reliability; Gaussian distribution; statistical analysis; Kolmogorov-Smirnov test; point estimate method.
Address
Karen C. Chou Department of Mechanical & Civil Engineering, 205 Trafton Science Center E., Minnesota State University, Mankato, MN 56001, U.S.A.
Glenn C. Cox Lockwood Greene Engineers, Knoxville, TN, U.S.A.
Allison M. Lockwood Department of Civil & Environmental Engineering, University of Tennessee, Knoxville, U.S.A.
Abstract
Since the linear elastic fracture analysis has been proved to be insufficient in predicting the failure of strain hardening materials, a number of fracture concepts have been studied which remain applicable in the presence of plasticity near a crack tip. This work thereby presents a new finite element model to predict the elastic-plastic crack-tip field and fatigue life of center-cracked panels(CCP) with ductile fracture under large-scale yielding conditions. Also, this study has been carried out to investigate the path-dependence of J-integral within the plastic zone for elastic-perfectly plastic, bilinear elastic-plastic, and nonlinear elastic-plastic materials. Based on the incremental theory of plasticity, the p-version finite element is employed to account for the accurate values of J-integral, the most dominant fracture parameter, and the shape of plastic zone near a crack tip by using the J-integral method. To predict the fatigue life, the conventional Paris law has been modified by substituting the range of J-value denoted by DJ for DK. The experimental fatigue test is conducted with five CCP specimens to validate the accuracy of the proposed model. It is noted that the relationship between the crack length a and DK in LEFM analysis shows a strong linearity, on the other hand, the nonlinear relationship between a and DJ is detected in EPFM analysis. Therefore, this trend will be depended especially in the case of large scale yielding. The numerical results by the proposed model are compared with the theoretical solutions in literatures, experimental results, and the numerical solutions by the conventional h-version of the finite element method.
Key Words
large scale yielding; J-integral; fatigue life; HRR-singularity; EPFM; CCP specimen; p-version of F.E.M.; modified Paris Law.
Address
Kwang S. Woo Department of Civil Engineering, Yeungnam University, Gyeongsan 712-749,Korea
Chong H. Hong Department of Civil Engineering, Tamna University, Seoguipo 697-340, Korea
Prodyot K. Basu Department of Civil Engineering, Vanderbilt University, TN 37212, U.S.A.
Abstract
The novel form of composite walling system consists of two skins of profiled steel sheeting with an in-fill of concrete. Such walling system can be used as shear elements in steel framed building subjected to lateral load. This paper presents the results of small-scale model tests on composite wall and its components manufactured from very thin sheeting and micro-concrete tested under monotonic and cyclic shear loading conditions. The heavily instrumented small-scale tests provided information on the load-deformation response, strength, stiffness, strain condition, sheet-concrete interaction and failure modes. Analytical models for shear strength and stiffness are derived with some modification factor to take into account the effect of quasi-static cycling loading. The performance of design equations is validated through experimental results.
Abstract
In gradient-dependent plasticity theory, the yield strength depends on the Laplacian of an equivalent plastic strain measure (hardening parameter), and the consistency condition results in a differential equation with respect to the plastic multiplier. The plastic multiplier is then discretized in addition to the usual discretization of the displacements, and the consistency condition is solved simultaneously with the equilibrium equations. The disadvantage is that the plastic multiplier requires a Hermitian interpolation that has four degrees of freedom at each node. Instead of using a Hermitian interpolation, in this article, a 3-node incompatible (trigonometric) interpolation is proposed for the plastic multiplier. This incompatible interpolation uses only the function values of each node, but it is continuous across element boundaries and its second-order derivatives exist within the elements. It greatly reduces the degrees of freedom for a problem, and is shown through a numerical example on localization to yield good results.
Key Words
gradient-dependent plasticity; incompatible element; trigonometric interpolation; strain localization.
Address
Faculty of Engineering & Surveying, The University of Southern Queensland, Toowoomba, QLD 4350, Australia
Abstract
It is known that lap splices in the longitudinal reinforcement of reinforced concrete (RC) bridge columns are not desirable for seismic performance, but it is sometimes unavoidable. Lap splices were practically located in the potential plastic hinge region of most bridge columns that were constructed before the 1992 seismic design provisions of the Korea Bridge Design Specification. The objective of this research is to evaluate the seismic performance of reinforced concrete (RC) bridge piers with lap splicing of longitudinal reinforcement in the plastic hinge region, to develop an enhancement scheme for their seismic capacity by retrofitting with glassfiber sheets, and to assess a damage of bridge columns subjected to seismic loadings for the development of rational seismic design provisions in low or moderate seismicity region. Nine (9) test specimens with an aspect ratio of 4 were made with three confinement ratios and three types of lap splice. Quasi-static tests were conducted in a displacement-controlled way under three different axial loads. A significant reduction of displacement ductility was observed for test columns with lap splices of longitudinal reinforcements, whose displacement ductility could be greatly improved by externally wrapping with glassfiber sheets in the plastic hinge region. A damage of the limited ductile specimen was assessed to be relatively small.
Key Words
RC bridge pier; seismic performance; lap splice; retrofit; glassfiber; quasi-static test.
Address
Department of Civil Engineering, Chung-Ang University, San 40-1, Naeri, Daedeogmyeon, Anseong Gyeonggi-Do, 456-756, Republic of Korea
Abstract
A mixed eight-node hexahedral element formulated via the Hu-Washizu principle as well as the field extrapolation technique is presented. The mixed element with only three translational degrees of freedom at each node can provide extremely accurate and reliable performance for popular benchmark problems such as spacial beams, plates, shells as well as general three-dimensional elasticity problems. Numerical calculations also show that when extremely skewed and coarse meshes and nearly incompressible materials are used, the proposed mixed element can still possess excellent behaviour. The mixed formulation starts with introduction of a parallelepiped domain associated with the given general eight-node hexahedral element. Then, the assumed strain field at the nodal level is constructed via the Hu-Washizu variational principle for that associated parallelepiped domain. Finally, the assumed strain field at the nodal level of the given hexahedral element is established by using the field extrapolation technique, and then by using the trilinear shape functions the assumed strain field of the whole element domain is obtained. All matrices involved in establishing the element stiffness matrix can be evaluated analytically and expressed explicitly; however, a 24 by 24 matrix has to be inverted to construct the displacement extrapolation matrix. The proposed hexahedral element satisfies the patch test as long as the element with a shape of parallelepiped.
Key Words
Hu-Washizu principle; field extrapolation; assumed strain formulation; eight-node parallelepiped; mixed formulation; shear and membrane locking.
Address
Yung-I Chen Bureau of High Speed Rail, Ministry of Transportation and Communications, 13F, No. 7, Sec. 2, Sianmin Blvd., Banchiao City, Taipei County, 220, Taiwan, R.O.C.
Guan-Yuan Wu Department of Fire Science, Central Police University, No. 56, Shu Jen Road, Ta Kang, Kwei San, Taoyuan, 333 Taiwan, R.O.C.
