Abstract
This paper presents the results of a study to show how the development of a crack alters the structural behavior of I-shaped steel beams and how this can be used to evaluate nondestructive evaluation techniques. The approach is based on changes in the dynamic behavior. An approximate finite element model for a cracked beam with I-shaped cross-section is developed based on a simplified fracture model. The model is then used to review different damage cases. Damage detection techniques are studied to determine their ability to identify the existence of the crack and to identify its location. The techniques studied are the coordinate modal assurance criterion, the modal flexibility, and the state and the slope arrays.
Key Words
coordinate modal assurance criterion; cracking; damage detection; finite element modeling; modal flexibility; mode shapes; natural frequencies; nondestructive evaluation; state and slope arrays; steel beams
Address
Jun Zhao; A. Epstein and Sons, Inc., Chicago, IL, USA John T. DeWolf; Department of Civil & Environmental Engineering, University of Connecticut, Storrs, CT, USA
Abstract
In this paper, a dynamic analysis based on the fuzzy set theory is presented as a possible complementary tool to the classical stochastic methods for dynamic analyses. Material parameters of a structure are influenced by uncertainties and therefore they are considered to be fuzzy quantities with given distributions, that means fuzzy numbers with given membership functions. The fuzzy dynamic analysis is conducted with help of fuzzy arithmetic defined on the so-called -cuts. The results of the analysis are also obtained in the form of fuzzy numbers, which compared to the stochastic methods is less computationaly expensive while at the same time they still provide information about the distribution of a quantity. This method is demonstrated on an analysis of a two-dimensional frame subjected to possible seismic load, where the uncertain eigenmodes and eigenfrequencies are used in the modal analysis.
Key Words
earthquake design; eigenfrequencies; eigenmodes; finite element method; fuzzy numbers
Address
Petr Štemberk and Jaroslav Kruis; Faculty of Civil Engineering, Czech Technical University, Th?kurova 7, 166 29 Praha 6, Czech Republic
Abstract
A first endeavor is made to exploit the differential quadrature method (DQM) as a simple, accurate, and computationally efficient numerical tool for the large deformation analysis of thin laminated composite skew plates, which has very strong singularity at the obtuse vertex. The geometrical nonlinearity is modeled by using Green?s strain and von Karman assumption. A recently developed DQ methodology is used to exactly implement the multiple boundary conditions at the edges of skew plates, which is a major draw back of conventional DQM. Using oblique coordinate system and the DQ methodology, a mapping-DQ discretization rule is developed to simultaneously transform and discretize the equilibrium equations and the related boundary conditions. The effects of skew angle, aspect ratio and different types of boundary conditions on the convergence and accuracy of the presented method are studied. Comparing the results with the available results from other numerical or analytical methods, it is shown that accurate results are obtained even when using only small number of grid points. Finally, numerical results for large deflection behavior of antisymmetric cross ply skew plates with different geometrical parameters and boundary conditions are presented.
Key Words
large deformation; thin laminated skew plates; differential quadrature method
Address
P. Malekzadeh; Department of Mechanical Engineering, School of Engineering, Persian Gulf University, Bushehr 75168, Iran Center of Excellence for Computational Mechanics in Mechanical Engineering, Shiraz University, Shiraz, Iran
Abstract
A decoupling technique for simulating near-field wave motions in two-phase media is introduced in this paper. First, an equivalent but direct weighted residual method is presented in this paper to solve boundary value problems more explicitly. We applied the Green?s theorem for integration by parts on the equivalent integral statement of the field governing equations and then introduced the Neumann conditions directly. Using this method and considering the precision requirement in wave motion simulation, a lumped-mass FEM for two-phase media with clear physical concepts and convenient implementation is derived. Then, considering the innate attenuation character of the wave in two-phase media, an attenuation parameter is introduced into Liao?s Multi-Transmitting Formula (MTF) to simulate the attenuating outgoing wave in two-phase media. At last, two numerical experiments are presented and the numerical results are compared with the analytical ones demonstrating that the lumped-mass FEM and the generalized MTF introduced in this paper have good precision.
Address
S. L. Chen; College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China Z. P. Liao; Institute of Engineering Mechanics, China Seismological Bureau, Harbin 150080, China J. Chen; The State Key Laboratory of Vibration, Shock & Noise, Shanghai Jiao Tong University, Shanghai 20030, China
Abstract
A harmonic type differential quadrature approach for nonlinear dynamic analysis of multi-degree-of-freedom systems has been developed. A series of numerical examples is conducted to assess the performance of the HDQ method in linear and nonlinear dynamic analysis problems. Results are compared with the existing solutions available from other analytical and numerical methods. In all cases, the results obtained are quite accurate.
Key Words
structural dynamics; harmonic differential quadrature; nonlinear analysis
Address
Omer Civalek; Akdeniz University, Civil Engineering Department, Division of Mechanics, 07200, Antalya, Turkiye
Abstract
The effect of cable loosening on the nonlinear parametric vibrations of inclined cables is discussed in this paper. In order to overcome the small-sag limitation in calculating loosening for inclined cables, it is necessary to first derive equations of motion for an inclined cable. Using these equations and the finite difference method, the effect of cable loosening on the nonlinear parametric response of inclined cables under periodic support excitation is evaluated. A new technique that takes into account flexural rigidity and damping is proposed as a solution to solve the problem of divergence. The regions of inclined cables that undergo compression are also indicated.
Key Words
inclined cable; loosening; parametric vibration
Address
Qingxiong Wu; College of Civil Engineering, Fuzhou University, 523 Gongye Road, Fuzhou, Fujian, China Kazuo Takahashi; Department of Civil Engineering, Faculty of Engineering, Nagasaki University, 1-14, Bunkyo-machi, Nagasaki, Japan Baochun Chen; College of Civil Engineering, Fuzhou University, 523 Gongye Road, Fuzhou, Fujian, China
Abstract
This paper deals with optimal stacking sequence design of laminate composite structures. The stacking sequence optimisation of laminate composites is formulated as a combinatorial problem and is solved using Simulated Annealing (SA), an algorithm devised based on inspiration of physical process of annealing of solids. The combinatorial constraints are handled using a correction strategy. The SA algorithm is strengthened by embedding Tabu search in order to prevent recycling of recently visited solutions and the resulting algorithm is referred to as tabu embedded simulated Annealing (TSA) algorithm. Computational performance of the proposed TSA algorithm is enhanced through cache-fetch implementation. Numerical experiments have been conducted by considering rectangular composite panels and composite cylindrical shell with different ply numbers and orientations. Numerical studies indicate that the TSA algorithm is quite effective in providing practical designs for lay-up sequence optimisation of laminate composites. The effect of various neighbourhood search algorithms on the convergence characteristics of TSA algorithm is investigated. The sensitiveness of the proposed optimisation algorithm for various parameter settings in simulated annealing is explored through parametric studies. Later, the TSA algorithm is employed for multi-criteria optimisation of hybrid composite cylinders for simultaneously optimising cost as well as weight with constraint on buckling load. The two objectives are initially considered individually and later collectively to solve as a multi-criteria optimisation problem. Finally, the computational efficiency of the TSA based stacking sequence optimisation algorithm has been compared with the genetic algorithm and found to be superior in performance.
Abstract
It is well known that the accuracy of finite element solutions deteriorate in the presence of severe mesh distortions. But distortion is often unavoidable in mesh procedure involving complex geometry. Lee and Bathe (1993) studied the influence of mesh distortion on the serendipity and Lagrange quadrilateral elements. Lautersztajn and Samuelsson (2000) discussed the effects of geometric distortions on four-node isoparametric quadrilateral elements and concluded that the element performance can be rendered ?insensitive? to a particular type of mesh distortion by increasing the order of the interpolation functions for the displacement field. In order to overcome the influence of element distortions, unsymmetric 8-node (Rajendran and Liew 2003) and unsymmetric 20-node element (Ooi et al. 2004) are developed to reproducing any linear and quadratic displacement field under any admissible mesh distortions. However, they will produce an asymmetrical stiffness matrix, so these formulations require an asymmetrical solver to solve the resulting stiffness equations. The goal of this paper is to discuss the effects of element distortions on the accuracy and efficiency of enriched quadrilateral elements with bubble functions. A bubble function is defined as a function that vanishes along the element boundaries. Bubble functions have been introduced to construct plate element models (Auricchio and Taylor 1995, Cook et al. 2002, Hong et al. 2001). They are employed to solve advection-diffusion problems by Brezzi, Franca and Farhat (Brezzi et al. 1992, Brezzi and Russo 1994, Franca and Farhat 1995). Furthermore, the limitation of bubble functions is discussed by Franca and Farhat (1994) and error analysis of residual-free bubbles is discussed by Brezzi et al. (1999) and Sangalli (2000).
Key Words
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Address
Shi-Pin Ho and Yen-Liang Yeh; Department of Mechanical Engineering, National Cheng Kung University, Tainan, Taiwan, R.O.C.
