Abstract
Modal analysis of cracked cantilever composite beams, made of graphite-fibre reinforced polyamide, is studied. By using the finite element and component mode synthesis methods, a numeric model applicable to investigate the vibration of cracked composite beams is developed. In this new approach, from the crack section, the composite beam separated into two parts coupled by a flexibility matrix taking into account the interaction forces. These forces are derived from the fracture mechanics theory as the inverse of the compliance matrix calculated with the proper stress intensity factors and strain energy release rate expressions. Numerical results are obtained for modal analysis of composite beams with a transverse non-propagating open crack, addressing the effects of the location and depth of the crack, and the volume fraction and orientation of the fibre on the natural frequencies and mode shapes. By means of modal data, the position and dimension of the defect can be found. The results of the study confirmed that presented method is suitable for the vibration analysis of cracked cantilever composite beams. Present technique can be easily extended to composite plates and shells.
Abstract
This paper presents the section model for analysis of RC circular tower structures based on nonlinear material laws. The governing equations for normal strains due to the bending moment and the normal force are derived in the case when openings are located symmetrically in respect to the bending direction. In this approach the additional reinforcement at openings is also taken into account. The mathematical model is expressed in the form of a set of nonlinear equations which are solved by means of the minimization of the sums of the second powers of the residuals. For minimization the BFGS quasi-Newton and/or Hooke-Jeeves local minimizers suitably modified are applied to take into account the box constraints on variables. The model is verified on the set of data encountered in engineering practice. The numerical examples illustrate the effects of the loading eccentricity and size of the opening on the strains and stresses in concrete and steel in the cross-sections under consideration. Calculated results indicate that the additional reinforcement at the openings increases the resistance capacity of the section by several percent.
Key Words
tower; structure; reinforced concrete; opening; box-constrained optimization.
Address
Marek Lechman; Building Research Institute, 00-611 Warsaw, Filtrowa 1, Poland Andrzej Stachurski; Institute of Control and Computation Engineering, Warsaw University of Technology, 00-665 Warsaw, Nowowiejska 15/19, Poland
Abstract
The paper presents a finite element model for studying timber-concrete composite beams under long-term loading. Both deformability of connection system and rheological behaviour of concrete, timber and connection are fully considered. The creep of component materials and the influence of moisture content on the creep of timber and connection, the so-called ?echano-sorptive?effect, are evaluated by means of accurate linear models. The solution is obtained by applying an effective step-by-step procedure in time, which does not require storing the whole stress history in some points in order to account for the creep behaviour. Hence the proposed method is suitable for analyses of composite beams subjected to complex loading and thermo-hygrometric histories. The possibility to accurately predict the long-term response is then shown by comparing numerical and experimental results for different tests.
Key Words
composite beams; concrete; creep; finite element method; long-term behaviour; mechano-sorptive effect; rheological phenomena; shrinkage; timber; wood.
Address
Department of Civil Engineering, University of Trieste, Piazzale Europa 1, 34127 Trieste, Italy
Abstract
Time delay exists inevitably in active control, which may not only degrade the system performance but also render instability to the dynamic system. In this paper, a novel active controller is developed to solve the time delay problem in flexible structures. By using the independent modal space control method, the differential equation of the controlled mode with time delay is obtained from the time-delay system dynamics. Then it is discretized and changed into a first-order difference equation without any explicit time delay by augmenting the state variables. The modal controller is derived based on the augmented system using the discrete variable structure control method. The switching surface is determined by minimizing a discrete quadratic performance index. The modal coordinate is extracted from sensor measurements and the actuator control force is converted from the modal one. Since the time delay is explicitly included throughout the entire controller design without any approximation, the system performance and stability are guaranteed. Numerical simulations show that the proposed controller is feasible and effective in active vibration control of dynamic systems with time delay. If the time delay is not explicitly included in the controller design, instability may occur.
Key Words
flexible structure; variable structure control; time delay.
Address
Guo-Ping Cai; Department of Engineering Mechanics, Shanghai Jiaotong University, Shanghai 200240, China Simon X. Yang; Advanced Robotics and Intelligent Systems (ARIS) Lab, School of Engineering, University of Guelph, Guelph, Ontario N1G 2W1, Canada
Abstract
A new method for deriving analytical solution of the annular elastic plate on elastic foundation under axisymmetric loading is presented. The formulation is based on application of Hankel integral transforms and Bessel functions?properties in the corresponding boundary-value problem. A representative example is studied and the obtained solution is compared with published numerical results indicating excellent agreement.
Key Words
annular plate; elastic foundation; Hankel transforms.
Address
D. G. Pavlou and N. V. Vlachakis; Department of Mechanical Engineering, TEI Halkidas, 34400 Psahna, Halkida, Evoia, Greece M. G. Pavlou; ERGOSE S.A., Works of Greek Federal Railway Organization, Karolou 27, 10437 Athens, Greece
Abstract
Applications of the Trefftz boundary element method (BEM) to anti-plane electroelastic problems are presented in this paper. Both direct and indirect methods with domain decomposition are discussed in details. Each crack is treated as semi-infinite thin slit defined in a subregion, for which a particular solution of the anti-plane problem, satisfying exactly the crack-face condition, is derived. The stress intensity factors defined at each crack tip can be directly computed from the coefficients of the particular solution. The performance of the proposed formulation is assessed by two examples and comparison is made with results obtained by other approaches. The Trefftz boundary element approach is demonstrated to be suitable for the analysis of the anti-plane problem of piezoelectric materials.
Key Words
Trefftz method; piezoelectric; anti-plane; boundary element.
Address
Department of Engineering, Australian National University, Acton ACT 0200, Australia
Abstract
A numerical approach combining the finite element method with two different stability criteria namely the Budiansky and the phase-plane buckling criteria is used to study the dynamic buckling phenomena of plate and shell structures subjected to sudden applied loading. In the finite element analysis an explicit time integration scheme is used and the two criteria are implemented in the Finite Element analysis. The dynamic responses of the plate and shell structures have been investigated for different values of the plate and shell imperfection factors. The results indicate that the dynamic buckling time, which is normally considered in predicting elasto-plastic buckling behavior, should be taken into consideration with the buckling criteria for elastic buckling analysis of plate and shell structures. By selecting proper control variables and incorporating them with two dynamic buckling criteria, the unique dynamic buckling load can be obtained and the problems of ambiguity and contradiction of dynamic buckling load of plate and shell structure can be resolved.
Key Words
buckling time; dynamic buckling; dynamic buckling criteria; dynamic buckling load; plate and shell structure; finite element method.
Address
Institute of High Performance Computing, 1 Science Park Road, #01-01 The Capricorn, Singapore Science Park II, Singapore 117528
Address
Aimin Jiang?nDepartment of Civil Engineering, Zhejiang University, Hangzhou, 310027, P.R. China West Branch of Zhejiang University of Technology, Quzhou, 324006, P.R. China Haojiang Ding?nDepartment of Civil Engineering, Zhejiang University, Hangzhou, 310027, P.R. China
