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Hussein A.,El-Tawil M.,El-Tahan W.,Mahmoud, A. A. 국제구조공학회 2008 Structural Engineering and Mechanics, An Int'l Jou Vol.28 No.2
This paper considers the solution of the stochastic differential equations (SDEs) with random operator and/or random excitation using the spectral SFEM. The random system parameters (involved in the operator) and the random excitations are modeled as second order stochastic processes defined only by their means and covariance functions. All random fields dealt with in this paper are continuous and do not have known explicit forms dependent on the spatial dimension. This fact makes the usage of the finite element (FE) analysis be difficult. Relying on the spectral properties of the covariance function, the Karhunen-Loeve expansion is used to represent these processes to overcome this difficulty. Then, a spectral approximation for the stochastic response (solution) of the SDE is obtained based on the implementation of the concept of generalized inverse defined by the Neumann expansion. This leads to an explicit expression for the solution process as a multivariate polynomial functional of a set of uncorrelated random variables that enables us to compute the statistical moments of the solution vector. To check the validity of this method, two applications are introduced which are, randomly loaded simply supported reinforced concrete beam and reinforced concrete cantilever beam with random bending rigidity. Finally, a more general application, randomly loaded simply supported reinforced concrete beam with random bending rigidity, is presented to illustrate the method.
Crack propagation speed in ultra high performance concrete (UHPC)
Pyo, S.,Alkaysi, M.,El-Tawil, S. Butterworth Scientific ; Elsevier Science Ltd 2016 Construction and Building Materials Vol.114 No.-
This paper investigates crack speed in ultra-high performance concrete (UHPC) using pre-notched three-point bending specimens. The experimental parameters are fiber volume fraction and rate of loading. A hydraulic servo-controlled testing machine is used to apply lower notch tip strain rates, in the range of 0.025-1.01/s, while a newly developed impact testing system is used to achieve higher notch tip strain rates, ranging from 6.8 to 41.11/s. A high-speed camera is used to record images of the UHPC specimens during testing. Notch tip strain and crack speed are computed from the images, which show that crack speed increases asymptotically as the crack initiation strain rate increases. Crack speeds of up to 514m/s were achieved at the lower notch tip strain rates and up to 1454m/s for the higher notch tip strain rates. The achieved relationships are incorporated into a recently proposed crack-velocity dependent dynamic fracture model. The model is validated using published experimental data and used to show that, like conventional concrete, the strain rate sensitivity of UHPC is strongly associated with the characteristics of dynamic crack growth.
Spectral SFEM analysis of structures with stochastic parameters under stochastic excitation
Galal, O.H.,El-Tahan, W.,El-Tawil, M.A.,Mahmoud, A.A. Techno-Press 2008 Structural Engineering and Mechanics, An Int'l Jou Vol.28 No.3
In this paper, linear elastic isotropic structures under the effects of both stochastic operators and stochastic excitations are studied. The analysis utilizes the spectral stochastic finite elements (SSFEM) with its two main expansions namely; Neumann and Homogeneous Chaos expansions. The random excitation and the random operator fields are assumed to be second order stochastic processes. The formulations are obtained for the system solution of the two dimensional problems of plane strain and plate bending structures under stochastic loading and relevant rigidity using the previously mentioned expansions. Two finite element programs were developed to incorporate such formulations. Two illustrative examples are introduced: the first is a reinforced concrete culvert with stochastic rigidity subjected to a stochastic load where the culvert is modeled as plane strain problem. The second example is a simply supported square reinforced concrete slab subjected to out of plane loading in which the slab flexural rigidity and the applied load are considered stochastic. In each of the two examples, the first two statistical moments of displacement are evaluated using both expansions. The probability density function of the structure response of each problem is obtained using Homogeneous Chaos expansion.
Spectral SFEM analysis of structures with stochastic parameters under stochastic excitation
O.H. Galal,W. El-Tahan,M.A. El-Tawil,A.A. Mahmoud 국제구조공학회 2008 Structural Engineering and Mechanics, An Int'l Jou Vol.28 No.3
In this paper, linear elastic isotropic structures under the effects of both stochastic operators and stochastic excitations are studied. The analysis utilizes the spectral stochastic finite elements (SSFEM) with its two main expansions namely; Neumann and Homogeneous Chaos expansions. The random excitation and the random operator fields are assumed to be second order stochastic processes. The formulations are obtained for the system solution of the two dimensional problems of plane strain and plate bending structures under stochastic loading and relevant rigidity using the previously mentioned expansions. Two finite element programs were developed to incorporate such formulations. Two illustrative examples are introduced: the first is a reinforced concrete culvert with stochastic rigidity subjected to a stochastic load where the culvert is modeled as plane strain problem. The second example is a simply supported square reinforced concrete slab subjected to out of plane loading in which the slab flexural rigidity and the applied load are considered stochastic. In each of the two examples, the first two statistical moments of displacement are evaluated using both expansions. The probability density function of the structure response of each problem is obtained using Homogeneous Chaos expansion.
Dong-Joo Kim,Antoine E. Naaman,Sherif El-Tawil 한국콘크리트학회 2009 International Journal of Concrete Structures and M Vol.3 No.2
This paper provides a brief summary of the performance of an innovative slip hardening twisted steel fiber in comparison with other fibers including straight steel smooth fiber, high strength steel hooked fiber, SPECTRA (high molecular weight polyethylene) fiber and PVA fiber. First the pull-out of a single fiber is compared under static loading conditions, and slip ratesensitivity is evaluated. The unique large slip capacity of T-fiber during pullout is based on its untwisting fiber pullout mechanism, which leads to high equivalent bond strength and composites with high ductility. Due to this large slip capacity a smaller amount of T-fibers is needed to obtain strain hardening tensile behavior of fiber reinforced cementitious composites. Second, the performance of different composites using T-fibers and other fibers subjected to tensile and flexural loadings is described and compared. Third, strain rate effect on the behavior of composites reinforced with different types and amounts of fibers is presented to clarify the potential application of HPFRCC for seismic, impact and blast loadings.
Kim, Dong-Joo,Naaman, Antoine E.,El-Tawil, Sherif Korea Concrete Institute 2009 International Journal of Concrete Structures and M Vol.3 No.2
This paper provides a brief summary of the performance of an innovative slip hardening twisted steel fiber in comparison with other fibers including straight steel smooth fiber, high strength steel hooked fiber, SPECTRA (high molecular weight polyethylene) fiber and PVA fiber. First the pull-out of a single fiber is compared under static loading conditions, and slip rate-sensitivity is evaluated. The unique large slip capacity of T-fiber during pullout is based on its untwisting fiber pullout mechanism, which leads to high equivalent bond strength and composites with high ductility. Due to this large slip capacity a smaller amount of T-fibers is needed to obtain strain hardening tensile behavior of fiber reinforced cementitious composites. Second, the performance of different composites using T-fibers and other fibers subjected to tensile and flexural loadings is described and compared. Third, strain rate effect on the behavior of composites reinforced with different types and amounts of fibers is presented to clarify the potential application of HPFRCC for seismic, impact and blast loadings.