Dynamics of Space-Fractional Euler–Bernoulli and Timoshenko Beams

This paper investigates the dynamics of the beam-like structures whose response manifests a strong scale effect. The space-Fractional Euler–Bernoulli beam (s-FEBB) and space-Fractional Timoshenko beam (s-FTB) models, which are suitable for small-scale slender beams and small-scale thick beams, respectively, have been extended to a dynamic case. The study provides appropriate governing equations, numerical approximation, detailed analysis of free vibration, and experimental validation. The parametric study presents the influence of non-locality parameters on the frequencies and shape of modes delivering a depth insight into a dynamic response of small scale beams. The comparison of the s-FEBB and s-FTB models determines the applicability limit of s-FEBB and indicates that the model (also the classical one) without shear effect and rotational inertia can only be applied to beams significantly slender than in a static case. Furthermore, the validation has confirmed that the fractional beam model exhibits very good agreement with the experimental results existing in the literature—for both the static and the dynamic cases. Moreover, it has been proven that for fractional beams it is possible to establish constant parameters of non-locality related to the material and its microstructure, independent of beam geometry, the boundary conditions, and the type of analysis (with or without inertial forces).

Analysis of a partially loaded paraboloid of revolution and possible approximations of its solution

In this paper a partially loaded paraboloid of revolution is investigated by the theory of bent shallow shells. After establishing the sixth order linear system of equations it is concluded that the unknown coefficients cannot be expressed, cannot be given as practical formulas, thus useful approximate solutions are constructed for practical usage. The applicability limit of the column reaction approximated by concentrated load is investigated and the generated error of membrane action for this approximation is determined.

Evaluation of Cumulative Damage of RC Members under Repeated Impact Loading

In the civil and structural engineering field, there are so many problems regarding act of impact loading against some structures due to natural disaster. So it is important to evaluate the damage condition of them after impact loading, and to estimate the residual performance of them. This study is focused on a reinforced concrete (herein after called RC) structure such as caisson breakwater and rock-shed. In order to quantitatively evaluate the dynamic behavior and cumulative damage of RC members under low-velocity single and repeated impact loading, we conducted numerical approach by using the theory of Continuum Damage Mechanics (herein after called CDM). At the result, we clarified not only impact behavior of the members but also the relationship between cumulative kinetic energy of repeated impact loading and cumulative damage of the members. In addition, applicability limit of our model based on scalar damage modeling was clarified.

Selection of Treatment Process for Textile Dye Wastewater Based on Their Bio-chemical Characteristics

In Bangladesh most of the industries follow chemical treatment process for wastewater treatment without any effluent quality assessment. The aim of this study was to select an effective treatment process for effluent based on its bio-chemical characteristics. Wastewater samples from Textile Industries were collected in 9 batches over a period of 2 months (from17th November, 2011 to 28th April, 2012). Approximately 40liters composite samples were collected of several dying batches from inlet of the equalization tank. Sludge was collected from outlet point of settling tank. The physical, chemical and bio-chemical quality of untreated wastewater were assessed by analyses of some particular parameters in the laboratory and compared with ECR standard. Average concentration of EC (mS/cm), pH, COD (mg/L), BOD (mg/L) and BOD loading (kg/m3.d) were respectively 3.71, 9.24, 1472, 1024, and 0.205 respectively. For lower BOD loading, the treatment performance was found better..COD decreased rapidly during the first 8 hours of aeration and after 16 hours of aeration it became uniform. During the first 8 hr COD removal was more than 50% of the initial COD loading. The standard value of COD (200mg/l) was obtained within 12 to 16 hours of aeration for the initial BOD loading less than or equal 0.15 kg/m3.day and 24 hours of aeration for initial BOD loading 0.16 to 0.26 kg/m3.day and more than 24 hour for initial BOD loading greater than 0.26 kg/m3.day. The study revealed that volumetric loading is an important parameter for wastewater which to a great extent sets applicability limit of treatment process. From this laboratory model study, treatment process options have been recommended for industrial effluent having different bio-chemical characteristics.DOI: http://dx.doi.org/10.3329/jesnr.v6i1.22060 J. Environ. Sci. & Natural Resources, 6(1): 163-166 2013

Improvements to J-Estimation Scheme for Predicting Moment-Rotation Response of Circumferential Through-Wall Cracks in Piping

This paper presents improvements to the LBB.ENG2 method for predicting the moment-rotation response of a circumferential through-wall cracked (TWC) pipe under combined tension and bending loads. The LBB.ENG2 method provides closed-form equations for J-integral (J) estimation using a load-displacement relationship, where the Mode I stress intensity factor (K) solution, beam differential equations, and limit load solutions are utilized for elastic and plastic displacements under a thin-shell assumption. Due to its good predictions and simplicity, LBB.ENG2 has been incorporated into the recent probabilistic fracture mechanics codes, PRO-LOCA and xLPR. The LBB.ENG2 method, however, has a limited applicability inherited from the thin-shell assumption and the K solution. That is, it might yield an unrealistic J for a thick pipe, or very short and long cracks. In this study, improvements are made to the method, and the thin-shell assumption is revisited. First, in order to extend the applicability limit of the K solution and, hence, the limit of the LBB.ENG2 method, newly developed and more accurate K solutions are implemented in a suitable form to derive equations explicitly for prediction of the crack instability point. Second, thin-shell and thick-shell assumptions are compared and technical justification for the use of the thin-shell theory is provided. In addition, based on the LBB.ENG2 method, moment-rotation response curves of circumferential through-wall cracked pipes are generated.