B N Rao
Articles written in Sadhana
Volume 33 Issue 6 December 2008 pp 733-751
This paper presents a study on the effect of blow-holes on the reliability of a cast component. The most probable point (MPP) based univariate response surface approximation is used for evaluating reliability. Crack geometry, blow-hole dimensions, external loads and material properties are treated as independent random variables. The methodology involves novel function decomposition at a most probable point that facilitates the MPP-based univariate response surface approximation of the original multivariate implicit limit state/performance function in the rotated Gaussian space. Once the approximate form of the original implicit limit state/performance function is deﬁned, the failure probability can be obtained by Monte Carlo simulation (MCS), importance sampling technique, and ﬁrst- and second-order reliability methods (FORM/SORM). FORTRAN code is developed to automate calls to ABAQUS for numerically simulating responses at sample points, to construct univariate response surface approximation, and to subsequently evaluate the failure probability by MCS, importance sampling technique, and FORM/SORM.
Volume 34 Issue 6 December 2009 pp 967-986
Probabilistic sensitivities provide an important insight in reliability analysis and often crucial towards understanding the physical behaviour underlying failure and modifying the design to mitigate and manage risk. This article presents a new computational approach for calculating stochastic sensitivities of mechanical systems with respect to distribution parameters of random variables. The method involves high dimensional model representation and score functions associated with probability distribution of a random input. The proposed approach facilitates first-and second-order approximation of stochastic sensitivity measures and statistical simulation. The formulation is general such that any simulation method can be used for the computation such as Monte Carlo, importance sampling, Latin hypercube, etc. Both the probabilistic response and its sensitivities can be estimated from a single probabilistic analysis, without requiring gradients of performance function. Numerical results indicate that the proposed method provides accurate and computationally efﬁcient estimates of sensitivities of statistical moments or reliability of structural system.
Volume 35 Issue 3 June 2010 pp 279-301
This paper presents an elasto-plastic element free Galerkin formulation based on Newton–Raphson algorithm for damage growth analysis. Isotropic ductile damage evolution law is used. A study has been carried out in this paper using the proposed element free Galerkin method to understand the effect of initial damage and its growth on structural response of single and bi-material problems. A simple method is adopted for enforcing EBCs by scaling the function approximation using a scaling matrix, when non-singular weight functions are used over the entire domain of the problem deﬁnition. Numerical examples comprising of one-and two-dimensional problems are presented to illustrate the effectiveness of the proposed method in analysis of uniform and non-uniform damage evolution problems. Effect of material discontinuity on damage growth analysis is also presented.
Volume 36 Issue 1 February 2011 pp 35-51
In this paper, a unit cell based approach is followed, where a unit cell consisting of one aggregate surrounded by mortar matrix is used for numerical simulation of mechanical response of cement concrete. Unit cell approach is a simple mathematical approximation that helps us to simplify the simulation of mechanical response of multi-phase composites. To model the failure of matrix, brittle cracking model is used, where the entire fracture zone is represented by a band of micro cracked material. Current study involves;
failure analysis of the concrete unit cell when it is subjected to tensile loads, and
parametric study of variation of peak strength with shape and volume fraction of aggregate.
In this study, circular and square aggregates at various orientations are modelled. The simulation results predict that the peak tensile stresses are not very sensitive to the volume fraction of aggregates, when the unit cell is subjected to tensile loads. This paper effectively demonstrates the power of unit cell model in simulating the nonlinear mechanical response of cement concrete when it is subjected to tensile loading.
Volume 36 Issue 4 August 2011 pp 463-488
This paper presents a practical approach based on High Dimensional Model Representation (HDMR) for analysing the response of structures with fuzzy parameters. The proposed methodology involves integrated ﬁnite element modelling, HDMR based response surface generation, and explicit fuzzy analysis procedures. The uncertainties in the material, geometric, loading and structural parameters are represented using fuzzy sets. To facilitate efﬁcient computation, a HDMR based response surface generation is employed for the approximation of the fuzzy ﬁnite element response quantity.
Volume 37 Issue 5 October 2012 pp 609-628
Mesoscale models are highly competent for understanding behaviour of unreinforced masonry structures. Their only limitation is large computational expense. Fully Equivalent Operational Model forms an equivalent mathematical model to represent a particular phenomenon where explicit relationship between inputs and outputs are unknown. This paper explores the ability of a major variant of High Dimensional Model Representation (HDMR) technique, namely Cut-HDMR, to construct the most efﬁcient Fully Equivalent Operational Model for nonlinear ﬁnite element analysis of mesoscale model of an unreinforced masonry structure. Conclusions are reached on various aspects such as, suitability of interpolation schemes and order of Cut-HDMR approximation.
Volume 40 Issue 4 June 2015 pp 1313-1341 Mechanical Sciences
Corrosion of embedded rebars is a classical deterioration mechanism that remains as one of the most significant problems limiting the service life of concrete structures exposed to chloride-laden environments. The primary objective of this study is to propose and verify a numerical framework that can efficiently quantify non-uniform corrosion penetration depth along the perimeter of the rebar in concrete exposed to chloride environment. This framework investigates the corrosion process during both the corrosion initiation and propagation phases by exploring the effects of not only the rebar existence but also its sizes and locations. The corrosion initiation phase is examined through a comprehensive chloride ingress model that identifies the most important parameters that influence the intrusion of chlorides into RC. The corrosion propagation phase is studied based on a decisive parameter, namely, the corrosion rate. In addition, the framework evaluates the non-uniform corrosion states that correspond to two scenarios of corrosion penetration depth: corrosion of segment of the rebar and uneven corrosion along the rebar perimeter. Numerical solution shows that, in general, chloride build-up along the perimeter of the corner bar is not only faster but also higher than that of the middle bar. Moreover, for the given values of cover thickness and water-to-binder ratio, time-to-corrosion initiation for the corner bar is faster than that for the middle bar. Furthermore, the larger the rebar, in general, the bigger the obstruction, and therefore, the higher the chloride build-up. Qualitative comparisons of the evaluated non-uniform corrosion scenarios with the variety of available laboratory and field data show good agreement.