Sameer B. Mulani

Stochastic critical stress intensity factor response of single edge notched laminated composite plate using displacement correlation method

Abstract The second-order statistics of critical stress intensity factor (SIF) of single edge notched fiber reinforced composite plates with random system properties and subjected to uniaxial tensile loadings is investigated. This paper is an extension of reference (Lal and Kapania, 2013) by the present authors by considering more number of input random system parameters for higher accuracy. A C0 finite element method based on a higher-order shear deformation plate theory using displacement correlation method via isoparametric quarter point element is proposed for basic formulation. A stochastic finite element method using first-order perturbation technique and Monte Carlo simulation (MCS) is employed to examine the mean, coefficient of variance, and probability density faction of critical first mode SIF. The effect of different fiber orientations, crack length, plate thickness, a number of layers, and the lamination schemes with random system properties on the statistics of SIF of single edge crack laminated composite plate is evaluated. The tensile failure load is predicted using Hashin’s failure criteria. The present approach is validated with results available in literature and by employing independent MCS.

Nonstationary Random Vibration Analysis of Wing with Geometric Nonlinearity Under Correlated Excitation

An algorithm that integrates Karhunen-Loeve expansion (KLE), nonlinear finite element method (NFEM), and a sampling technique to quantify the uncertainty is proposed to carry out random vibration a...

Precise Direction of Symmetrically Tilt Small Angle Boundaries Developed during Recrystallization of Cross Rolled Aluminium

A 6°and 3° [001] symmetrical tilt small angle grain boundaries in Al obtained by cross rolling and annealing have been investigated by High Resolution Electron Microscopy (HREM) and Molecular Dynamic Simulation (MDS) techniques. Both HREM and simulated images reveal that the grain boundary planes in these boundaries run along a direction that is close to , but the simulated images give a more precise direction of the grain boundary plane. The simulated images reveal that the boundaries in their lowest energy configuration follow a direction that lies along a lattice vector that has either the magnitude of the square root of a non- prime odd integer or an integral multiple of a non-prime odd integer. The relationships between grain boundary plane and the lattice vector with the magnitude that is the square root of a nonprime odd integer and run along the grain boundary will be discussed in the light of the alignment of dislocations in the formation of small angle grain boundaries.

Non-Stationary Random Vibration Analysis Using Multi-Correlated Random Processes Excitations

An algorithm that integrates Karhunen-Loeve expansion (KLE) and the finite element method (FEM) is proposed to perform non-stationary random vibration analysis of structures under excitations, represented by multi random processes and that are correlated in both time and spatial domains. In KLE, the auto-covariance functions of random processes are discretized using orthogonal basis functions. The KLE for multi-correlated random processes relies on expansions in terms of correlated sets of random variables reflecting the cross-covariance of the random processes. During the response calculations, the eigenfuntions of KLE used to represent excitations are applied as forcing functions to the structure. The proposed algorithm is applied to a two degree of freedom system and a stiffened panel for both stationary and non-stationary correlated excitations. Two methods are proposed to obtain the structural responses: 1) the modal superposition method, and 2) the direct method. Both the effectiveness and the computational efficiency of the proposed methods are studied through numerical simulations. Results show that both the modal superposition method and the direct method can describe the statistics of the dynamic response with sufficient accuracy. However, the modal superposition method is applicable using finite element programs whereas the direct method is more efficient for complex systems. The structural responses due to same type of correlated random processes are bounded by the response obtained by both perfectly correlated and uncorrelated random process excitations. If the impact of cross-correlation is ignored, the response will be larger for the perfectly correlated case and smaller for the uncorrelated case than that for the actual conditions. The structural response increases with a decrease in the correlation length and with an increase in the correlation magnitude. The proposed methodology can be applied for the analysis of any complex structures and any type of random excitations.