A hybrid method for stochastic response analysis of a vibrating structure

Response analysis of a linear structure with uncertainties in both structural parameters and external excitation is considered here. When such an analysis is carried out using the spectral stochastic finite element method (SSFEM), often the computational cost tends to be prohibitive due to the rapid growth of the number of spectral bases with the number of random variables and the order of expansion. For instance, if the excitation contains a random frequency, or if it is a general random process, then a good approximation of these excitations using polynomial chaos expansion (PCE) involves a large number of terms, which leads to very high cost. To address this issue of high computational cost, a hybrid method is proposed in this work. In this method, first the random eigenvalue problem is solved using the weak formulation of SSFEM, which involves solving a system of deterministic nonlinear algebraic equations to estimate the PCE coefficients of the random eigenvalues and eigenvectors. Then the response is estimated using a Monte Carlo (MC) simulation, where the modal bases are sampled from the PCE of the random eigenvectors estimated in the previous step, followed by a numerical time integration. It is observed through numerical studies that this proposed method successfully reduces the computational burden compared with either a pure SSFEM of a pure MC simulation and more accurate than a perturbation method. The computational gain improves as the problem size in terms of degrees of freedom grows. It also improves as the timespan of interest reduces.

Hydrogen Bonds Computing Server (HBCS): an online web server to compute hydrogen-bond interactions and their precision

Hydrogen bonds in biological macromolecules play significant structural and functional roles. They are the key contributors to most of the interactions without which no living system exists. In view of this, a web-based computing server, the Hydrogen Bonds Computing Server (HBCS), has been developed to compute hydrogen-bond interactions and their standard deviations for any given macromolecular structure. The computing server is connected to a locally maintained Protein Data Bank (PDB) archive. Thus, the user can calculate the above parameters for any deposited structure, and options have also been provided for the user to upload a structure in PDB format from the client machine. In addition, the server has been interfaced with the molecular viewers Jmol and JSmol to visualize the hydrogen-bond interactions. The proposed server is freely available and accessible via the World Wide Web at http://bioserver1.physics.iisc.ernet.in/hbcs/.