Inverse mass matrix via the method of localized lagrange multipliers

An efficient method for generating the mass matrix inverse is presented, which can be tailored to improve the accuracy of target frequency ranges and/or wave contents. The present method bypasses the use of biorthogonal construction of a kernel inverse mass matrix that requires special procedures for boundary conditions and free edges or surfaces, and constructs the free-free inverse mass matrix employing the standard FEM procedure. The various boundary conditions are realized by the method of localized Lagrange multipliers. Numerical experiments with the proposed inverse mass matrix method are carried out to validate the effectiveness proposed technique when applied to vibration analysis of bars and beams. A perfect agreement is found between the exact inverse of the mass matrix and its direct inverse computed through biorthogonal basis functions

Vulnerability analysis of large concrete dams using the continuum strong discontinuity approach and neural networks

Probabilistic analysis is an emerging field of structural engineering which is very significant in structures of great importance like dams, nuclear reactors etc. In this work a Neural Networks (NN) based Monte Carlo Simulation (MCS) procedure is proposed for the vulnerability analysis of large concrete dams, in conjunction with a non-linear finite element analysis for the prediction of the bearing capacity of the Dam using the Continuum Strong Discontinuity Approach. The use of NN was motivated by the approximate concepts inherent in vulnerability analysis and the time consuming repeated analyses required for MCS. The Rprop algorithm is implemented for training the NN utilizing available information generated from selected non-linear analyses. The trained NN is then used in the context of a MCS procedure to compute the peak load of the structure due to different sets of basic random variables leading to close prediction of the probability of failure. This way it is made possible to obtain rigorous estimates of the probability of failure and the fragility curves for the Scalere (Italy) dam for various predefined damage levels and various flood scenarios. The uncertain properties (modeled as random variables) considered, for both test examples, are the Young’s modulus, the Poisson’s ratio, the tensile strength and the specific fracture energy of the concrete

Stochastic Galerkin Method for Optimal Control Problem Governed by Random Elliptic PDE with State Constraints

In this paper, we investigate a stochastic Galerkin approximation scheme for an optimal control problem governed by an elliptic PDE with random field in its coefficients. The optimal control minimizes the expectation of a cost functional with mean-state constraints. We first represent the stochastic elliptic PDE in terms of the generalized polynomial chaos expansion and obtain the parameterized optimal control problems. By applying the Slater condition in the subdifferential calculus, we obtain the necessary and sufficient optimality conditions for the state-constrained stochastic optimal control problem for the first time in the literature. We then establish a stochastic Galerkin scheme to approximate the optimality system in the spatial space and the probability space. Then the a priori error estimates are derived for the state, the co-state and the control variables. A projection algorithm is proposed and analyzed. Numerical examples are presented to illustrate our theoretical results