Manolis Papadrakakis

Structural reliability analyis of elastic-plastic structures using neural networks and Monte Carlo simulation

Abstract This paper examines the application of Neural Networks (NN) to the reliability analysis of complex structural systems in connection with Monte Carlo Simulation (MCS). The failure of the system is associated with the plastic collapse. The use of NN was motivated by the approximate concepts inherent in reliability analysis and the time consuming repeated analyses required for MCS. A Back Propagation algorithm is implemented for training the NN utilising available information generated from selected elasto-plastic analyses. The trained NN is then used to compute the critical load factor due to different sets of basic random variables leading to close prediction of the probability of failure. The use of MCS with Importance Sampling further improves the prediction of the probability of failure with Neural Networks.

Structural optimization using evolution strategies and neural networks

The objective of this paper is to investigate the efficiency of combinatorial optimization methods, in particular algorithms based on evolution strategies (ES) when incorporated into the solution of large-scale, continuous or discrete, structural optimization problems. Two types of applications have been investigated, namely shape and sizing structural optimization problems. Furthermore, a neural network (NN) model is used in order to replace the structural analysis phase and to compute the necessary data for the ES optimization procedure. The use of NN was motivated by the time-consuming repeated analyses required by ES during the optimization process. A back propagation algorithm is implemented for training the NN using data derived from selected analyses. The trained NN is then used to predict, within an acceptable accuracy, the values of the objective and constraint functions. The numerical tests presented demonstrate the computational advantages of the proposed approach which become more pronounced in large-scale optimization problems.

Structural optimization using evolutionary algorithms

The objective of this paper is to investigate the efficiency of various evolutionary algorithms (EA), such as genetic algorithms and evolution strategies, when applied to large-scale structural sizing optimization problems. Both type of algorithms imitate biological evolution in nature and combine the concept of artificial survival of the fittest with evolutionary operators to form a robust search mechanism. In this paper modified versions of the basic EA are implemented to improve the performance of the optimization procedure. The modified versions of both genetic algorithms and evolution strategies combined with a mathematical programming method to form hybrid methodologies are also tested and compared and proved particularly promising. The numerical tests presented demonstrate the computational advantages of the discussed methods, which become more pronounced in large-scale optimization problems.

A method for the automatic evaluation of the dynamic relaxation parameters

Abstract Dynamic relaxation, a vector iteration method which belongs to the family of methods under the title of three-term recursive formulae, is described with viscous and kinetic damping. An automatic procedure is developed for the evaluation of the iteration parameters, thus avoiding any trial run or any eigenvalue analysis of the modified stiffness matrix. Starting values for the maximum eigenvalue could be obtained from the Gershgorin bound, and for the minimum eigenvalue any positive number less than the estimated maximum eigenvalue. The method is applied to geometrically and material nonlinear problems, and comparisons are made with an improved conjugate gradient method and a direct stiffness method.

Robust and efficient methods for stochastic finite element analysis using Monte Carlo simulation

Abstract In the present paper the weighted integral method and the Monte Carlo simulation are used together with innovative solution strategies based on the Preconditioned Conjugate Gradient method (PCG) to produce robust and efficient solutions for the stochastic finite element analysis of space frames. The numerical tests presented demonstrate the superiority of the proposed computational strategies compared to the widely used Neumann expansion method both in terms of accuracy and computational efficiency. The superiority is more pronounced in cases where the analysis needs to be performed for large variations of the stochastic parameters.

Post-buckling analysis of spatial structures by vector iteration methods

Abstract The present study is concerned with the application of two vector iteration methods in the investigation of the large deflection behavior of spatial structures. The dynamic relaxation and the first order conjugate gradient belong to this category of methods which do not require the computation or formulation of any tangent stiffness matrix. The convergence to the solution is achieved by using only vectorial quantities and no stiffness matrix is required in its overall assembled form. In an effort to evaluate the merits of the methods, extensive numerical studies were carried out on a number of selected structural systems. The advantages of using these vector iteration methods, in tracing the post-buckling behavior of spatial structures, are demonstrated.

A Hybrid Particle Swarm—Gradient Algorithm for Global Structural Optimization

: The particle swarm optimization (PSO) method is an instance of a successful application of the philosophy of bounded rationality and decentralized decision making for solving global optimization problems. A number of advantages with respect to other evolutionary algorithms are attributed to PSO making it a prospective candidate for optimum structural design. The PSO-based algorithm is robust and well suited to handle nonlinear, nonconvex design spaces with discontinuities, exhibiting fast convergence characteristics. Furthermore, hybrid algorithms can exploit the advantages of the PSO and gradient methods. This article presents in detail the basic concepts and implementation of an enhanced PSO algorithm combined with a gradient-based quasi-Newton sequential quadratic programming (SQP) method for handling structural optimization problems. The proposed PSO is shown to explore the design space thoroughly and to detect the neighborhood of the global optimum. Then the mathematical optimizer, starting from the best estimate of the PSO and using gradient information, accelerates convergence toward the global optimum. A nonlinear weight update rule for PSO and a simple, yet effective, constraint handling technique for structural optimization are also proposed. The performance, the functionality, and the effect of different setting parameters are studied. The effectiveness of the approach is illustrated in some benchmark structural optimization problems. The numerical results confirm the ability of the proposed methodology to find better optimal solutions for structural optimization problems than other optimization algorithms.

Parallel solution methods for stochastic finite element analysis using Monte Carlo simulation

In the present paper innovative solution strategies for parallel computer implementation have been developed in connection with the Monte Carlo Simulation (MCS) and the weighted integral method to produce efficient numerical handling of stochastic finite element analysis for 2D plane stress/strain problems. Furthermore, MCS in conjunction with the local average method is also used to extend the stochastic finite element analysis to 3D solid structures. Although MCS approaches have the major advantage that accurate solutions can be obtained for any type of problem whose deterministic solution is known either numerically or analytically their applicability is hindered by the high computational effort that is required. The implementation of innovative parallel solution techniques in this study resulted in cost effective treatment of these highly computationally demanding problems. One- and two-level domain decomposition methods have been implemented. Numerical results revealed that the proposed approaches permit an efficient treatment of stochastic finite element analysis for real-scale 2D plane stress/strain and 3D solid structures.

The mosaic of high performance domain Decomposition Methods for Structural Mechanics: Formulation, interrelation and numerical efficiency of primal and dual methods

A multitude of domain decomposition methods (DDM) for structural mechanics is available in the literature today. A unified framework for formulating primal and dual DDM is thus presented in this paper, aiming at providing a mathematical platform for a uniform treatment of high performance DDM in structural mechanics. A novel approach for developing new DDM from existing methods is also proposed and is applied to dual and primal methods. In the field of the FETI methods, this approach leads to a new category of methods derived from existing FETI variants. Furthermore, two alternative formulations of the balancing domain decomposition method are described, while interrelations between the introduced and existing methods are established. Finally, comparative numerical tests demonstrate the differences in the computational performance of the methods in question.

The TRIC shell element: theoretical and numerical investigation

The TRIC facet triangular shell element, which is based on the natural mode method, is seen under the light of the non-consistent formulation proposed by Bergan and co-workers. Under this formulation, the convergence requirements are fulfilled even with relaxed conditions on the conformity demands of the displacement shape functions. The intrinsic connection between the non-consistent formulation and the natural mode method is demonstrated, establishing thus a rigorous theoretical foundation for the TRIC element. Under the perspective of the non-consistent formulation, TRICs convergence characteristics are established by satisfying apriori the patch test due to its inherent properties and thus guaranteeing convergence to the exact solution. Furthermore, the elements accuracy, robustness and efficiency are tested in a number of judiciously selected numerical examples on benchmark plate and shell problems, while a CPU time comparison with a pure displacement-based isoparametric shell element demonstrates its computational merits.