Paolo Venini

Control of structures using neural networks

Active control of structures against environmental loads such as those due to wind and earthquakes has received much attention recently. Feasibility studies, numerical and experimental, have shown that it is a viable alternative to conventional methods in enhancing the performance of structures under such loadings. Most of the research thus far has concentrated on developing mathematical models and algorithms based on optimal control theory and the necessary hardware to implement the control. Research on control based on neural networks has been very limited in spite of the potential advantages of this method such as its inherent ability to handle nonlinear systems, incorporate leads or delays, and recover from partial system failure. This paper presents a method of control of structures based on neural networks. The rationale for neural network-based control is first outlined, followed by a brief description of the analytical and experimental investigations, and finally illustrative numerical examples are given of control of a non-linear single-degree-of-freedom structure by neural net.

Free vibrations of uncertain composite plates via stochastic Rayleigh-Ritz approach

Abstract The eigenproblem associated with the free vibrations of uncertain composite plates is dealt with herein. The elastic moduli of the system, the stiffness of the Winkler foundation on which the plate rests and the mass density are considered to be uncertain. Given their random field-based description, a new method is presented for the computation of the second order statistics of the eigenproperties of the laminate. For the sake of clarity, the deterministic version is introduced first and its stochastic extension is then presented and deeply analyzed. Numerical studies are also performed to validate the theoretical approach.

A new locking-free equilibrium mixed element for plane elasticity with continuous displacement interpolation

With reference to plane elastic problems, we first show that using the Johnson and Mercier (JM) element (C. Johnson, B. Mercier, Numer. Math. 30 (1978) 103) for the stresses and an H 1 piecewise linear interpolation for the displacements leads to a severe locking when the Lamcoefficient k tends to infinity, i.e. in the case of an incompressible material. Motivated by the need to have a continuous displacement field that emerges in several engineering applica- tions, we use an eigenvalue argument to prove that locking is due to the presence of the (element-average) pressure among the degrees of freedom. We therefore relax the incompressibility constraint by introducing a quadrilateral macroelement basically consisting of two adjacent JM triangles sharing the same average pressure, in a sense switching from a (locking) T1P0 approximation to a locking-free Q1P0. Numerical tests on the pathological Cook cantilever are performed to assess the validity of the proposed approach in which comparisons between the newly devised element and the original JM element with L 2 displacements are presented. � 2001 Published by Elsevier Science B.V.

An adaptive wavelet-Galerkin method for an elastic-plastic-damage constitutive model : 1D problem

We present a wavelet-Galerkin method for the analysis of elastic-plastic-damage systems. Jus model (J.W. Ju, Int. J. Solids Struct. 25 (1989) 803) is explicitly considered and numerically tested but the method applies equally well to a broad range of damage-mechanics models. A three-step elastic-predictor, plastic-corrector, damage-corrector strategy is the core of the proposed approach. We use a displacement approach with wavelet interpolating functions instead of classical polynomials. This allows to clearly locate those sites in the system where damage is taking place, thanks to the high-pass filtering action operated by the wavelets. This opens the way to inexpensive self-adaptive strategies that are introduced and preliminary tested herein.

Reliability as a measure of active control effectiveness

This contribution presents a state-space framework for performing the reliability analysis of uncertain structural systems in the presence of active control and stochastic excitation. The control framework is general enough to allow use of modern robust techniques, e.g. H2 and H1, as well as more classical regulations such as LQG. To deal with system uncertainties, the perturbative version of the finite-element method is adopted with the aim of computing the statistics of the extreme response of the structure. Eventually, reliabilities are computed via asymptotic techniques for both the controlled and uncontrolled cases within a few numerical examples. # 1999 Civil-Comp Ltd and Elsevier Science Ltd. All rights reserved.

A wavelet-like Galerkin method for numerical solution of variational inequalities arising in elastoplasticity

The well-known problem of elasticity that may be written as a variational equation [4] has been recently extended to non-linear elastoplastic behaviours [13] giving rise to a class of variational inequalities of second kind [9]. This paper presents a wavelet Galerkin method for the numerical solution of such a class of problems, extensively studied and solved in the past by means of more traditional approaches. The novelty of the scheme presented herein is represented by the capability of wavelets to locate regions where plasticity is growing without the need of any further indicator. This is useful for adaptive remeshing as well as for gaining insight into internal variable models with applications to dynamic analysis and damage identification. Copyright

Robust control of uncertain structures

Objective of this paper is to present robust control strategies able to handle acceleration feedback. The robustness of the controller is investigated in respect to both stability and performance measures. The uncertainty set is chosen as a convex one with either real or complex structured uncertainty. H1 control is firstly used to comply with the stability requirements whereas a m synthesis approach is then adopted as far as the performance is concerned. The degradation of the performance in respect to the size of the perturbation is eventually proposed as a merit parameter to rank diAerent controllers. Numerical simulations are proposed on a MDOF structural system under earthquake excitation. # 1998 Elsevier Science Ltd. All rights reserved.

Rayleigh-Ritz analysis of elastically constrained thin laminated plates on Winkler inhomogeneous foundations

Abstract Anisotropic layered composite plates laying on Winkler foundations are analyzed in this paper. Different boundary conditions are examined: ideal constraints as well as elastic ones are taken into account. For any given structure, i.e. for any lamination sequence, a method is developed to determine the relevant eigenproperties such as the first fundamental frequencies and the associated eigenmodes. The main objectives of the paper include: (i) identification of a lamination sequence so as to extremize the eigenvalues of the system; (ii) determination of the effects of elastic foundations, homogeneous as well as inhomogeneous, on the properties of the system; (iii) incorporating in the formulation constraints of elastic nature, for their relevance in view of practical applications; (iv) investigating the effectiveness of the Rayleigh-Ritz method in limit cases such as high gradients and stiffnesses. The Rayleigh-Ritz method is used herein as analysis method: polynomial functions defined over the entire domain of definition of the structure are derived which satisfy the geometric boundary conditions and may locally violate the natural ones. The solution is then expanded as a finite sum of such functions which thus constitute a basis of finite dimension. Numerical examples are worked out to demonstrate the monotonic convergence of the Rayleigh-Ritz based solution to the ideally constrained one when the stiffness of the boundaries grows large.

OPTIMAL ROBUST DESIGN OF NOVEL MATERIALS: PROBLEMS OF STABILITY AND VIBRATIONS

A numerical method for the optimal design of thin anisotropic laminates is presented, layer thicknesses and lamination angles being the design variables. An optimal solution is pursued with respect to frequency domain objectives, e.g. fundamental frequency and Euler critical load. A special feature of the method is the semi-analytical second order design sensitivity that is computed with the aid of a Rayleigh-Ritz analysis approach. A modified sequential quadratic programming scheme is then introduced, where standard quasi-Newton approximations are avoided by an exact calculation of the Hessian matrix. Furthermore, the robustness of the method with respect to scatter in material properties such as mass density and elastic moduli is assessed. A stochastic extension of the Rayleigh-Ritz approach is developed on this purpose that allows the location of those regions in the design space that are most sensitive to physical parameter randomness. This allows the use of a modified objective function that penalize...

Mixed Variational Formulations for Micro-cracked Continua in the Multifield Framework

Within the framework of multifield continua, we move from the model of elastic microcracked body introduced in (Mariano, P.M. and Stazi, F.L., Strain localization in elastic microcracked bodies, Comp. Methods Appl. Mech. Engrg. 2001, 190, 5657–5677) and propose a few novel variational formulations of mixed type along with relevant mixed FEM discretizations. To this goal, suitably extended Hellinger-Reissner principles of primal and dual type are derived. A few numerical studies are presented that include an investigation on the interaction between a single cohesive macrocrack and diffuse microcracks (Mariano, P.M. and Stazi, F.L., Strain localization due to crack–microcrack interactions: X–FEM for a multifield approach, Comp. Methods Appl. Mech. Engrg. 2004, 193, 5035–5062).