Marco Savoia

Structural reliability analysis through fuzzy number approach, with application to stability

Abstract Structural reliability analysis in the presence of scarce or uncertain data is performed in the framework of possibility theory. Fuzzy numbers are used to define an equivalence class of probability distributions compatible with available data and corresponding upper and lower cumulative density functions. A procedure is then proposed to perform reliability analysis using extended fuzzy operations. It gives estimates of small and large fractiles of output variables which are conservative with respect to probability. A criterion to define the membership functions of fuzzy numbers starting from available information is also described. The method is used to perform reliability analysis against buckling. In civil engineering problems, usually very few data are available to define structural imperfections; often, normative requirements only are available in structural design stages. The results presented confirm the theoretical predictions described in Ref. [Comput. Meth. Appl. Mech. Eng. 160 (1998) 205], i.e., reliability analysis using fuzzy number theory gives conservative bounds of small/large fractiles with respect to probability.

A Variational Approach to Three-Dimensional Elasticity Solutions of Laminated Composite Plates

The displacements in a laminated composite are represented as products of two sets of unknown functions, one of which is only a function of the thickness coordinate and the other is a function of the in-plane coordinates (i.e., separation of variables approach), and the minimization of the total potential energy is reduced to a sequence of iterative linear problems. Analytical solutions are developed for cross-ply and angle-ply laminated composite rectangular plates. The solution for simply-supported cross-ply plates under sinusoidal transverse load reduces to that of Pagano. Numerical results for stresses and is placements for antisymmetric angle-ply laminates are presented. The three-dimensional elasticity solutions developed are important because they can be used to study the behavior of composite laminates, in addition to serving as reference for approximate solutions by numerical methods and two-dimensional theories.

THREE-DIMENSIONAL THERMAL ANALYSIS OF LAMINATED COMPOSITE PLATES

Abstract In this paper, results of the stress analysis of multilayered plates subject to thermal and mechanical loads are presented in the context of the three-dimensional quasi-static theory of thermoelasticity. The governing equations for a plate composed of monoclinic layers and subject to any given temperature and mechanical load distributions are derived in terms of displacements. Making use of a Navier-like approach, exact three-dimensional solutions are obtained for cross-ply and antisymmetric angle-ply laminated rectangular plates subject to thermomechanical loads. Polynomial and exponential temperature distributions through the thickness are considered. Numerical results for plates with the simply supported boundary conditions are presented. It is shown that the inplane shear stresses at the corners are unbounded when plate faces are subject to uniform heating.

Layer-wise shell theory for postbuckling of laminated circular cylindrical shells

The layer-wise shell theory of Reddy is used to study the postbuckling response of circular cylindrical shells. The Rayleigh-Ritz method is used to solve the equations by assuming a double Fourier expansion of the displacements with trigonometric coordinate functions. Numerical results for postbuckling response of axially compressed multilayer cylinders with simply supported edge conditions are presented for different values of shell imperfections.

Non-linear model for R/C tensile members strengthened by FRP-plates

Abstract Transverse cracking in reinforced concrete (R/C) members strengthened by FRP plates and subjected to axial loads is analyzed. A non-linear model is developed, where cohesive stresses in concrete across cracks and non-linear bond–slip law between steel bars and concrete are used. The non-linear governing equations are solved via finite difference method. Comparisons with experimental results confirm the validity of the model. Numerical examples are also presented, simulating tests on plated and unplated R/C members with displacement, force, or crack opening control. The examples show that external FRP-plating is effective in reducing crack width and, consequently, in increasing axial stiffness of tensile members.

Fuzzy number theory to obtain conservative results with respect to probability

Fuzzy number and possibility theories are used for problems where uncertainties in the definition of input data do not allow for a treatment by means of probabilistic methods. Starting from a scarce/uncertain body of information, fuzzy numbers are used to define possibility distributions as well as upper and lower bounds for a wide class of probability distributions compatible with available data. It is investigated if relations between possibility distributions and probability measures are preserved also when the fuzzy number represents an output variable computed making use of extended fuzzy operations. General real one-to-one and binary operations are considered. Asymptotic expressions (for small/large fractiles) for the membership function of the fuzzy number and for CDFs given by probability theory are obtained. It is shown that fuzzy number theory gives conservative bounds (with respect to probability) for characteristic values corresponding to prescribed occurrence expectations. These results are of special interest for computational applications. In fact, it is easier to define fuzzy variables than random variables when no or few statistical data are available (as in the case of structural design stages). Moreover, extended fuzzy operations are much simpler than analogous operations required in the framework of probability, especially when several variables are involved.

Coupling Response Surface and Differential Evolution for Parameter Identification Problems

In the present article, a new surrogate-assisted evolutionary algorithm for dynamic identification problems with unknown parameters is presented. It is based on the combination of the response surface (RS) approach (the surrogate model) with differential evolution algorithm for global search. Differential evolution (DE) is an evolutionary algorithm where N different vectors collecting the parameters of the system are chosen randomly or by adding weighted differences between vectors obtained from two populations. In the proposed algorithm (called DE-Q), the RS is introduced in the mutation operation. The new parameter vector is defined as the one minimizing the second-order polynomial function (RS), approximating the objective function. The performances in terms of speed rate are improved by introducing the second-order approximation; nevertheless, robustness of DE algorithm for global minimum search of objective function is preserved, because multiple search points are used simultaneously. Numerical examples are presented, concerning: search of the global minimum of analytical benchmark functions; parameter identification of a damaged beam; parameter identification of mechanical properties (masses and member stiffnesses) of a truss-girder steel bridge starting from frequencies and eigenvectors obtained from an experimental field test.

Differential Evolution Algorithm for Dynamic Structural Identification

In the present article, differential evolution algorithm is used to perform structural identification of mass and stiffness properties of civil structures from dynamic test results. Identification is performed initially starting from exact values of modal parameters (frequencies and mode shapes). Robustness of the algorithm is then tested by adopting pseudo-experimental input data, obtained by adding to exact data some statistic scattering, representing experimental measurement error. Different objective functions are adopted in identification procedure, and results are compared with those obtained adopting classical gradient method. The method is used to identify masses, elastic moduli, and stiffnesses of external constraints of a RC frame structure and a steel–concrete bridge. Numerical results confirm that adopting both frequencies and mode shapes instead of frequencies only strongly increases sensitivity of objective function to identification parameters. Scattering of identified parameters is much smaller, with coefficient of variation of the same order of magnitude of that of pseudo-experimental data used as input values in dynamic identification procedure.

Torsional response of inhomogeneous and multilayered composite beams

Abstract The elastic response of inhomogeneous orthotropic beams with general cross-section and subject to uniform torsion is investigated. The problem is formulated both in terms of the warping and of the Prandtl stress function. Moreover, the exact solution for rectangular orthotropic beams constituted by any number of layers is derived, making use of a series form which is unaffected by unstable behaviours. Several examples are presented, showing that approximate solutions based on simplified kinematical models can yield very poor estimates of the torsional rigidity. Finally, it is shown that the plating of homogeneous beams by means of thin carbon or glass fibre-reinforced laminae can be used to make the torsional rigidity 8–10 times as much.

A two-dimensional theory for the analysis of laminated plates

A new displacement-based two-dimensional theory for the analysis of multilayered plates is presented. The theory is based on the only kinematic constraint of transverse inextensibility, whereas no restrictions are imposed on the representation of the in-plane displacement components. A governing system of integral-differential equations is obtained which can be given a closed-form solution for a number of problems where no boundary layer are present. It is also shown that most of the 2-D plate models can be directly derived from the presented theory. The possibility of developing asymptotic solutions in the boundary layers is discussed with reference to the problem of a plate in cylindrical bending. Finally some numerical solutions are compared with those given by the plate model by Lo et al. (1977) and with F.E.M. solutions.