M. A. R. Loja

Analysis of piezolaminated plates by the spline finite strip method

Abstract This paper deals with the development of a family of higher order B-spline finite strip models applied to the static and free vibration analysis of laminated plates, with arbitrary shape and lay-ups, loading and boundary conditions. The lamination scheme can be such that the embedded and/or surface bonded piezoelectric actuating and sensing layers are included. The structure is discretised in a specified number of strips, and the geometry and displacement components of each strip are represented by interpolating functions that are products of linear or cubic B-spline, and linear or quadratic Lagrange functions along the y and x orthonormal directions. The accuracy and relative performance of the proposed discrete models are compared and discussed among the developed and alternative models.

Differential Evolution on the Minimization of Thermal Residual Stresses in Functionally Graded Structures

Global optimization techniques present considerable advantages when applied to non-linear and/or non-convex design spaces, where local search techniques can easily be trapped in local minima. In the present work, it is considered the application of Differential Evolution to the optimization of thermal residual stresses distribution in a sandwich panel, which is composed by an aluminium core and functionally graded outer layers. With this aim, numerical examples were carried out in order to evaluate the influence of different design parameters on the thermal residual stresses distribution. From those results, it is possible to conclude from the adequacy of the Differential Evolution strategy to minimize thermal residual stresses values, under different scenarios. It is worth to note the obtained increasing smoothness of residual stresses distribution, specially on the material transition interface.

Optimal Design of Piezolaminated Structures Using B-Spline Finite Strip Models and Genetic Algorithms

In this work, a set of numerical models is developed using the B-spline finite strip approach for linear analysis of piezolaminated plates and shells with particular focus to box girder type structures. These models are linked to global optimization techniques, such as genetic algorithms, which may consider either binary or floating point encoding of design variables, along with the inherent particularities of genetic operators at implementation level. Examples are discussed to illustrate the performance of these models.

A Hybrid Procedure to Identify the Optimal Stiffness Coefficients of Elastically Restrained Beams

Abstract The formulation of a bending vibration problem of an elastically restrained Bernoulli-Euler beam carrying a finite number of concentrated elements along its length is presented. In this study, the authors exploit the application of the differential evolution optimization technique to identify the torsional stiffness properties of the elastic supports of a Bernoulli-Euler beam. This hybrid strategy allows the determination of the natural frequencies and mode shapes of continuous beams, taking into account the effect of attached concentrated masses and rotational inertias, followed by a reconciliation step between the theoretical model results and the experimental ones. The proposed optimal identification of the elastic support parameters is computationally demanding if the exact eigenproblem solving is considered. Hence, the use of a Gaussian process regression as a meta-model is addressed. An experimental application is used in order to assess the accuracy of the estimated parameters throughout the comparison of the experimentally obtained natural frequency, from impact tests, and the correspondent computed eigenfrequency.

Optimal design of piezolaminated structures using B-spline strip finite element models

A package of B-spline finite strip models is developed for the linear analysis of piezolaminated plates and shells. This package is associated to a global optimization technique in order to enhance the performance of these types of structures, subjected to various types of objective functions and/or constraints, with discrete and continuous design variables. The models considered are based on a higher-order displacement field and one can apply them to the static, free vibration and buckling analyses of laminated adaptive structures with arbitrary lay-ups, loading and boundary conditions. Genetic algorithms, with either binary or floating point encoding of design variables, were considered to find optimal locations of piezoelectric actuators as well as to determine the best voltages applied to them in order to obtain a desired structure shape. These models provide an overall economy of computing effort for static and vibration problems.

Dynamic response of soft core sandwich beams with metal-graphene nanocomposite skins

Sandwich structures are able to provide enhanced strength, stiffness, and lightweight characteristics, thus contributing to an improved overall structural response. To this sandwich configuration one may associate through-thickness graded core material properties and homogeneous or graded properties nanocomposite skins. These tailor-made possibilities may provide alternative design solutions to specific problem requisites. This work aims to address these possibilities, considering to this purpose a package of three beam layerwise models based on different shear deformation theories, implemented through Kriging-based finite elements. The viscoelastic behaviour of the sandwich core is modelled using the complex method and the dynamic problem is solved in the frequency domain. A set of case studies illustrates the performance of the models.

Developments on finite element methods for medical image supported diagnostics

Variational image-processing models offer high-quality processing capabilities for imaging. They have been widely developed and used in the last two decades, enriching the fields of mathematics as well as information science. Mathematically, several tools are needed: energy optimization, regularization, partial differential equations, level set functions, and numerical algorithms. For this work we consider a second-order variational model for solving medical image problems. The aim is to obtain as far as possible fine features of the initial image and identify medical pathologies. The approach consists of constructing a regularized functional and to locally analyse the obtained solution. Some parameters selection is performed at the discrete level in the framework of the finite element method. We present several numerical simulations to test the efficiency of the proposed approach.

Adaptive empirical distributions in the framework of inverse problems

ABSTRACT This article presents an innovative framework regarding an inverse problem. One presents the extension of a global optimization algorithm to estimate not only an optimal set of modeling parameters, but also their optimal distributions. Regarding its characteristics, differential evolution algorithm is used to demonstrate this extension, although other population-based algorithms may be considered. The adaptive empirical distributions algorithm is here introduced for the same purpose. Both schemes rely on the minimization of the dissimilarity between the empirical cumulative distribution functions of two data sets, using a goodness-of-fit test to evaluate their resemblance.

Using the finite element method to understand calculus

This paper presents a complementary, alternative teaching and learning methodology based on the use of the finite element method to illustrate mathematical models and to explore their (numerical) solutions in the context of vector calculus properties understanding. This methodology is illustrated via a set of examples focused on specific engineering problems, but its scope can also be widened to other scientific areas. The examples presented on this paper allow concluding that this approach may be an interesting way to re-think and complement the perspective usually considered in the transmission of mathematical concepts. The use of a freeware finite element method computational package, FreeFEM++ may also be an important issue to stimulate the dissemination of this phenomena modelling and comprehension approach.

Functionally graded particulate composite plates: A dydactic case study

This work is part of an educational symbolic platform which was designed to aid and promote the learning of the mechanical behaviour of thin, simply supported rectangular plates. The integration of such simulation tools into the teaching process as an assisting tool can be an additional factor to contribute for a successful competences achievement on this subject. The present case study is focused on the deflection analysis of a functionally graded particulate composite plate submitted to a user-defined transverse loading.